# AfterMath

 Some Recent Papers to Consider Regarding the Dark Matter Problem — Posted Sunday August 7 2022 For some time I've gone on and on about how I believe modified gravity can provide a better explanation for the effects of dark matter, which I don't believe exists. Here's an update, by way of some introductory stuff. Consider the Schwarzschild metric for a body having the point mass $$M$$: $$ds^2 = A \,c^2 dt^2 - \frac{1}{A}\, dr^2 - r^2 \left( d\theta^2 + \sin^2\theta \,d\phi^2 \right) \tag{1}$$ where $$A = 1 - \frac{2 GM}{c^2 r} \tag{2}$$ The all-important constant factor $$2 GM/c^2$$ in (2) is actually an integration constant that arises when one solves the Einstein field equations for a point mass. The field equations are thus used to determine $$A$$, and they have been fantastically successful in predicting all manner of cosmological phenomena, all of which have been confirmed by experiment and direct observation. However, while the coordinates $$\theta$$ and $$\phi$$ are the usual spherical coordinates, $$r$$ is not the simple radial distance from the point mass. It's complicated by the fact that distance and time are warped as one moves inward or outward from the mass. If you assume some position $$r$$ and measure the circumference $$C$$ around the body at that same position, then your true radial position is given by the familiar $$C = 2 \pi r$$ equation. You can't just use a measuring tape to determine $$r$$, as the tape will relativistically contract as it's lowered down toward the mass. Einstein's equations are Lorentz and coordinate invariant, but they are not conformally invariant, a feature of relativistic geometry that many physicists believe is inherent in Nature. To make Einstein's gravity theory conformally symmetric requires a modification of that theory, and when this is done we find that $$A = 1 - 3 \beta \gamma - \frac{\beta (2 - 3 \beta \gamma)}{r} + \gamma r + \Lambda r^2 \tag{3}$$ where $$\beta$$ and $$\gamma$$ are integration constants and $$\Lambda$$ is proportional to the cosmological constant. For $$\gamma=0$$ we have $$\beta = G M/c^2$$, and with the assumption that $$\Lambda$$ is negligible (3) becomes equivalent to (2). Thus, the conformal variant of Einstein's theory introduces one additional constant of integration to the fold, leading some cosmologists to believe it might explain dark matter. Indeed, the linear term in $$r$$ in (3) provides one such avenue for explaining dark matter, as it represents an acceleration term at large distances. However, by a clever combination of coordinate and conformal transformations on (1), it can be shown that the $$\gamma$$ term can be made to vanish, resulting in (2). This implies that conformal invariance cannot explain dark matter (a simpler calculation is provided here). While I cannot see any flaw in this argument, the radial coordinate in (3) bothers me. It's related to the Schwarzschild radius $$r$$ via the transformation $$r \rightarrow \frac{(2- 3 \beta \gamma) r}{2 - 3 \beta \gamma - \gamma r}$$ making interpretation of the transformed radial coordinate vastly more complicated. In order to preserve my faith in conformal relativity, I have to believe that this transformed coordinate does not correlate with a strictly falling gravitational potential from the point mass, which is the problem with conventional Einsteinian gravity with regard to dark matter.

 A Mental Health Expert's Assessment of Alex Jones — Posted Sunday August 7 2022 A police officer interviews a suspect for the murder of his wife. The suspect is a Scottish kilt maker, claiming to have sold a large number of kilts to a giant alien blancmange (white dessert pudding) which swallowed his wife whole: Detective: Now then, the facts are these: You received an order for 48,000,000 kilts from a blancmange from the planet Skyron in the Galaxy of Andromeda. You'd just shown your wife an entry form for Wimbledon, which you'd filled in, when you turned round and saw her legs disappearing into the blancmange. Is that correct? Suspect: Yes, sir. Detective: Are you mad? Suspect: No, sir. Detective: Well, that's a relief. Because if you were, your story would be less plausible. This sketch from an old Monty Python episode points out the danger of rational people believing preposterous stories. On a more serious note, Dr. Todd Grande is a licensed mental health counselor who has posted numerous videos on YouTube in which he discusses a wide range of mental disorders. He frequently refers to the Diagnostic and Statistical Manual of Mental Disorders, the so-called bible of abnormal psychology that analyzes in depth the ten primary mental disorders of the human mind. While he often talks about the mental health issues of specific people, his views are offered as options and not as legal or professional diagnoses. In his most recent video, Grande offers his views on the mental state of Alex Jones, the demogogic radio and television conspiracy theorist who was recently put on trial for defaming one of the parents of a child killed in the Sandy Hook massacre of December 2012, in which 26 people were shot to death, including 22 children. For the past ten years, Jones has vehemently claimed that the massacre was an elaborate hoax perpetrated by the U.S. government to promote gun control. He also claimed that the parents of the dead children participated in the hoax. A jury has now awarded one parent $49 million for defamation and punitive damages, and more Sandy Hook parents are expected to follow suit. In my lay opinion, Jones represents a truly serious and dangerous sickness of the American people. His followers have supported Jones and his conspiracies by donating hundreds of millions of dollars to him, and his radio programs and questionable commercial and business interests have given him an enormous following of mostly conservative, undereducated Republican voters. His followers are also adorers of former President Donald Trump, who has personally promoted both Jones and his conspiracy theories and beliefs. The video is about 15 minutes long, and I encourage you to watch it. I believe you'll agree that Jones displays the same sociopathic, psychopathic and narcissistic tendencies as Hitler, Goebbels, Mussolini and Trump. Worse, by continuing to fawn over mentally and morally sick leaders, the American people are in serious danger of destroying their own country.  It Could Be Worse — Posted Saturday August 6 2022 My father was only 16 on his first visit to California in 1921, when his struggling jazz band "The Melody Boys" arrived for a gig in Long Beach. When he told me that an acre of undeveloped property along Wilshire Boulevard back then could be purchased for$100, I asked him why he didn't go for it. He said he didn't have $100 to spare, as it was a lot of money at the time. That area today is Los Angeles' "Miracle Mile," with an acre worth many millions of dollars. That's inflation for you. One of my favorite silent Laurel & Hardy films is 1928's Their Purple Moment (available on YouTube), in which the boys skip out on their wives (with "friends") to enjoy a night out at a fancy local dance club. They order steaks and beer (odd, since this was still during Prohibition), and Hardy remarks on the fine food being served to them: A similar meal might be$40 today, but even that and today's 9% inflation doesn't begin to compare with that of Argentina, which is around 90%. At 73, I'm retired and on a fixed income, and I don't relish the thought of running out of funds before I die. (Maybe all those years at the gym and watching what I eat weren't such a great idea after all.)

 Try It — Posted Saturday August 6 2022 After church, many residents of Tennessee head over to their local Cracker Barrel restaurant for lunch. But lately they've gotten upset over a new item on the menu: meatless, plant-based sausage. Some are even claiming the restaurant is now catering to "woke" progressives, and they're just not having it. Cracker Barrel's not worried, as it still has regular pork sausage and will continue to offer it to its customers. It's just part of a projected $25 billion annual "beyond meat" trend that is becoming popular around the country. I don't buy regular hamburger meat any more, as for two years I've bought only "Impossible Burger" and "Beyong Meat" patties and similar products from my local Costco. Yes, I'm a progressive, thinking that red meat is bad for the environment and the consumer, but it really comes down to taste and texture—I really can't tell the difference, and that's what matters the most to me. That said, I don't care for "Impossible Chicken Nuggets," not because it tastes bad but because it's expensive and doesn't taste much like chicken at all. The availability of plant-based chicken substitute has lagged behind its meat variant, most probably because of technical issues. But they're working on it, and perhaps in the near future chickens will be able to breathe a little easier.  There Will Be Weeping and Gnashing of Teeth — Posted Saturday August 6 2022 State-level Republican leaders are doing all they can to stop action on mitigating climate change. Consequently, I will no longer fund any humanitarian relief to Red States suffering from climate change-induced floods, droughts, fires, poverty or disease, as they'd only cash the checks and vote for Trump (Matthew 7:6 and Matthew 10:14). May God forgive me.  Black Holes Are Stable. That's Great. — Posted Friday August 5 2022 Not accounting for Hawking radiation, the stability of black holes (at least slowly rotating black holes) has now been proved, and all it took was a simple little 912-page paper to prove it. The proof of Fermat's nearly 400-year-old "last theorem" was a romp in the park by comparison. No, I haven't read it. I probably couldn't understand it, anyway.  The Opposite of "Woke" is "Asleep," and America Prefers to Sleep — Posted Friday August 5 2022 Tomorrow, Congress will begin voting on President Biden's massive climate, prescription drug and spending bill, estimated to cost around$300 billion. With Democratic Senators Manchin and Sinema now on board, the Democrats have a decent chance to push through the bill, although it will most certainly be countered by 100% opposition by the Republicans. Is Republican opposition a purely partisan stance, or is there a much deeper reason lurking behind the party's hostility to what seems to be a good bill for America? I see two explanations, both of which are dark and deep, as poet Robert Frost might put it. For one, America has experienced numerous and enormously distressing events in the past 20 years, from the 9/11 attacks, the 2008 financial meltdown, the absurdly insane Trump presidency, the January 2021 insurrection, horrific school massacres, the highly-publicized police murder of innocent black citizens to the (hopefully) retreating two-year-long COVID-19 pandemic and its negative economic and social impacts. It would be a mistake to assume that these events have not had a deep and lasting impact on the American psyche. I'm not a psychologist, but I've had conversations with psychologists who believe that something very real and disturbing has occurred in the minds of Americans in the past two decades. One possible result is what some psychologists call the Great Regression, "kiddification" or "infantilization of adults," in which otherwise rational and mature adults seek comfort and solace in games, activities, movies and attire that are normally the domain of children. Surely we've all noticed the glut of inane superhero films featuring comic book characters like Batman, Spiderman, Captain America, Iron Man and many others, characters that I stopped being interested in when I was 13. These films are raking in many hundreds of billions of dollars, and their popularity is due mostly to adult attendance. Yes, adults dressing up as Captain Kirk and Klingons have been around since the 1970s, but the Great Regression has become a major market ploy for today's film makers. Secondly, and perhaps connected with this, is the fervent and not-to-be-ignored desire of white American evangelicals to return to the good old days of the 1950s, when women and minorities knew their place and white men ruled all levels of American government and society. One cannot ignore the chants of "Jews shall not replace us" at recent protest marches carried out in Southern states, or the ongoing apathy that white evangelicals have exhibited when scores of innocent minorities (mostly Blacks and Asians) are slaughtered by police. At an even deeper and darker level, there appears to be a sincere desire of white evangelicals for hastening the return of Jesus Christ, even if it means advocating global nuclear war. I don't believe that evangelicals truly want to see a self-inflicted End of the World, but the arrogance and hubris they display and demand from their Republican leaders does not rule out that possibility. Today's seemingly implacable enmity and rising hostility between the United States and Russia and China does not bode well for the world, but the "Better dead than Red" appeal of 1950s patriotic ideology merges well today with the artificially accelerated return of Christ. Lastly, don't get me started on the Republicans' views on climate change and its similar ability to destroy the planet. Bibilical prophecy is fine, but not when prophecy is self-inflicted. God save us from ourselves.

 Their Stiff, Green Gallop — Posted Thursday August 4 2022 The South American tapir. Small and docile, and hardly capable of pulling a chariot. Horses in South and North America became extinct during the Pleistocene Epoch over 10,000 years ago. They weren't reintroduced onto the continent until the 1500s, when Spanish conquistadores brought them from Spain when they invaded the Americas. recent study conducted at the Assateague Islands off the coasts of Maryland and Virginia indicates that feral horses that have lived there for hundreds of years were most likely introduced by Spanish ships that foundered and/or sank in the 1500s, when onboard horses managed to survive and swim ashore. Reading the article made me think of The Doors song Horse Latitudes from their 1967 "Strange Days" album. "Horse latitudes" refers to the habit of ships pushing their livestock overboard at sea when ocean winds ceased for long periods, and ship crews could no longer feed or water them. The article also reminded me of The Book of Mormon, which describes great military battles carried out with horse-drawn chariots, driven by warriors armed with steel weapons. This supposedly occurred beginning in North America in the 600s B.C., when neither horses nor steel existed. Mormon apologists have had their hands full explaining these anachronisms, although some have claimed that pig-size tapirs, not horses, were used to pull the chariots. They might just have well have claimed that the angel Moroni magically provided the horses (and steel), or that once-native lions, rhinos, camels, elephants or other beasts were tamed for the same purpose.

 The Dark Matter Wars — Posted Thursday August 4 2022 I've enjoyed astrophysicist Ethan Siegel's articles for years now, learning much about cosmology along the way. But he's an unabashed believer in the existence of dark matter, something that I and many others just can't accept. Two of Siegel's most recent articles on the subject can be read here and here. They're admittedly pretty convincing, but they belie the basic fact that dark matter particles haven't been detected after dozens of exquisite, sophisticated, very costly and time-consuming experiments have been conducted. Like pixie dust and angels dancing on a pinhead, dark matter will never be proven until the particles have been demonstrably, unequivocably and repeatably seen in a detector. The particles are presumed to be stable, very light in mass and non-interacting with light and ordinary matter, but they nonetheless must be detectable if they exist. If dark matter does not exist, the situation pretty much boils down to demanding a revision of Einstein's 1915 gravity theory. Although that theory has been proven countless times over the past 100 years (and has never experienced a single failure), as Einstein himself noted the theory must be only an approximation of the underlying truth. Although the theory is Lorentz and coordinate invariant, it is not conformally invariant, and that seems to be a major motivation for modifying the theory. Siegel's point of view seems to be that Einstein's theory is perfectly fine just the way it is, needing no major modification. After all, if dark matter exists (as weird as its properties must be), then it is perfectly understandable in terms of existing Einsteinian gravity. But, dang it all, dark matter just hasn't been found. Conversely, modifying Einsteinian gravity is a simple matter and can presumably be done with pencil and paper. Many efforts hqve been made over the years, but most have been made in an attempt to unify gravity with quantum mechanics. Since gravity dominates on the largest of all scales, it seems that quantum mechanics should be left out. After all, modern quantum theory ignores the tiny effects of gravity at the micro scale, so leaving out quantum physics in gravity seems to be returning the favor. I was planning to throw in some equations here, but I'm really tired of all this. I'll just say that the most basic, conformally-invariant version of Einstein's theory provides the same predictions as the 1915 theory while including an additional integration constant that might explain dark matter as a consequence. Again, the reader is encouraged to read the foundational 1989 paper by Mannheim and Kazanas for details. PS: The three known neutrino flavors have been suggested as candidates for dark matter, but their tiny masses and other properties have pretty much eliminated them as contenders. A relatively new theory, massive gravity, is now being looked at, in which gravitons (the particles presumed responsible for the gravitational interaction) are not massless but carry some non-negligible mass. Gravitons should be ubiquitous throughout the universe, so perhaps their total number might explain dark matter. On the other hand, while gravitons are believed by everyone to exist, they haven't been detected, either. Sigh.

 On the Brittney Griner Mess — Posted Thursday August 4 2022 You may have seen the 1978 prison drama Midnight Express, about a young American man who gets caught smuggling drugs out of Turkey. After a lengthy and costly trial, he's sentenced to a long and hellish prison sentence in that country. That film was on my mind when I first traveled to Egypt, as I had been warned that any prescription medications I might be carrying had to be provably legitimate, lest I find myself facing that country's equally harsh drug laws. Now we have the politically-fraught case against women's basketball star Brittney Griner, who was caught in Russia with a miniscule amount of hash oil, which she insisted was for her own medicinal use. After being imprisoned for five months while awaiting her trial, she's now been convicted of drug smuggling with criminal intent. The Russian court will most likely sentence her to a number of years, but the pending prisoner swap between Russia and the United States will probably find Griner back home in a few months. The swap is expected to return a notorious Russian arms dealer (and possibly a convicted Russian murderer) to his homeland, in my view a bad deal all around. But I say fine, let it happen. I'm sure Griner has learned her lesson, although the world will be worse off as a result of her stupid actions. Meanwhile, the United States should enact a law stating that if U.S. citizens carrying illicit drugs—for any reason, for any purpose and in any amount—to foreign countries with harsh drug laws, then no deals will be made to get them out should they be caught, and they'll have to face the consequences of their actions. Update: Griner has been sentenced to 9 years in a Russian penal colony (aka gulag). This is unusually harsh, even considering the tense political atmosphere between the U.S. and Russia. But I suspect she'll be out before long as part of the pending prisoner swap. I hope so, and I'm sure she won't be returning to Russia ever again.

 Not So Fast — Posted Wednesday August 3 2022 Mental health professionals have repeatedly warned that Donald Trump is a sociopath (and perhaps a psychopath) with no regard for human decency, the rule of law or other norms and societal limits on his behavior. These pathologies, in a very real sense, are among his greatest strengths as a fascist leader who is plotting his return to power. Salon writer Chauncey Devega is warning progressive Americans that despite the DOJ's apparent criminal investigation of former President Donald Trump and the January 6 Committee's overwhelming evidence that Trump has committed felony crimes against America, the DOJ's efforts are not only emboldening Trump but are also encouraging his supporters to stand behind him even more. Although Trump's approval rating has slipped in recent months, the results of yesterday's primary elections and prior elections show that his influence remains strong among Red State voters. God forgive me, but it makes me so mad to think that the residents of Kentucky, who lately have been the victims of horrific floods and record heat waves, voted overwhelmingly for Trump in 2016 and 2020 and will likely do so again should he run in 2024. Like Trump, Kentucky's voters still do not believe in climate change or science, as evidenced by Kentucky's proud hosting of the Ark Encounter, a full-scale replica of Noah's biblical ark. It's replete with exhibits showing that man existed alongside friendly dinosaurs, while Ark Encounter founder Ken Ham pushes the Young-Earth belief that the Earth is only 6,000 years old. Meanwhile, Kentucky is one of the leading Red States in terms of federal funding in excess of state revenue. This tells me that as a Californian, a sizable percentge of my federal income tax (about $30,000 last year) was going to support people in states who deny climate change, science, minority rights, family planning or any culpability regarding Donald Trump's crimes against the country. Biting the hands that feed you Again, Dear God, forgive me for being so vindictive.  July 1936 — Posted Saturday July 30 2022 America's Republicans tend to believe that the unusual heat waves, droughts, floods and wild fires we're experiencing are all just normal blips in the weather, although these events are extending into Europe and Asia as well. Most scientists believe it's due to anthropogenic climate change, although extreme heat events have been around before. Two months before my second sister was born in September 1936, the United States was hit by a record-setting, weeks-long heat wave. I recall my mother telling me how miserable she was at the time, seven months pregnant and with no air conditioning to speak of in the tiny house they were living in. I looked up the weather records for Quincy, Illinois this morning, and sure enough, the city hit a record $$114^{\circ}$$F on July 15 of that year. That date still stands as the hottest on record, although it was a one-off at the time, not something one might have expected would occur every year in the future. When I came along 13 years later, the family was living in Duarte, California. That winter of 1949 was also a one-off, the only time it snowed heavily in the San Gabriel Valley. My mother wasn't exactly pleased with that, either.  "Exploit to Exhaustion" is the World's Business Model — Posted Saturday July 30 2022 "Crunch All You Want, We'll Make More!" was a popular slogan of the Doritos Chip company. Sadly, it doesn't apply to natural resources like air, water and land. Mathematicians have long noted that a 3-dimensional sphere is "unbounded but finite," and the same observation applies to the Earth, whose resources are finite but disappearing in forms useful to us humans. Yes, the amount of water on the planet is the same as it was 4.5 billion years ago, but the amount of water suitable for consumption is dwindling rapidly due to overuse and pollution. Many millions of years ago the Earth's oceans were drinkable, but land erosion, underwater volcanic action and other natural factors introduced soluble salts that gradually turned them saline (can't blame us humans for that!) Meanwhile, fresh water sources remained intact via the hydrologic cycle until the advent of billions of humans, whose uses and demands are depleting fresh supplies past the point of sustainability. And at the same time, entropy is increasing inexorably, making everything a disordered mess, humans or no. Later this year, the Earth will welcome its 8 billionth human, joining billions of others all wanting to live like Americans and the residents of other first-world countries. Unfortunately, most of these newcomers will be disappointed. HBO's Bill Maher isn't my favorite comedian, but his latest show speaks the truth about the sad state of affairs: And yes, I'm just as much to blame as anyone.  The Great Salt Lake is Disappearing — Posted Friday July 29 2022 California's largest body of water is the ill-fated Salton Sea. Created by a massive overflow of the Colorado River in 1905, this land-locked lake has been shrinking ever since, fed only by scant occasional rainfall and meager inflows from nearby agricultural sources. Now nearly dead, the Salton Sea was declared an environmental disaster in 2020. The Salton Sea was once a thriving sport fishing, recreational and celebrity mecca in the 1940s through 1960s, hailed by many as California's answer to the French Riviera(!) But continued water loss due to evaporation and resulting salination has killed off most of the fish and associated wildlife. My father loved going to the Salton Sea, and he dreamed of buying some land there in the 1950s. He passed away in 1981, never learning of the environmental disaster that would destroy it. About once every ten years or so, rare northerly wind conditions bring the stench of dying fish up here to Pasadena, some 150 miles away. Now the same thing appears to be happening to Utah's Great Salt Lake, but it's a victim of ensuing climate change. The lake is much bigger than the Salton Sea, and it sits adjacent to Salt Lake City, with a population of 200,000 people. If the Great Salt Lake dries up, it would present enormous health problems to the area due to dust-borne toxic materials like arsenic and cyanobacterial particles and lung-clogging, wind-driven particulate matter. I find it particularly annoying that the State of Utah, presumably the most religious state in the Union, nevertheless voted overwhelmingly for Donald Trump in 2016 and 2020 despite his record of documented gross immoral and un-Christian behavior. The State's mostly Mormon population also vehemently denies climate change along with any number of unrelated progressive issues, and its 3.2 population is dominated by one million registered Republican voters. In 1848, the fields of Mormon pioneering farmers were overrun by insects devouring their crops. According to the mythic Miracle of the Gulls story, the crops were saved when millions of seagulls local to the Great Salt Lake arrived to eat the insects. I find it ironic that today, some 170 years later, the seagulls and other avian species are threatened by the lake's dwindling water supply due to urban and agricultural overuse and climate change, all of which the state's residents refuse to believe in.  No Dark Matter is a Success? — Posted Thursday July 28 2022 In my post of July 9, I talked about the latest and most detailed and accurate test for dark matter. It came up empty, but that doesn't bother noted astrophysicist Ethan Siegel, who still sees the test as a great accomplishment. I sorta agree, in the sense that even a null test provides some information, but Siegel goes further, seeing the result as a record-setting success, despite the fact that it came up empty. It reminds me of the work of Michelson and Morley in the late 1880s, in which they tried to prove the existence of the luminiferous aether, a universal substance that provided the "stuff" physicists then believed was needed to allow for light to traverse the interstellar medium (that is, something for light to "wave" against). Their experiments were also famously null, but they showed conclusively that the aether simply didn't exist, and that light could travel in the vacuum of space just fine all by itself. I cannot help but note that the Michelson-Morley experiments did not drive the need for further, more elaborate and costly tests to see if the aether was indeed non-existent. Instead, it was a settled matter, something that today's physicists seem unwilling or unable to accept with regard to dark matter. Off topic: Today marks the third anniversary of my wife's death. I no longer shed torrents of tears every day, but she's never far from my mind and heart. Dear God, bless her, comfort her, keep her, and welcome her into Your Kingdom.  Has Droopy Been Compromised? — Posted Tuesday July 26 2022 "Why oh why did I ever accept the Attorney General appointment?" While fascist Republican elements of America are working at light speed to retake the country, Sleepy Joe Biden and Droopy Merrick Garland are doing nothing to stop it. Sure, the January 6 Committee is moving along, having long since provided sufficient evidence to indict and convict former President Donald Trump of obstruction of justice, inciting a murderous mob and sedition, but the Committee is acting like the detached half of a brain-dead Democratic Party that appears to have no chance of surviving the 2022 midterm elections. And could that be the reason for Attorney General Merrick Garland's seeming unwillingness to prosecute Trump, regardless of the mountains of evidence the Committee has already provided? Garland is surely aware that if the Republican Party retakes the House and Senate this November, Party members have pledged to impeach Garland, citing Garland's inaction on school violence and recent pro-abortion protests carried out against the Supreme Court. But the threat of impeachment by itself cannot explain Garland's complete judicial absence with regard to Trump's crimes. There's got to be something more. Sure, avoiding an indictment of Trump might placate Republicans to some extent, but their vengeful kill-the-wounded, take-no-prisoners political posture would not save Garland from future action. Instead, if Garland were to announce that he will not seek prosecution of Trump on the basis of insufficient evidence (as insane as that might seem), he might endear himself to the incoming Republican majorities and save himself from future embarrassment. That's the only explanation I can think of. Merrick Garland — the poster child for the Democratic Party's complete inability to govern.  Memory Lane Is Being Paved Over — Posted Tuesday July 26 2022 Those of us who grew up in the 1950s will remember the milk delivery guy, the Helms Bakery truck and the ice cream man. I can't for the life of me now understand how these people made a living. It couldn't have been great, but their meager incomes must have been sufficient to have families, purchase groceries and even buy houses. While struggling with a full time job in the late 1960s to put myself through college (also full time), a co-worker (one B. Reynolds) told me he'd previously worked as an Alta Dena Dairy delivery man. He worked from 3 am to noon, driving around in his truck while placing milk bottles and butter on the front porch steps of his company's customers. He quit only when his wife demanded he get a better paying job.* The Helms Bakery guy came around in mid-afternoon, stopping on the street to open up the back of his truck for waiting customers wanting to buy bread, cookies and cakes. The Helms Company once dominated the bread delivery business, with a huge factory on Venice Boulevard in Los Angeles that looked like a blocks-long medieval fortress (it still stands today). Its many hundreds of delivery vans and trucks operated from the 1920s to the 1970s, but it had to shut down due to unsustainable operating costs. I would sometimes save my school lunch money for the Helms man, as 25 cents then would buy a bunch of snacks. But my fondest memory is that of the ice cream truck, which would come past our house on Bloomdale Street in Duarte, California every single day. He'd stop for just one or several customers and open the back of his truck to fish out a Dream Bar (10 cents) or a Sidewalk Sundae (15 cents) while streams of dry ice vapor would pour out. I still remember the truck's jingle, which I could hear all the way up the street. They're all gone now, with the possible exception of the ice cream man. But he's struggling with the costs of gasoline, the truck, and his need to stay afloat in a world where an annual income of$50,000 isn't enough to live on (and the number of customers willing to pay $5 for an ice cream cone are vanishing). Just how the hell they got by in the 1950s is beyond me. * Here's a memory I've carried around since the summer of 1968, when I was working at a chemical plant right before my second year of college started. At the plant was a tall, skinny co-worker named Wayne W., a white guy about 40 years old or so, making about the same paltry wage that I was. He was single and a tad weird, but otherwise he was alright, definitely not gay or anything, and I got to know him somewhat. I recall that he had bought a house that summer and wanted me to see it, so one day we went to McDonald's and then drove over to his house to eat lunch. It was somewhere in Azusa, not far from our work (we only had half an hour off for lunch), and I remember his house being even worse than the crackerbox I grew up in. It was old and depressing, with no carpets or furniture to speak of, with ragged strips of cloth serving as window drapes. We sat on some wooden boxes he had to eat our hamburgers and fries, and I remember that the hardwood floor was sagging in the center of the living room where we ate, indicating some kind of structural problem. Still, Wayne expressed great pride in his home, although all I could think of was getting out of there, as it reminded me of the kind of house I was likely to have should my college career end abruptly in failure, and that I too would be a 40-something flunky struggling to get a paltry something out of life. I felt sorry for Wayne, as I realized that this was probably the best he was going to have in his life, while I felt a little better for myself, as I was in college and could at least hope I'd graduate someday and do better. I have no idea what happened to Wayne or his little piece of the American dream, but today I thank God every day for all the undeserved blessings He's given me.  What is There, Then? — Posted Saturday July 23 2022 In her latest video, German physicist Sabine Hossenfelder talks about the nature of time, particularly the nature of the past. She uses a clever device in special relativity to show that simultaneity—the occurrence of two events that happen at the exact same time —is meaningless. That's because observers in two different inertial systems see things happening at different times, and that what one sees as two simultaneous events the other does not. I see a parallel to this in modern cosmological theory, which posits that on average and at large scales all the stuff in the universe—matter and radiation—is perfectly uniform, so that nothing really changes going from one place to another. This is known as the cosmological principle, which is described by the Friedmann-Lemaître-Robertson-Walker metric, the most accurate description of the universe we have. But if spacial differences don't matter, and if time differences don't matter, then perhaps both space and time are only figments of our imagination, created in our brains to make sense of the world outside our heads. Similarly, modern quantum theory posits that matter and radiation are only combinations of fields, so perhaps the stuff of the universe doesn't exist externally to our brains as well. If God exists, then surely this is the realm in which He resides, a spaceless and timeless realm in which everything exists simultaneously and in the same place (or no place, if space itself doesn't exist). If all this is true, then one may rightfully ask "What is there, then?" Outside of God, to me the answer is mathematics, which exists independently and on the outside of everything else. Indeed, noted MIT physicist Max Tegmark views mathematics as almost a physical entity, with mathematical equations and relations existing eternally and without any relationship to anything else. The famous physicist Paul Dirac (in my opinion, the greatest scientist who ever lived) once stated that "God is a mathematician, and He used beautiful mathematics in creating the world." Mathematics doesn't require space, time, matter, radiation or fields, so maybe Tegmark and Dirac are right.  Only Dereliction of Duty?! — Posted Thursday July 21 2022 "Awful but not unlawful." — Trump's ace in the hole. If you've been following the news you'll get the notion that the January 6 Committee, wallowing amid an infinitude of criminal evidence against Donald Trump but still unsure that he can be prosecuted, seems to have decided on a single charge — dereliction of duty (DoD). But while DoD is a punishable offense according to the United States Code, it only applies to members of the military. Indeed, the Committee's hearing today will feature Virginia Democratic Representative Elaine Luria, a 20-year veteran of the U.S. Navy, who has previously stated While there are penalties for members of the military who are found derelict in their duties, [I am not sure] Mr. Trump could be charged with a criminal offense as a result of his inaction. (I find it odd that the person called "Commander in Chief of the Military Forces of the United States" may not be held to military standards.) Despite all the damage Trump and his minions have done to the country, DoD appears to be the only crime the Committee can hang its hat on. With over$250 million in his private re-election war chest, Trump can hire the best lawyers on the planet to defend him (should he be charged). By putting all their eggs in one contentious basket, the Committee is effectvely letting Trump off the hook. Today, a number of retired U.S. generals and admirals weighed in on the issue. They agree that Trump is guilty of DoD, but they don't advocate charging him with any crime. I stand by the prediction I made in yesterday's post.

 Dark Matter vs Modified Gravity — Posted Wednesday July 20 2022 In April 1918 the German mathematical physicist Hermann Weyl proposed a beautiful variant of Einstein's 1915 general theory of relativity, whose theory today is still the de facto theory of gravitation. Weyl's motivation at the time was to derive Maxwell's electrodynamics from the same geometrical basis that forms gravity, and to do that he had to make a basic modification of Riemannian geometry, the geometry that Einstein's theory is based on. If one takes a vector quantity and moves it around (say, along a sphere), it may change direction, but its length will remain the same. Weyl saw this as an unnecessary restriction of Riemannian geometry, and by relaxing it he found it provided just enough room to describe electrodynamics. Weyl's idea thus became the first apparently workable theory to unify gravity and electromagnetism within a purely geometrical construct. But it was not to be—Einstein himself (who was initially enamored of Weyl's theory) found a fatal flaw (not in the mathematics, but in the theory's physical interpretation), and by 1921 Weyl's theory was all but dead. But Weyl's basic idea survived, and is known variously today as scale invariance, gauge invariance and conformal invariance, the latter being reserved primarily for cosmology. Mathematically, it means that physics should not change if the fundamental metric tensor $$g_{\mu\nu}$$ is varied locally by the Weyl conformal transformation $$g_{\mu\nu} \rightarrow \Omega^2 g_{\mu\nu}$$, where $$\Omega(x)$$ is any real function of the spacetime coordinates. There are a number of other invariant principles in physics, and why conformal invariance (CI) should be added to the list depends on the preferences of physicists and cosmologists. But there is one aspect of CI that has become increasingly popular, and that has to do with the dark matter problem. Dark matter is conventionally believed to be the missing matter responsible for extreme stellar velocities, galaxy cluster rotation speeds and some forms of gravitational lensing. But despite billions of dollars spent on detection experiments over the past three decades, absolutely no evidence of dark matter particle has been seen. This disappointment has led many to believe that dark matter simply does not exist (like the luminiferous aether of the late 19th century), and that the answer lies in a modification of Einsteinian gravity instead. Unfortunately, Einstein's 1915 theory is not scale-invariant, so if scale invariance is a fundamental property of Nature then the theory must be modified. Weyl himself found a way to do this, and he discovered an invariant geometrical quantity that is equivalent to what one refers to as the Einstein tensor. However, while the Einstein tensor is linear, the Weyl tensor must be squared, and this makes Weyl geometry much more complicated. Weylian gravity for matter-free space wasn't solved until 1989, when Mannheim and Kazanas found the solution. It involves an extra integration constant which, when omitted, results in the traditional Einstein solution. But retaining the constant appears to provide an answer to the dark matter problem. A more detailed description of all this can be read in this fascinating new article in the online magazine The Conversation, in which a new research paper on the dark matter problem is outlined. In that paper, the authors describe a kind of "scoring system" that compares the relative benefits and drawbacks of unseen dark matter versus scale-invariant gravity, and the authors conclude that modified gravity is a far better alternative to dark matter. It's cheaper, too, because in lieu of costly experiments it requires only pencil and paper. The authors' paper is available for download here, and while it is lengthy (147 pages) and rather mathematical, it should be accessible to any undergraduate physics student.

 What a Waste of Time — Posted Wednesday July 20 2022 "We investigate crimes, not people." — Attorney General Merrick Garland This is the clearest evidence I know indicating that former President Donald Trump will not be indicted or prosecuted for the January 6, 2021 attack on the Capitol Building. Yes, crimes were committed (including murder, insurrection and treason), but they were perpetrated by Trump loyalists. They have been and will be rounded up, charged, convicted and sentenced, but Trump himself will escape justice because Garland is simply too afraid to go after him. A week ago, the New York Times published this article by Andrew Weissmann, one of the federal prosecutors in the Mueller Investigation of 2016-2019. Weissmann believes the January 6 Committee should be conducting a "hub and spoke" investigation, one in which the crimes committed do not begin and end with the immediate perpetrators, but are traced to the conspiratorial center of the attack. Instead, Weissmann believes, the Committee is treating the attack as a single event, devoid of any serious intention of treating it as a conspiracy beginning at the Trump White House and branching out to dozens of "spokes," like fake electors, phony promises to overturn the 2020 election by a sitting Vice President, complicit rightwing media, criminally-ignored subpoenas and missing Secret Service texts. A few days later, Weissmann was interviewed by Politico regarding direct involvement of Trump in a conspiracy to overturn the election and to incite the Capitol Building rebellion. The interview is a word salad of sorts, but I think Weissmann unintentionally blew it when he stated The moral culpability of somebody who is aware that armed people are coming to the Capitol, does nothing to prevent it, is aware of who they're for and who they're against. And then when violence erupts completely condones it, you know, that has a political consequence, even if it doesn't have, strictly speaking, a legal consequence. If there's no "legal consequence" on Trump's part, then Garland will have no case against him. Trump can lie all he wants, but if he's not under oath he is not committing any crimes. To top it off, the Committee and Garland are stumbling over the issues of "intent" and Trump's "state of mind," which are of primary importance in any criminal case. Trump could stand on a soapbox and encourage a murderous armed mob and later call them patriots and tell them he loves them after they've murdered, injured and destroyed property, but proving he actually intended them to commit these crimes will be difficult in a court of law. Garland knows all this. He's simply waiting for the Committee to finish its investigations (assuming there is an end), and when pressed he'll shrug his shoulders and say that Trump cannot be charged with any crimes. He is probably also concerned that an indictment against Trump would cause more violence, even a civil war. I predict, perhaps after the fall mid-term elections, that Trump will triumphantly declare ACQUITTED!, as he did following the Mueller investigation. Then he'll run again for the presidency and, with the undying support of his tens of millions of loyal followers, win the election. Then he'll issue an en masse pardon for all those charged or imprisoned for participating in the 6/21 rebellion.

 Canada is Calling Me — Posted Sunday July 17 2022 When Robb Elementary School in Uvalde, Texas was attacked by a lone gunman three weeks ago, we now learn that 376 police officers and armed responders (aka "good guys with guns") arrived to neutralize the shooter. While they awaited orders, assessed the situation, stood around or sat frozen in fear (and even sanitized their hands), the gunman (aka "the bad guy with a gun") murdered 19 school children and two teachers. "Murder" is perhaps too gentle a description. The AR-15 assault rifle fires 5.56 military ammo with a bullet diameter about the same as a .22—much smaller than a .45, but at supersonic speeds and with much greater energy. When it strikes the human body, the bullet's energy typically evicerates and dismembers its target. Many of the Uvalde victims were literally torn apart, and the children who were struck in the face or head were unrecognizable, identifiable only through their DNA. The response to the tragedy by the NRA and the Republican Party was the same as their response to all the other mass shooting tragedies: America needs more guns, lots more guns, as only a good guy with a gun can stop a bad guy with a gun. The AR-15 is a military weapon designed only to kill lots of people quickly. It has no real value for hunting, and its size and weight make it useless for home defense. All assault-type weapons should be banned immediately, and registered owners should be required to turn them in for reimbursement. Canada is not perfect, but it does not have the problems America is now experiencing, especially crazy politicians and gun worship. I'm now seriously considering moving there.

 Should the Ten-Year-Old Rape Victim be Prosecuted, Republicans? — Posted Thursday July 14 2022 In John 7:53-8:11, Jesus defends a woman arrested for adultery, the punishment being death by stoning. Women in those days were little more than chattel and, if rape victims did not complain loudly enough while being raped, they were considered guilty of adultery. The woman's age in the Gospel is not given, but she could have easily been a teenager. When reports that a 10-year-old Ohio girl had been raped, made pregnant and then had to leave the state for an abortion because the procedure is now a criminal offense in that state, Fox News, Republican lawmakers and other conservative pundits called the story an outright lie perpetrated by pro-abortion liberals. When it was revealed that the story was in fact true, and that the rapist had confessed and been arrested, Republicans decided to go after the doctor who performed the procedure. I guess we can all breathe a sigh of relief that the 10-year-old girl (who had been raped twice by her self-confessed assailant, the first when she was nine) is not being prosecuted legally (or perhaps stoned) by Republican lawmakers for her crime. As a Christian, I abhor abortion, but I leave it up to the parties involved and their God to resolve whatever moral and ethical issues are involved. But for the Republican Party, abortion has become solely a political issue to be milked for all the votes they can garner from it.

 The Final Problem—A Different Ending? — Posted Thursday July 14 2022 The Return of Donald Trump? In Sir Arthur Conan Doyle's 1893 novel The Final Problem, Sherlock Holmes manages to track down and corner his archnemesis, Professor James Moriarty. Moriarty has been able to dodge Holmes repeatedly, but it looks as if Holmes has finally gained the upper hand, and is about to bring Moriarty to justice. Nevertheless, Moriarty is proudly defiant: You hope to place me in the dock. I tell you that I will never stand in the dock. You hope to beat me. I tell you that you will never beat me. If you are clever enough to bring destruction upon me, rest assured that I shall do as much to you. I see this same defiance in former President Donald Trump, whose equivalent Holmes is not the feckless wimp, Attorney General Merrick Garland, but the January 6 Commission. While Professor Moriarty is a brilliant mathematician and true criminal genius (Holmes once expressed his appreciation of Moriarty's mathematical tract "On the Dynamics of an Asteroid"), he has limited funds and a limited number of devoted criminal cohorts to do his bidding. Trump, by comparison, is a mental dunce but with tens of millions of amazingly stupid followers besotted with his celebrity and ill-begotten wealth. But Trump is equally defiant, and his ongoing crimes (even while under investigation) demonstrate the true extent of his hatred of the justice system as well as the nation itself. In the conclusion of The Final Problem, Holmes and Moriarty fight to the death, which ends when both men plunge over the Reichenbach Falls. Holmes' literary death brought screams of protests against Doyle, who was forced to resurrect Holmes in a subsequent story, The Return of Sherlock Holmes. But I fear a different ending to our current problem, one in which Garland and the January 6 Commission simply give up in resignation and throw themselves over the falls, with a triumphant Trump returning in 2024.

 Sneak Preview — Posted Monday July 11 2022 Imagine holding a grain of sand at arm's length above your head at night. The area of the sky hidden by that grain of sand is minute, but it holds thousands of faint galaxies that have now been photographed by the James Webb Space Telescope: At the center of this first image is an ordinary galaxy cluster, whose light traveled some 4.6 billion years before falling on the telescope's primary mirror. The center of the cluster appears at the image's center and, as predicted by Einstein's general theory of relativity, it is gravitationally lensing the galaxies behind it, producing the ring-like arcs of light around the center. Those rings can be analyzed to provide an accurate estimate of the cluster's mass, while the structures of other more distant galaxies in the photo will provide unprecedented information on star and galaxy formation. This photo is just the first of a suite of photographs and data that will be presented by NASA tomorrow. July 12, 2022 will mark the beginning of a historic new chapter in our understanding of the universe, and perhaps how we got here and why.

 Here It Comes — Posted Sunday July 10 2022 On Tuesday, July 12, NASA will release the first of a series of photos and data taken by the now fully operational Webb Space Telescope. Designed to capture very low-frequency light from the earliest universe, this is light that has been extremely red-shifted due to the expansion of the universe since the Big Bang. Here's a test picture, showing a glimpse of that very early universe: Photos and data provided by Webb will be analyzed and studied for many years, and will undoubtedly provide mankind with a truer understanding of how our universe began. Thousands of papers will be published, new theories will be proposed, revised, discarded and upheld, and perhaps we'll also learn more about how God pulled all this off. With 7.8 billion people now living on an increasingly polluted and impoverished planet ruled by monsters, con men, fools and idiots, I feel that something is gonna break before long. I for one would like to see just a little more beauty and truth before that happens.

 Yet Another "Critical Witness" — Posted Sunday July 10 2022 Former Donald Trump administrative strategist and sycophant Steve Bannon has agreed to testify to the January 6 Committee regarding the 2021 Capitol Building attack and insurrection. Trump has given Bannon permission to bypass executive privilege and proceed with his testimony, as if such perpetual immunity existed in the first place. I see two likely agendas at work here. One, Bannon has probably been instructed by Trump to lie (even under oath) for the purpose of obstructing justice or derailing the Commission's work. The Commission would then have to sort out the truth from Bannon's lies, further delaying its deliberations. And two, the appearance of yet another major witness will absolutely extend the Commission's already stretched schedule, solely for the purpose of delaying the Commission's hotly-awaited announcement of its findings. Bannon's testimony (perhaps joined by even more critical witnesses to come) could force the Commission's efforts to run right up against the November mid-term elections, at which time its findings might be seen as either irrelevant or a political ruse to block Trump's planned 2024 presidential bid. It's also possible that Trump-adoring 1/6 witnesses (including Trump himself) might simply tell the truth and face the immediate consequences, believing that a 2024 Republican president (possibly Trump himself) would pardon them. Dear Lord, it's all so transparent.

 Earthman is Us — Posted Sunday July 10 2022

 Our Disappearing Water — Posted Sunday July 10 2022 As fresh water supplies run out everywhere due to increasing population demand, climate change and pollution, water supply scientists, engineers and lawmakers are considering revising the rules currently governing water sharing between drought-stricken states like California, Nevada, Arizona and Utah. As a former engineer who designed water treatment, distribution and conservation plans, I am frustrated that one option continues to be overlooked or outright discarded, which is water reclamation. In an age when technology has produced advanced wastewater treatment options that can produce drinkable water supplies from any source, the term "toilet to tap" continues to linger over those options, be they applicable to landscape irrigation, industrial use, groundwater replenishment or even direct consumption. This has got to change. The idea of recycling domestic wastewater—sewage—has always called up the "yuck factor," regardless of the fact that all of the planet's finite water has undergone countless cycles of purification and reuse via the hydrologic cycle, going through the gastrointestinal tracts of dinosaurs and living animals, plants and people alike. I cannot adequately convey the frustration I experienced many years ago when, lecturing to lay people in public meetings, that water molecules do not somehow "remember" being in contact with bacterial and industrial wastes, while culminating all the same in the belief that such water must be disposed of permanently. This "remembrance" of elementary particles like water molecules is the basis of homeopathic medicines, which consist of nothing more than a toxic material diluted so many times with tap water that not a single toxic atom or molecule remains in the water solution. And why is this supposed to be an effective medication? Because, believers say, the water remembers being in contact with the toxic material, and so conveys immunity against it. This insanity has been shown to be scientifically and experimentally wrong, yet it underlies an annual billion-dollar business built on people who are either ignorant or stupid. Yet, when asked if they'd consume reclaimed water that's 99.999999% pure, they still say "yuck." I still remember pitching the idea of recharging a groundwater basin used by a major beer brewing company, whose motto "It's the Water" might have been taken the wrong way! But the Southwestern drought is not only reality, it appears to be permanent and getting worse. Artificially speeding up the hydrologic cycle by reverse osmosis, desalination and similar technologies must become part of a renewed, nationwide effort to conserve our dwindling water resources.

 And Yet Another Dark Matter Search Bites the Dust — Posted Saturday July 9 2022 The most exacting, detailed search to date for dark matter has come up empty, but researchers plan to press on with the hunt for another five years. To me, this is a prime example of "sunk costs," more literal than figurative for the following reason. Like a few of its predecessors, the LUX-ZEPLIN dark matter detector is based on the notion that an isolated mass of liquid xenon will emit flashes of observable light should a dark matter particle happen by and interact with a xenon atom. The L-Z experiment is located in a subterranean research facility in Lead, South Dakota, more than 3,000 feet below ground surface (where the effects of interfering cosmic rays are negligible). The heart of the experiment consists of 22,000 pounds of liquid xenon, an inert gaseous element that has to be cooled to -160$$^o$$ Fahrenheit before becoming a liquid. Hauling that much xenon more than half a mile down, maintaining its liquidity, and staffing the experiment must have been quite expensive. Working in a hole that deep can't be pleasant, although the staff's elevator ride must be a lot of fun. I'm still of the opinion that dark matter is just so much pixie dust of the mind, and that a workable theory of modified gravity will provide the answer. Such a theory may require a lot of pens and paper, but it certainly will not incur the billions of dollars now being spent on all these ongoing, expensive, fruitless experiments.

 Superboy Sez — Posted Friday July 8 2022 America's Republicans keep yearning for the good old 1950s, but I wish they'd bear in mind that sensitivity to racial, ethnic and religious differences is a timeless concept. Here's a page from one of my old comic books, circa 1951. Yes, all the characters are white, but at least there was some sensitivity to different cultures even then (perhaps Republicans would prefer the 1300s instead).

 Things Haven't Changed Much in 246 Years — Posted Monday July 4 2022 Here's an example of the self-righteous garbage I regularly post on various websites, but quite appropriate for this Fourth of July:

 Trump's America and Westworld — Posted Sunday July 3 2022 I was an early fan of the futuristic science fiction series Westworld until the second season, when the intertwining plots got just too complicated for me to follow (many other viewers had the same feeling). But the series has managed to plod along, and is now in its fourth season. It's better now, at least for me, as the show's writers seem to have learned from their mistakes, although my guess is that this may be the series' final season. The show is not to be confused with the mediocre 1973 film of the same name, in which realistic humanoid robots go berserk and start attacking the real humans. However, the human "guests" in the 1973 movie share the same foibles and shortcomings as they do in the series—they're all wealthy and willing to pay top dollar to engage in some realistic shoot-em-up play-acting with their robotic "hosts." But by and large, the guests in the 1973 film are not bad people, they're just looking for a good time; it's the robots that are the bad guys. These roles have been reversed in the series, as most of the guests are truly despicable people seeking to partake in killing and debauchery for the fun of it, while the robots are just there to be abused, slaughtered and raped. While they all have short-term memories and a kind of pseudo-consciousness, the robots are all programmed to follow scripts given to them by the technicians that repair the damage done to them and wipe their memories at the end of the day. These scripts can vary, depending on how the human guests behave during their stay. But due either to unforeseen technical circumstances or even some sort of machine evolution, the hosts begin to remember what has been done to them. And that's when things start to go awry at the Westworld theme park. The series began in late 2016, coinciding with the unfortunate presidential election of Donald Trump. As both the series and the Trump administration progressed, I began to realize that the robots in Westworld were far superior to their guests in terms of actual humanity. They were evolving, demonstrating intelligence and altruism, while the humans were devolving into savages. At the same time, I sensed a very clear parallel between the Westworld humans and Trump's America. I believe that Salon writer Melanie McFarland also shares this belief. With all the rightwing stupidity, ignorance, arrogance, hatred and greed now taking over America today, McFarland's query "Why not just hand the world over to the robots?" is well-posed.

 The Higgs Particle at 10 — Posted Friday July 1 2022 This month marks the 10th anniversary of the observational confirmation of the Higgs particle at the Large Hadron Collider. The Higgs process was first proposed by British theorist Peter Higgs and collaborators in 1964, but the theory languished for decades until physicists realized its importance. In this recent Scientific American article, the Higgs process is outlined, along with the assertion that it ruined the life of Peter Higgs (a rather shy and aloof man) because of all the fame that came with it (including the Nobel Prize in Physics). The famous Caltech physicist Richard Feynman once lamented that the Nobel Prize was one of the worse things that happened in his life as well. I still do not understand the full importance of the Higgs process. Many years ago I wrote a truly awful paper on how the process was a consequence of the gauge invariance principle fathered by the German mathematical physicist Hermann Weyl, but exactly how the Higgs particle and its associated scalar field conveys mass to all the other particles in the universe continues to escape me. Still, the 2012 Higgs discovery marks an enormous step toward the truth of our physical world, and deserves celebrating.

 Just Wondering — Posted Friday July 1 2022 Former President Donald Trump and his cabal are paying the legal fees of witnesses called by subpoena to testify at the January 6 Commission hearings, raising concerns over direct or indirect witness tampering. If they are placed under oath, they are required to tell the truth, but if they are not under oath (or if they choose to illegally ignore their subpoenas) they can lie to their hearts' content. I wonder what FOX News would say if President Biden's team offered to pay the legal fees for these same witnesses.

 Get Ready, America: Garland's About to Pull a "Mueller" — Posted Wednesday June 29 2022 While minority criminals are quickly rounded up and sentenced for minor crimes, former President Donald Trump eludes justice despite overwhelming evidence of his guilt for inciting a murderous mob and committing treason against the United States of America. Here, artist Ruben Bolling shows the reason why Attorney General Merrick Garland is so hesistant to indict Trump: The answer: Garland's a wimp

 Blast from Bill's Past — Posted Monday June 20 2022 Growing up in the 1950s, I became addicted to comics books, especially Superman, Superboy, Action Comics, Adventure Comics, World's Finest and Mystery in Space, along with Donald Duck and Uncle Scrooge. I learned how to read at an early age, and the science aspect of many of these comics instilled in me a love of science and math. I remember I outgrew them around 1961, but I still have hundreds of the books, carefully preserved and stored away, which I plan to pass on to my grandchildren. Meanwhile, this is all I can remember of a carefully-drawn comic strip I created (now lost) that I placed at the door of my college classroom in the Spring of 1971: It's Monday morning at Smallville College, and Clark Kent, secretly Superboy, confidently strides into the classroom! "Ha! Watch me ace Dr. Baine's physical chemistry exam!" But the Boy of Steel is in for a surprise! "What the $$\dots$$?! The professor's exam is much tougher than I thought! It will take all of my super-intelligence just to pass! Damn!" Clark did pass, as I did, and that semester was the only time I got on the Dean's List. This silly reminiscence comes courtesy of Ruben Bolling, whose latest strip inspired it: If you don't know what a Boltzmann Brain is, you should read this.

 Goldsmith on Garland — Posted Monday June 20 2022 Oh dear, what am I to do? Jack Goldsmith, former Assistant Attorney General under George W. Bush, writes in today's New York Times that current Attorney General Merrick Garland's got a huge problem on his hands. With the impending conclusion of the January 6 Commission's investigation of Donald Trump's involvement in the infamous insurrection of 2021 and the evidence collected to date, Garland will most likely have sufficient legal reason to indict Trump of inciting a deadly rampage and conspiracy to defraud the government, along with a very possible charge of treason against the United States of America. But will he? Goldsmith notes that proceeding with an indictment would "further enflame our already-blazing partisan acrimony" while leaving President Biden hamstrung with the consequences to the end of his term. But, if Garland opts not to pursue any charges, he will effectively declare the death of justice, democracy and the rule of law in the country and pave the way for future presidential crimes, of which a possible future President Donald Trump would certainly engage in with renewed vigor and audacity. What Goldsmith leaves out of his article is the possible nationwide violence that might erupt regardless of Garland's move. If he goes ahead with an indictment against Trump, the former president's rabid, gun-crazed supporters would almost certainly stage violent uprisings similar to the one they conducted in 2021. Conversely, if Garland drops the case entirely the nation's progressives might rise up. However, since they're the country's only remaining Adults in the Room, they'd likely just shrug it off and go home disappointed. My guess is that these scenarios are the ones going through Garland's head right now, as he weighs truth and justice against lies and injustice and the threat of a new American Civil War. As Goldsmith notes, Garland's reputation will be stained for life either way, but Garland is likely leaning toward the least violence-prone option. And being the spineless wimp I believe Garland to be, I will be truly sorry I didn't move to Canada when I had the chance.

 Photons from the Past — Posted Saturday June 18 2022 This is my father's old Brownie Target Six-16 still camera, which he bought sometime in the 1940s. He replaced it with a Kodak Instamatic in the 1960s, which was garbage by comparison in terms of image quality. I last used the Brownie in 1971, when I graduated from college. My father was born in January 1905, and when I was little he'd tell me about the movies he saw in the silent film days. We'd watch Silents, Please and Fractured Flickers on TV, and on occasion we'd see The Hunchback of Notre Dame (1923), The Phantom of the Opera (1925) and other silent classics. I remember asking him dumb questions like "What did food taste like in the 1920s?" and "What did people sound like in the 1920s?" Not surprisingly, I developed an unusual affection for the 1920s that has diminished only slightly to this day. I have many hundreds of silent films in mp4 format now, but I watch them only occasionally. To a lesser extent, I have much the same fascination with Civil War photographs. Unlike engravings, paintings and similar artwork from the pre-photographic past, all this has to do with an awareness that what we're seeing is a true window into past worlds, whose images are composed of photons that impinged upon light-sensitive plates and film, capturing people and locations that in most cases no longer exist. It's ironic that the Kodak photographic film I grew up with is now almost completely gone, having been replaced by digital media, while the Eastman-Kodak company itself is also nearly extinct today. My father was also fascinated with movies, and I still have his old 16-mm projector from the 1920s, along with a can of film he shot at the 1933 World's Fair in Chicago. Regrettably, he only photographed sites and locations of the fair, with no shots of him or my mother (they married in 1932). Still, there are people passing by in the film, enjoying the fair, and all dressed in formal early 1930s attire. There were no shorts, T-shirts or flip-flops in those days! One of my favorite online sites is John Bengtson's Silent Locations, which is a huge repository of silent film-related history. He has written a number of books, one of which is a favorite of mine, Discovering Early Hollywood Through the Films of Buster Keaton. It has been estimated that roughly 80% of all silent films are now lost forever. Back in the day, the films were shown in the theaters, they made whatever money they did, and then the prints were either discarded or burned to recover their silver content. With almost no exception, the films' creators had no sense of film historicity. Similarly, something like 99% of all Civil War photos are probably lost, for much the same reason. You might want to know that most of the photos we have of President Lincoln were also nearly lost forever. In his great 1992 book Lincoln—An Illustrated Biography by Philip Kunhardt, you'll learn how a chance visit to an auction in New York in 1902 led to the discovery of thousands of glass-plate photographic negatives scheduled for destruction. The buyer, Frederick Meserve, bought the lot for a mere pittance. Among the plates were dozens of discarded photos of Lincoln, which today—besides their enormous historical value—are worth many millions of dollars. Update: Speaking of photons, I can't help but reflect on their ultimate fundamental importance in physics. Massless, they move at the speed of light, and so travel on what is known as a null geodesic, meaning that their associated line element vanishes: $$ds^2 = g_{\mu\nu} dx^\mu dx^\nu = 0 \tag{1}$$ Consequently, a photon is aware of neither time nor space, and in effect it exists everywhere, at same time and for all eternity. When you turn on a light, photons are created, and travel from the light source to your eye (or camera or detector), where they are annihilated on your cornea or the detector. But because of (1) the photon in a sense always exists, so its creation and death are nothing more than Einstein's twin paradox taken to the extreme. When a photon lands on an object and is absorbed, its energy is also absorbed and converted into a different form. All experimental observations involve photons or their equivalent electromagnetic phenomena, so their effects persist in our memories and in the objects they touch. That is one reason why I am so fascinated with old photographs and films, because the photons that made them are still apparent. The expression "God is light" therefore takes on a deeper and more profound meaning. Again Jesus spoke to them, saying, "I am the light of the world. Whoever follows Me will not walk in darkness, but will have the light of life." — John 8:12

 The Student Loan Debt Debacle — Posted Saturday June 18 2022 My late wife graduated with a B.S. in Chemical Engineering from the University of Cairo, then came to America to get her M.S. with honors in the same subject. Meanwhile, I received four degrees (a B.S., two M.S. and a PhD) here in Southern California. We both paid for all of our education, never having to take out any student loans. Many in our generation did the same. So it is fair that the federal government is talking today about forgiving student loan debt? My wife didn't think so, believing that if you take on any debt you are legally and morally required to pay it back. I didn't agree with her for two reasons. One, the cost of higher education is now exorbitant, often far exceeding the return on investment (my alma mater, the University of Southern California, now charges over $60,000 a year for tuition, while many state colleges are similarly unaffordable); and two, many of the so-called universities and institutions of higher learning today give out degrees that aren't worth the paper they're printed on. It's no wonder than many graduates are unemployed (or underemployed) and stuck with student loan debt exceeding their ability to pay. President Biden has said he's in favor of forgiving some student loan debt, starting at$10,000 and maybe going higher. I agree with this, but to me it depends on whether the degree has actually paid off in the form of a good job and better prospects. However, Fox News and its conservative viewers strongly disagree: Higher education is a fervent ally of progressive elements within the Democratic Party, providing sizable financial support, ideas, and personnel. So, it's a way for the administration to buy votes while paying off its loyal supporters in the academic and activist communities. Note that conservatives view "higher education" (which I consider anything past high school) as something negative, as they view higher learning as liberal, socialistic and anti-God, and something that only a "progressive" would pursue. A number of Republican lawmakers have even suggested that non-faith-based universities in the United States should be closed. However, they complained loudly when Trump University was shut down and fined for fraud and misrepresentation. I've always believed that higher education teaches us to think for ourselves, regardless of the subject matter. Some conservatives, however, seem to believe that people should not think for themselves, but that others should do their thinking for them.

 It's Getting Hotter and Drier — Posted Saturday June 18 2022 CNN climatologist Bill Weir has written this new article describing the now unprecented (at least in our lifetimes) drought in the American Southwest and the effects of our water usage on the Colorado River. Whatever your views on climate change may be, you have to agree that we've overextended our reliance on cheap, plentiful water, much as we've likely relied on cheap, plentiful gasoline. The abundance of Earth's resources isn't infinite, and the presence of 7.8 billion humans has made an all-too-obvious impact on the availability of those resources. To me, it's all about short-term thinking, and not considering or planning for succeeding generations of humans, not to mention the needs of other life forms. Yes, I have central air conditioning, but I don't use the air conditioner more than one hour a day, take 5-minute showers, and have replaced my lawns with artificial grass. But is that enough? I'm seriously thinking about leaving Southern California, my home of 73 years, perhaps as one of its first environmental refugees seeking a more livable spot in which to relocate. What are your thoughts? And don't me that "God will just make more."

 The Friedmann Equations Again — Posted Thursday June 16 2022 In his latest article, astrophysicist Ethan Siegel writes again about what appears to be one of his favorite topics, the Friedmann equations of general-relativistic cosmology. Although I took a single graduate course in astrophysics many years ago, I didn't fully appreciate Friedmann's work (which is now 100 years old). But Siegel's posts got me interested sometime in 2017, and I can now see why he's so enamored with the formalism. Although they're very easy to derive from Einstein's field equations, the Friedmann equations are nothing less than an accurate model of what constitutes the universe and its ultimate fate. That model today is called the Friedmann-Lemaître-Robertson-Walker spacetime, which is the basis of modern cosmology. The first of Friedmann's equations is $$H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\, \rho - \frac{k c^2}{a^2} + \frac{\Lambda c^2}{3}$$ Here, $$H$$ is the Hubble parameter, which expresses the rate of expansion of the universe, $$a(t)$$ is the expansion scale factor (with $$\dot{a} = da/dt$$), $$G$$ is Newton's gravitational constant, $$c$$ is the speed of light, $$\rho$$ is the density of matter and radiation in the universe, $$k$$ is the curvature of the universe (most probably exactly zero), and $$\Lambda$$ is the cosmological constant, which is very small. The Hubble parameter is often referred to as the Hubble constant, but it's not a constant at all, as it changes with time. It's often expressed as $$H_0$$, which is the Hubble parameter as measured right now. It's very close to 70 kilometers per second per megaparsec, although there is substantial observational disagreement with that figure, it being somewhere between 67 and 73. Friedmann's second equation is perhaps more interesting. It is $$\frac{\ddot{a}}{a} = - \frac{4 \pi G}{3}\, \left( \rho + \frac{3 p}{c^2} \right) + \frac{\Lambda c^2}{3}$$ where $$p$$ is pressure. The left-hand side is the relative acceleration of the expansion rate, which (with small $$\Lambda$$) is negative, expressing the slowing of the expansion due to the inward gravitational effects of density and pressure. But given sufficient time, the universe's density and pressure will thin out, tending to zero, thus reducing the inward acceleration and allowing the cosmological constant $$\Lambda$$ to take over. The universe will then expand without bound, resulting in a rather bleak future of eventual nothingness. Observations of distant galaxies confirm this prediction. I'm trying to think back some 45 years to why I wasn't more impressed with the Friedmann equations and their predictions for the fate of the universe. I believe it had something to do with Friedmann's assumption of a universal time coordinate for the universe, in which clocks would tick away everywhere at the same rate. This violates Einsteinian relativity, which states that time is not absolute. In their 1975 book Introduction to General Relativity (still my favorite text of all time), authors Adler, Bazin and Schiffer write There exists a global time-coordinate which serves as the $$x^0$$ of a Gaussian coordinate system $$\ldots$$ [so that] the use of a distinguished time-coordinate marks the abandonment of a completely covariant treatment of the cosmological problem. This is the price one has to pay to simplify the cosmological models and to describe physical reality in convenient mathematical terms. This caveat is somewhat mollified by Friedmann's assumption of a universal co-moving coordinate system, which observations indicate is completely valid. The authors' warning now seems moot, but when I first read the book it had enormous influence on my attitude toward the Friedmann equations. Oh well, live and learn. Update: Ronald J. Adler, one of the coauthors of Introduction to General Relativity, has a new book out: General Relativity and Cosmology: A First Encounter. I don't have the book yet, but in addition to introductory material on general relativity it appears to emphasize gravitational waves, most likely in response to the burgeoning new field of gravitational astronomy. I find it remarkable and admirable that Adler, whose previous book first came out in 1965, is still writing and researching. God bless him. Update 2: I've now read the book. Sorry to say, but it seems like a dumbed-down version of Adler-Bazin-Schiffer's 1975 2nd edition book, although the material on gravitational waves is much clearer. Also, Adler now uses the more familiar comma/semicolon notation for partial derivatives/covariant derivatives in lieu of the subscript bar/double-bar notation, which I grew up on.

 Rall's Pessimistic, But With An Optimistic Bent, Sorta — Posted Thursday June 16 2022 Lately I've been trying hard to remain optimistic about things, despite what's going on in my country and the rest of the world. Meanwhile, political cartoonist, writer and author Ted Rall is not optimistic, but I couldn't pass up reproducing his latest comic:

 The Ultimate Nostalgia — Posted Saturday June 11 2022 I remember, with photographic clarity, being bathed by my mother in our kitchen sink when I was between the age of one and two. I know this is true, because she told me about it. It had to do with using as little water as possible at the time, due to a chronically overflowing septic tank in our back yard in Duarte, California. But I can barely remember what I did last week, and most neuroscientists will tell you that short term memory and long term memory are very different things, depending on one's age, and that long term memory can be unreliable without a backup device of some sort, like one's mother. The loss of very early memories is called infantile amnesia, and while even infants are capable of retaining short term memories, scientists tell us that these memories don't have the requisite language skills needed to embed the memories permanently in our brains. That, plus the fact that those memories are not necessary for future developmental growth—why should our brains retain memories that are not needed for survival or future use? I can remember many detailed instances of my maternal grandmother visiting us from Missouri in the summer of 1952, when I was three years old. Before that, not much, and after that, quite a bit. From the age of four on, I can see my life as almost a continuous tableau of memories. But what did I do last month or even last week? It's hazy, probably because at my age (73) things just aren't very different from day to day now. In physics we have the concept of a worldline, which traces the lifeline of any person or object through 4-dimensional spacetime, and the worldlines of people regularly overlap. For example, it's entirely possible that the person you married passed by you unnoticed at an early age while you were out grocery shopping with your parents. Are these overlaps of any cosmic importance, or are they just coincidences? Once is coincidence, and twice is happenstance, but three times is enemy action. — Auric Goldfinger Similarly, in physics we have the principle of quantum unitarity, which guarantees the permanence of information. If true, it means that a record of every worldline is preserved in some way, for every person and object, be it you or an elementary particle or field. It's truly hard to fathom. I wish I could recall the sights, sounds and conversations that I must have experienced since the day of my birth. Are our earliest experiences still retained in some form in our brains? And do they have any relevance to our lives today?

 Leonard Susskind at Berkeley — Posted Saturday June 4 2022 I have most of Stanford physicist Leonard Susskind's many online lectures in mp4 video format, in which he discusses (with much advanced math and detail) topics such as classical physics, relativity, string theory, cosmology, particle physics and statistical mechanics, but he is arguably most famous for his work on black holes and the holographic principle, which you can read up on in the link. Here he is again talking at the 2022 Oppenheimer Lecture at the University of Berkeley, where—with much non-mathematical hand waving involving several Peanuts characters—he outlines his belief that gravity and quantum mechanics are not so different, just "opposite sides of the same coin." Susskind's primary argument goes like this: Take a collection of elementary particles (say, electrons), entangle them in pairs with other identical particles (a straightforward thing to do), then transport one set of entangled particles to a distant location (say, Alpha Centauri). If you have a large enough collection of each set of particles, they will each coalesce into black holes via gravitational attraction. But the particles are still entangled (and so are the black holes), and this provides an avenue for all kinds of weird stuff, like wormholes (Einstein-Rosen bridges) and quantum teleportation. It sure is fascinating, but how in hell do you transport one particle collection to a distant star system? (Well, I suppose you don't have to, just move one collection to a different room in your house). But what Susskind seems to be saying is that far-removed entanglement supports the idea that our observable universe is composed of 3-dimensional objects and fields that are entangled with a distant 2-dimensional holographic sphere surrounding the entire universe, and that this sphere links quantum phusics with gravity in an intimate way. Sorry, but I find this all too much to believe, as it can never be tested. But the extreme energies need to test today's quantum gravity theories (like string theory) can't be tested, so I guess it can't be disproved, either. Here's the UC Berkeley video, which at least provides a neat overview of J. R. Oppenheimer, the great American physicist who directed the Manhattan Project and America's development of the atom bomb, but who subsequently ran afoul of America's experiment with McCarthyism:

 Why I Won't See the Latest Top Gun Movie — Posted Saturday June 4 2022 Tom Cruise in the 1983 sex comedy Risky Business. Stupid and filthy as hell, but Americans ate it up. As a general rule, I don't like actor Tom Cruise. His movies are mostly written to feature his boy-toy reputation and limited acting talents, and they're either implausible or just poor films. 2003's The Last Samurai was okay, as was 2005's The War of the Worlds, but I saw them only because I'm a huge Japanese film and science fiction fan. I went to see Cruise's original Top Gun film back in 1986 and felt it was just too over the top, so to speak. It was about a brash, young, hot-shot American fighter pilot whose piloting skills soared above all of his rivals, but there was one glaring plot problem that I spotted early on in the film: it was okay to be a handsome, talented, number-one hot-shot fighter pilot, but our hero simply didn't have a real-life enemy to pertect 'Merica against. The film's writers knew this, so they concocted a silly scenario where our hero could carry out his heroics against MIGs from a supposedly real, unknown foreign enemy. After Cruise shoots 'em all down and wins the day, the United States has to cover up the incident, so's no real foreign enemy will start a real war. I saw Cruise's character in Top Gun as similar to today's gun fetishists. Sure, plinkin', target shootin' and huntin' are okay, but there comes a time when a real he-man wants to shoot something more challenging, like a human being, but he's got to have a good reason to do it, like pertectin' his family. Sadly for today's gun fanatics, those opportunities just don't come along very often, if at all. Instead, we have killing of a different kind—gun nuts slaughtering children. The 1986 film was a huge moneymaker, although film critics hated it. But it spurred a renewed interest among young men and women to join the U.S. Air Force, and it gave an enormous shot in the arm to America's armed forces. Cruise's latest film, Top Gun: Maverick, is projected to hit a billion dollars or more in revenue, and it will likely also benefit the Air Force again, which provided the film with financial and technical support. And as the Salon article notes, the film is basically a two-hour, eleven-minute Cialis ad for conservative men who are past their, um, prime. Lastly but certainly not least, I put the 60-year-old Cruise's belief in Scientology on an even lower stupidity ranking than I do Mormonism. Sorry, but volcano gods and pseudo-evangelical moneygrubbing just don't make it for me.

 Hossenfelder on the Principle of Least Action — Posted Saturday May 21 2022 German physicist Sabine Hossenfelder finally gets around to my favorite subject in her latest video, which addresses the principle of least action (more appropriately called the stationary action or extremalization principle). Hossenfelder opens her talk by referring to the long sought-after theory of everything of physics, noting that in a sense we already have it with the principle of least action. Sure, quantum physics doesn't play well with gravitation, and so we don't have a workable theory of quantum gravity, but when we do it will certainly be describable by the action principle. I've been in love with the principle for five decades, as I see it as nothing less than the key to the universe, even as a proof of the existence of a wise and benevolent God—wise, because it shows incredible intelligence; and benevolent, because it's insanely beautiful. The principle is actually a method for optimizing events and processes in physics (it surely applies to biological systems as well, but to my knowledge no one has been able to apply the principle due to the sheer complexity of living organisms). Unlike trial and error, where one tries different approaches to a given problem to find the best one, the action principle gives the optimal solution automatically in one go. It's similar to the high-school calculus problem of finding the maximum or minimum of a function of a single variable, which involves taking the derivative of the function with respect to the variable and setting it to zero. Setting the second dervative to zero tells you whether the optimal solution is a maximum or a minimum (although strictly monotonic functions have no maxima or minima). The action principle is the same, except one takes the derivative of a certain integral with fixed end points over time, which usually involves the difference of the kinetic energy $$T$$ and the potential energy $$V$$, as in $$S = \int \left( T - V \right) \, dt$$ In quantum and gravitational physics, the action ususally involves all four dimensions (including time), as in $$S = \int \! \! \! \! \int \! \! \! \! \int \! \! \! \! \int \left[ \, T(x,y,z,t) - V(x,y,z,t) \, \right] \, dx \, dy \, dz \, dt$$ (Many famous problems in modern physics have been solved by guessing what the appropriate terms for the kinetic and potential energies are, as they're not always simple or obvious.) Taking the derivative of an integral is straightforward, and with least action it almost always involves the mathematical technique called integration by parts. The derivative operator itself is neither a total or partial derivative, but a kind of "what if" operator from the calculus of variations called "del" or $$\delta$$. The principle of least action is then succinctly and simply expressed as $$\delta S = 0$$ One aspect of the principle that Hossefelder raises has always puzzled me: no matter how complicated the problem, Nature seems to somehow "know" the principle, how to apply it instantaneously, and what the future outcome must be. The answer has to do with Caltech physicist Richard Feynman's path integral, which he originally formulated for quantum mechanics but can be applied to any given physics problem. It expresses the action principle as an infinite-dimensional integral of paths, and essentially states that a physical particle or quantum field going from A to B takes every possible path, each path being equivalent, with the right path depending on what the observer sees. This seems insane, but it works brilliantly, even though it appears to imply that the path integral somehow already knows what the future is. This does not destroy the notion of free will, but implies an almost metaphysical connection between the observer, what she is looking for, and the Universe. Hossenfelder's video is about 13 minutes, and well worth watching:

 An Interesting New Paper on Modified Gravity — Posted Tuesday May 17 2022 Primitive modified gravity (MG) theories have been around since Einstein announced his general theory of relativity in late 1915, but it wasn't until the problem of dark matter (DM) arose (originally in the 1930s but more formally in the 1980s) that MG began to be taken seriously as an alternative to DM. The problem involves excessive velocities of stars orbiting far from the centers of their host galaxies, which neither Newtonian or Einsteinian gravity theories can explain. Haloes of DM are assumed to be the reason, as the presence of unseen matter in galaxies neatly provides the additional gravitational attraction needed to explain these velocities. However, physicists have been at a loss to understand what DM might actually consist of, as all known and postulated forms of matter (including cold neutrinos, axions and massive photons) haven't been discovered. To date, billions of dollars have been spent on experiments designed to detect DM particles, all to no avail. It's entirely possible that DM simply doesn't exist, and that possibility has raised concerns about the nature of gravity itself. After all, Newtonian gravity is just an approximation of Einsteinian gravity, and it's likely that Einstein's theory is itself just an approximation of some deeper truth. In 1981, the Israeli physicist Mordehai Milgrom developed a non-relativisitic version of Newtonian gravity that seemed to provide the needed alternative to DM. His theory involved modifying the classical Newtonian gravitational potential and associated force law $$\Phi(r) = - \frac{GMm}{r}, \qquad F = - \nabla \Phi = - \frac{GMm}{r^2}$$ to include a small constant that provides an additional attractive force at great distances (you can read the details in the link). Admittedly, Milgrom's theory, called modified Newtonian gravity (or MOND), was an ad hoc fix, but it explained the stellar velocity problem. However, it didn't resolve other problems that DM seemed to explain (gravitational lensing, etc.), and the fact that it was non-relativistic limited its acceptance. Here's my take on all this. When one moves from Newtonian to Einsteinian gravity for a point mass source (the Schwarzschild metric for a stationary black hole and the Kerr metric for a rotating black hole), there appear additional terms to the classical potential $$\Phi(r)$$. These effective potentials don't explain DM, but they open up the possibility that a modification of Einsteinian gravity (which today is considered a classical theory) might be a workable solution to all DM-related issues. I don't know what that modification might be, but I suspect that quadratic ($$R^2$$) gravity or $$f(R)$$ gravity is a step in the right direction. Meanwhile, here is a short, readable, award-winning new paper on modified gravity that any undergranduate science student can understand. I think it's brilliant. Like Milgrom's theory, it's ad hoc and mon-relativistic, but its sheer simplicity is attractive as well as suggestive. The paper's authors add a simple term proportional to $$\log(r)$$ to the classical potential $$\Phi$$, achieving what to me is an even better theory than Milgrom's. They also propose that the universal potential quantum field $$\Psi$$ attributed to David Bohm is associated with the log term. Fascinating stuff!

 Our Anti-Science Rightwing Supreme Court — Posted Tuesday May 17 2022 Disclaimer: As a Christian I do not approve of abortion purely as a method of birth control, for getting rid of an unwanted child or as a quick fix for a drunken one-night stand. But when medical science shows that the fetus is severely deformed or otherwise unviable, or if the birth represents a substantial threat to the life of the mother, then I leave it up to the woman and her God or conscience to decide what is appropriate. In those cases, abortion should be legal, medically safe, affordable and available. This month's Scientific American has an article by Northwestern University's Wendy Parmet arguing that the rightwing-dominated Supreme Court has abandoned not only health care but science in its efforts to overturn Roe v. Wade and to allow states to establish their own laws regarding abortion. To date, some 26 states have already indicated that they will immediately ban all or most forms of abortion should the impending and anticipated overturn of Roe v. Wade proceed. A few of those states have indicated they will ban abortion after only five weeks following impregnation, a period of time during which most women don't even know they're pregnant. In view of that, how would state legal authorities even determine the woman was pregnant in the first place? Furthermore, as many pregnancies end in natural miscarriage, such abortion laws would deem the woman automatically guilty of either murder or manslaughter. The article follows up on the Court's previous decisions regarding COVID-19 vaccination, which effectively blocked efforts by the states to save lives via mandated vaccinations. When it comes down to it, abortion involves the medically and scientifically unsubstantiated belief that a fertilized ovum or unborn fetus has been ensouled, that is, if a god-like entity has endowed a single cell, mass of tissue or functioning or non-functioning unborn offspring with a soul. Such a belief is purely a religious one, and has nothing to do with secular legal matters, which the Supreme Court supposedly is empowered to adjudicate. As Dr. Parmet notes, America is headed toward some terribly dark places with this Supreme Court.

 The Hubble Tension Again — Posted Monday May 16 2022 Just because you measure something with extreme precision doesn't necessarily mean it represents the truth. I'm sure readers of this site are familiar with the so-called Hubble tension, the annoying discrepancy that exists between two high-precision measurements of the cosmological Hubble parameter, which is a measure of the rate of expansion of the universe. One measurement says it's about 67 kilometers per second per megaparsec, while the other claims it's about 9% higher, at 73 km/sec/mpc. The measurement techniques are vastly different, but each is seemingly scientifically irrefutable. This has given rise to the possibility that there is nothing wrong with either technique, but that they each are being skewed by new physics that scientists are unaware of. Dr. Wendy Freedman of the University of Chicago is a noted astrophysicist who has long studied the Hubble parameter (often referred to as the Hubble constant, but it's not a constant at all). In this new article she argues that perhaps there's no tension all all, and that the disagreement might be the result of imperfections in the techniques themselves—systematic error, if you will. Freedman is using a third technique she has developed called the "tip of the red giant branch stars," which promises to provide more accurate results. Her research to date indicates that the Hubble parameter is about 69.8 km/sec/mpc, which conveniently splits the difference between the other two approaches. Since red giant stars are, well, red, then her method should be testable using the recently launched infrared-focused James Webb Space Telescope, scheduled to go into full operation next month. Time will tell. By comparison, the most recent "tension" in physics has to do with the mass of the $$W^{-}$$ boson, which governs certain types of radioactive decays. The Standard Model of Physics calculates the mass to be 80.379 GeV/c^2, while the best observed mass is 80.433 GeV/c2. The calculated mass is based on horrendously difficult quantum field mathematics, and I can't help feeling that someone simply dropped a decimal someplace, as the difference doesn't seem to be a "tension" at all. Again, time will tell.

 Louie Louie—I Wanna Go Now — Posted Monday May 16 2022 More nostalgia. This is Louis at his high school dance, but it was also me as a freshman in February 1964 (thank you, Ruben Bolling): My one and only date in high school occurred at Duarte High School in California on Friday night, February 14 1964. It was very cold and extremely windy, and I was with Linda A. along with Peggy F. (now deceased) and her date. It was a "Sadie Hawkins" dance, where the girls invite the boys. I remember being Linda's third invitation choice, my selection being no doubt reflective of the extreme desperation she must have been experiencing at the time. I didn't know why the hell I was there, and I didn't know how to dance, either. I remember we had a mediocre band that played the Kingsmen's hit song Louie Louie (whose lyrics I still can't decipher) and other tunes, and the only other thing I recall is that I just wanted the evening to end. End it did, as did my entire four-year high school experience, which I loathed.

 The Amazing Friden Electro-Mechanical Calculating Wonder of the Age! — Monday May 16 2022 I'm just waxing nostalgic today. This is a Friden electro-mechanical calculator, circa 1965, which my wife and I used in our lab on a regular basis from 1972 to 1973 to do routine calculations. We needed only 6-digit accuracy, but I believe the one we had sported either 11-digit or 14-digit output capability. I remember trying out a long-division test on the thing to its maximum number of digits one day, and the thing cranked and cranked for many minutes before spitting out the answer. It weighed about 50 pounds, and had its own station in the lab. In late 1973 our lab director bought us a fully electronic, four-function calculator which drastically sped up our work, and it weighed maybe a pound. It was blue with red LED readout, and I remember it cost 500, but I don't remember the name or model of the unit. Meanwhile, the Friden calculator went out into the garbage. I still regret not fishing it out of the trash barrel and keeping it. I also used a Friden calculator as a chemistry undergraduate in 1970. We were learning quantum chemistry, and the professor insisted on its use because our slide rules just weren't accurate enough. I wonder what happened to that machine as well. The grandfather of the electro-mechanical calculator is the Difference Engine, developed by the brilliant British inventor Charles Babbage in the 1820s. It failed to impress his goverment backers, but later models proved that mechanical calculating engines worked, although they were prohibitively costly. They're only found in museums today. I captured the above photo from eBay, which has several Fridens available for purchase, either working or for parts only. They're all several hundreds of dollars, so I'm not tempted to get one.  Thoughts and Prayers, Yes, But ... — Posted Sunday May 15 2022 I'm not optimistic, but I pray to God that the mass shootings in Buffalo, New York and today's at Laguna Woods in California will spur America's leaders to actually do something about gun violence besides shrugging their shoulders. Republicans are already saying that "this is the price we pay for freedom" and all that rot but, until effective legislation is enacted that curbs access of weapons of mass murder to hate-filled bigots, this will just go on and on. Meanwhile, the civilized world thinks America is just plain insane. And yes, Fox News and Tucker Carlson are to blame.  But Does It Actually Work? — Posted Sunday May 15 2022 I have a much-loved in-law who is undergoing multiple transcranial magnetic stimulation (TMS) treatments for long-term depression. I've long opposed any kind of medical treatment involving magnetics (except when associated with MRI, which is completely different), and my doubts are somewhat supported by the Mayo Clinic and WebMD, which are both reputable but nevertheless rather noncommittal regarding the efficacy of TMS. When treated, clinical depression is most always enjoined with antidepressant medications and/or one-on-one or group therapy. On rare occasions, depression is treated by electroconvulsive (shock) therapy, which is sometimes effective (but not always). As a last resort, there is prefrontal cortex surgery (lobotomy), in which the patient either improves, stays the same, gets worse, or is reduced to a vegetative state. Wow, what a choice. I used to work in the water quality field, and I was occasionally confronted by representatives of companies selling water treatment systems based on magnet "therapy." Such treatment is based on the belief that magnets can remove impurities or pre-treat water supplies, making subsequent conventional treatment systems more effective. It's all hogwash, as is the use of magnetic bracelets to treat cancer and other diseases, but the seemingly eternal gullibility of the lay public will always provide a source of profit for hucksters and snake-oil salespeople. (Hey, it's only 20 bucks, so what have you got to lose?!) Along the same lines, we have the supposed benefits of drinking water that is completely devoid of all dissolved solids, such as the system sold by Zero Water, whose product removes more than 99.6% of everything in tap water. This is equivalent to drinking distilled or deionized water, which not only has a flat taste but is actually injurious to your body, which requires a certain amount of dissolved minerals (especially calcium and magnesium). Drinking the equivalent of store-bought distilled water (which is actually much cheaper than the Zero Water product) also has an acidic or leaching effect, as it pulls essential minerals out of your body, which are then lost in your urine. But the company claims that the water actually tastes good, leading me to believe that it replaces a portion of the minerals it takes out to avoid the flat or bitter taste. I've tasted both deionized water and distilled water (I've used it for years to rinse my car after washing to avoid water spots), and believe me the taste is truly awful. But despite the somewhat ambiguous commentary from the Mayo Clinic and WebMD regarding the effectiveness of TMS, I pray that my in-law will recover fully. I only hope it's not just another placebo (see my April 25 post on Prevagen.  On Prices and Dates — Posted Thursday May 12 2022 Oh, I'm sorry, you'll have to forgive our salesman Mr. Verity, as he tends to multiply everything by a factor of ten. So when he says the price of the bed is £800, he means in fact it's £8. Other than that, he's perfectly alright. — Another Monty Python Salesman, who tends to divide everything by ten. While watching last night's NOVA's Dinosaur Apocalypse episode I mentioned in my previous post, I reflected on the dating of things. Based on geological evidence and radiometric dating techniques, the last days of the dinosaurs occurred 66 million years ago, give or take a few tens of thousands of years. However, Republican conservatives in America have a much different take on things, largely based on the 17th century Irish bishop and church leader James Ussher, whose interpretation of Old Testament readings led him to surmise that the age of the Earth is only about 6,000 years old, and that the Creation event occurred precisely at 6 pm on 22 October 4004 BC (he must have meant Greenwich Mean Time). According to Ussher's dating, dinosaurs could not have been more than 6,000 years old, which is the belief of Ken Ham, the founder and curator of Kentucky's Ark Encounter, which includes a full-size replica of Noah's ark. (It's made of modern materials, as the never-existent gopher wood lumber described in the Book of Genesis is rather hard to come by nowadays.) Fans (like me) of the Monty Python show may liken Ham's dating tendencies to that of the salesmen in the Buying a Bed sketch, in which a newlywed couple is trying to buy a bed. The insane salesmen are always off by a factor of ten, which nevertheless is far better than Ham's thinking, which is off by a factor of ten thousand. Dog kennels? Yes, pets department, second floor.  Interesting Thursday — Posted Thursday May 12 2022 Readers of this site surely knew that I'd post this photo of the newly revealed black hole at the center of our galaxy. Taken by the Event Horizon Telescope, consisting of multiple radio telescopes stretching across the Earth and acting as a single enormous telescope, the photo is nevertheless a triumph of technological and observational genius. Also in the news today: the United States surpassed one million deaths attributed to COVID-19, only a little more than two years after the virus was confirmed as a worldwide pandemic. This far surpasses the estimated 675 deaths attributed to the 1918 influenza pandemic, according to the Centers for Disease Control and Prevention. Naturally, most Republicans dispute the COVID deaths, believing them instead to be caused by the flu, bad colds and other diseases, mainly because their new Lord and Savior Donald Trump initially considered COVID to be a "Democrat hoax." His foot-dragging in 2020 caused many hundreds of thousands of needless deaths, even though he and his family were later vaccinated against COVID. He also insanely praised the supposed benefits of hydrochloroquine, UV light and chlorine bleach injections as effective alternatives to vaccination. Lastly, I hope you caught last night's NOVA presentation of Dinosaur Apocalypse, which featured several amazing recent discoveries associated with the extinction of the dinosaurs, one even possibly occurring right after the asteroid hit some 66 million years ago. The NOVA airing nicely accompanies author Riley Black's recent book Last Days of the Dinosaurs, which I read yesterday with interest. An interesting news day, but please also pray for the people of Ukraine, who continue to fight the insane war of Trump's alter ego, Vladimir Putin.  The Non-Static Universe — Posted Monday May 9 2022 Of course, not everything Russian today is bad. Writing on the 100th anniversary of Russian cosmologist Alexander Friedmann's May 1922 discovery that the universe is expanding, physicist Vladimir Soloviev (wow, yet another "Vladimir") describes How Friedmann Shod Einstein, which details how Einstein's cosmological constant $$\Lambda$$ could not preserve a static, eternally fixed universe as Einstein had then believed in. Much like a marble balanced on the head of a pin, Einstein's static universe was unstable, and had to be either expanding or contracting. There's some nice photographs in Soloviev's article of Friedmann (who tragically died at the age of 37 from a typhoid-laced piece of fruit), along with other Russian cosmologists. Although the great Russian physicist Lev Landau survived Stalin's Great Purge, sadly the brilliant Matvei Bronstein did not, who was executed in 1938 at the age of 31 for his political views. What a friggin' waste. Remember that the next time you think of voting for a Republican, whose views most likely align with those of the warmongering, Stalinist Putin and the Putin-adoring Donald Trump.  Still Around — Posted Monday May 9 2022 In 1977 I gave my wife a Texas Instruments TI-58 programmable calculator, which as a fellow engineer and geek impressed her enormously. I already had a TI-59, which utilized rewritable memory-storage cards. At the now advanced age of 45 years, the darned thing still works perfectly, thanks to a new battery pack. I still have dozens of the original memory cards, mostly devoted to hydraulic calculations that I used at work. Sadly, I've been unable to locate my wife's TI-58, which she used at her work for many years. I can only suppose it stopped working at some point, and she disposed of it. For posterity, I bought another from eBay (it's truly amazing that this ancient stuff is still available). However, I still have her Faber-Castell slide rule, which she used as a chemical engineering student at the University of Cairo in Egypt from 1963 to 1968. God bless her spirit always.  So Many, Many Lies — Posted Monday May 9 2022 I watched CNN yesterday, in which host Jake Tapper interviewed Governor Tate Reeves (R-Mississippi) regarding his state's stand on abortion. Although an abortion opponent, Reeves noted that his state is not "currently focused" on contraception as an alternative to abortion. Given the disgusting about-face of former President Donald Trump's three Supreme Court appointees on abortion ("Roe v. Wade is 'settled law' "), which ensured their appointments), Reeves' comments are hardly trustworthy. (I apologize for suggesting this, but I wish Tapper had asked Reeves what he'd do if Reeves' wife were raped and impregnated by a Black man.) It's interesting to note that Mississippi has the highest rate of infant mortality and birth-related maternal deaths in the country, not to mention the highest level of poverty among minority women and children. Republicans in Mississippi claim to be "compassionate and caring" about minority women and children, but for some reason they refuse to provide decent services for their support and care. Meanwhile, Russian President Vladimir Putin is falsely blaming the Ukrainian War on Ukrainian "neo-Nazis," as he celebrates a massive Russian May 9 anniversary commemorating Russia's defeat of Germany in World War II. As a result, tens of thousands of Ukrainian civilians have been killed in the war, which shows no signs of ending soon. Dear God in Heaven, the lies just keep coming, and voters keep fallng for them. There's something truly pathological about ignorant and arrogant Republican conservatives in America who continue to believe in Trump's countless lies, despite overwhelming evidence that they're all completely false. Trump's lies are already too numerous to count, but his lies concerning climate change, COVID-19 (a Democrat "hoax"), vaccination and the great "genius" of Putin are arguably the worst. Today, tens of millions of Republicans openly worship Trump as their new Lord and Savior and secretely worship Putin (because Trump is still besotted with him). The New Testament is rife with warnings about the Last Days and about truth and deception (read Mark 7:21-23). At best, today's American white Christian evangelicals are simply deists who believe in a vengeful, hateful and destructive god while falsely claiming to be followers of Jesus Christ. God forgive them, and may God have mercy on us all.  Bringing Them Back — Posted Monday May 9 2022 Here's an interesting article from Quanta Magazine that talks about resurrecting certain species of extinct animals. I'm sure that you're aware of frozen mammoth carcasses from Siberia whose DNA is at least theoretically recoverable, but in all cases to date the genetic material has been too fragmented to allow full recovery. Instead, "de-extinction" hopes have relied on hybridization techniques, which would combine recovered DNA with that of living species (like creating a mammoth-elephant hybrid). As for bringing back a dinosaur from DNA held in mosquitoes from fossilized amber, you can forget about it. The article touches on a few ethical issues, such as how and where would resurrected animals be maintained (in zoos or private collections), but outside of the profit motive it might be possible to introduce them back into the environment, where they might be able to reestablish vanishing ecosystems. But with today's human population at nearly eight billion souls and climbing, future space and food restrictions would probably eliminate that possibility. The article goes on to note that preserved DNA has a half-life of only about 500 years before fragmentation becomes a real problem. That might still allow for the recovery of the Tasmanian tiger, the passenger pigeon, the dodo bird or other fairly recent species, but I don't find that very interesting. The article reminded me of a short mystery story I read in college over fifty years ago. I've been unable to find it, but the title was something like "The Ring in the Dust," in which police detectives investigationg a burglary and murder find few clues to go on. Nothing has apparently been stolen, but they do notice a dusty dresser that has an clear, circular ring on top, indicating that something on the dresser had been removed. Could the missing item have been the motive for the crime? The mystery is solved when the police later discover that the missing item is a stuffed and mounted Great Auk, a flightless bird that went extinct in the 19th century, worth many thousands of dollars. If you know of this story or who wrote it, please send me an email.  "The Curse of an Aching Heart" — Posted Friday May 6 2022 One of my favorite Laurel and Hardy short films is Blotto (issued February 1930), in which the boys sneak out to the Rainbow Club for some entertainment and drinking sans their wives. It features not only illegal Prohibition-era consumption of liquor but also some pre-1933 Hayes Code stuff, with a risqué dance sequence that is still rather shocking today (at least to me). The film was initially issued as a three-reeler (about 26 minutes), but from 1929 to 1931 Laurel and Hardy films were also shot separately, usually in longer Spanish, French and German versions, in which the boys spoke their lines phonetically. The Spanish version of Blotto (La Vida Nocturna, or "Night Life") runs over 37 minutes, and by sheer luck it is extant, as shown here: With the possible exception of their 1933 feature film Fra Diavolo ("The Devil's Brother"), Blotto has the best of all the Laurel and Hardy "laughing" routines, the difference being that in Blotto the boys are getting drunk on a mixture of cold tea, Tabasco sauce and pepper, thanks to Laurel's cunning wife (played in English by Anita Garvin and in Spanish by Linda Laredo). A shorter version of the film (in English) can be seen here. One of the best sequences in the English version is the maudlin singer who croons The Curse of an Aching Heart ("I'm now a wreck upon life's seas ..."), which soon has Laurel in tears. Again, one of the best early sound Laurel and Hardy films.  Vindictive and Selfish — Posted Wednesday May 4 2022 "The problem isn't enough food. The world has plenty of food. The problem is poverty, sexism, racism, tradition, disease, lack of sanitation, war, conflict, politics and more ... I want to tell you more, but I have to stop. Sometimes, to be honest, I want to scream." — Sharman Russell, author, writer and teacher Just guessing, but I think it's probable that the current tidal wave of Trumpian, white evangelical Christianity in America is grounded in political, cultural, racial and gender vindictiveness coupled with the notion of zero-sum resource availability and distribution. It's vindictive, because the ever-present thread of racial bias and political tribalism runs through their anti-family planning and anti-abortion thinking; i.e., "Let's make life more miserable for underclass women and minorities, and in doing so we can stick it to the libruls," and it's also resource hogging; i.e., "If we make it impossible for underclass women and minorities to sensibly plan their families and/or have abortions, not only will their lives be more miserable but they'll eventually stop having children and being a drain on our dwindling resources, which rightfully belong to us." Several years ago I did volunteer work at my local food bank in Pasadena, delivering food and supplies to the homebound. I was always flabbergasted at the sheer amount of supplies we hand on hand, including many tons of canned, fresh and refrigerated food, all made available by local supermarkets whose stocks were nearing their shelf life. In spite of our distribution efforts, much of it nevertheless was wasted and had to be thrown out. This new article Aeon not only addresses the causes and problems of hunger and poverty but also the near- and long-term benefits of a world having healthy, loved and adequately fed children. Writer Russell writes about her experiences in Africa's Malawi, but she also addresses similar problems here in America. Yes, it's easy to write a check to Doctors Without Borders or Save the Children, but it's not enough. It requires a sea-change in our thinking about the poor and hungry, especially non-white minorities and foreigners. My biggest fear is that the inadequacy of our charitable giving and caring is secretly based upon "If they're adequately fed, there will only be many more of them later on, and we don't want that." Not to sound sanctimonious, but let's remember the widow's offering. She gave all she had to the poor, which was infinitely more than the wealthy ever did.  Bounds (and Possible Leaps) in Gravity — Posted Wednesday May 4 2022 A colleague and mutual gravity freak once said to me "You know why we like gravity so much, don't you? It's because it's so much easier than quantum field theory." He was right. Feynman once remarked that nobody truly understands quantum mechanics, but it's possible that even God has trouble with quantum field theory. It roughly asserts that everything in the universe is a collection of oscillating quantum fields, which locally get excited with the excitations resembling physical particles. I can sorta understand this, as I can understand virtual particles popping into and out of existence according to the energy-time $$\Delta E \Delta t \ge \hbar/2$$ version of Heisenberg's uncertainty principle, but I do not understand how macroscopic objects like tables and rocks are so permanent. Is my dining room table an excitation of some massive quantum field? Am I? Or how about a single proton, which for all we know is eternal and unchanging? Seventy years ago Feynman developed a graphical method (Feynman diagrams) for calculating the probabilities of properties and events in quantum field theory, including decays and half-lives. One can use these diagrams out of the box to do otherwise messy calculations, and to quote Anthony Zee ( Quantum Field Theory in a Nutshell) "even a child can do it." But that relative simplicity breaks down when one considers loop diagrams, which invariably lead to divergent calculations with infinite probabilities. A relatively proficient undergrad can do calculations for finite (tree) diagrams, but loop diagrams require renormalization and cut-offs, which even graduate students tend to have trouble with (I could never do the calculations). Where was I? Oh yes, gravity. Einsteinian gravity is a classical theory, just like Newtonian mechanics, so one does not normally encounter troublesome divergences. Perhaps this is because gravity does not involve probabilities, as in quantum mechanics. Also, there are no operators in gravity, no kets or bras, or any of the other typical aspects of quantum physics. As a consequence, quantum mechanics and gravity famously don't get along with each other. But they do share one nice characteristic—integral quantities invariably go to zero at the limits (boundaries) of integration, so one can use the mathematical technique of integration by parts (IbP) freely and almost without thinking to simplify the calculations. The undergraduate science major gets introduced to IbP in her first semester of calculus, probably thinking that it's just another useful integration technique, but it's one of the most powerful (and common) techniques in all her future studies. But there's one particular boundary issue in gravity that is getting increasing attention, and that is Gauss-Bonnet gravity. In four dimensions ($$D = 4$$), the integral quantity $$S_{GB} = \int \!\! \sqrt{-g}\, \left( R_{\mu\nu\alpha\beta}\, R^{\mu\nu\alpha\beta} - 4 R_{\mu\nu}\, R^{\mu\nu} + R^2 \right) \, d^4x \tag{1}$$ vanishes at the boundaries of integration (that is, as $$x \rightarrow \infty, t \rightarrow \pm \infty$$ and thus can be omitted from consideration. (Actually, it can easily be shown that $$S_{GB} = \int \!\! \sqrt{-g}\, \left( R_{\mu\nu\alpha\beta}\, R^{\mu\nu\alpha\beta} + A R_{\mu\nu}\, R^{\mu\nu} - \frac{1}{3}\, \left( A + 1 \right) R^2 \right) \, d^4x$$ is equivalent to (1), where $$A$$ is any constant. The traditional Gauss-Bonnet identity invariably assumes $$A = - 4$$ as in (1), but perhaps a simpler and more logical choice would be $$A = 0$$ or $$A = -1$$. $$A = - 2$$ also works, but it doesn't provide anything new.) However, for higher dimensions (1) does not vanish, and this aspect of the identity has given rise to an increasing number of higher-dimensional gravity theories, especially $$D = 5$$. In most cases that I'm familiar with, higher dimensions have provided a possible avenue for the unfolding of quantum gravity theories, none of which (that I am aware of) are very convincing. Recently, efforts have been made to utilize a non-vanishing Gauss-Bonnet identity even for $$D = 4$$, two typical examples being this and this. What's interesting about these efforts is that they provide possible clues to the nature of dark energy and dark matter. Another thing I like is that the Gauss-Bonnet term derives from conformally invariant gravity theory, something I've long been a fan of.  Amazing Dino Discovery — Posted Monday May 2 2022 An almost perfectly preserved dinosaur "mummy" was recently discovered in Canada with its fossilized skin, armor and entrails all intact. This 110-million-year-old nodosaurus (a relative of the heavily armored ankylosaurus) measures 18 feet in length, weighing approximately 3,000 pounds in life. A strict herbivore, it would not have featured very prominently in any of the Jurassic World films. Its primary predator would have been a giant theropod like Allosaurus, although eating one would have been like one of us dining on a porcupine. Kudos to the fossil's curators, who spent 7,000 hours freeing it from its rock matrix.  Quantizing Conformal Gravity — Posted Monday May 2 2022 There's an interesting (and readable) new arXiv paper on the Quantization of Conformal Gravity that starts with the classical conformal Weyl tensor $$C_{\mu\nu\alpha\beta}$$ and then focuses on the role of the square of the Ricci scalar $$R$$, which I've always believed may play an important role in modified gravity. Careful reduction of the terms in the (unique) conformal Weyl action $$S = \int \!\! \sqrt{-g}\, C_{\mu\nu\alpha\beta} \, C^{\mu\nu\alpha\beta} \, d^4x$$ shows that it reduces to $$S = \int \!\! \sqrt{-g}\, \left( R_{\mu\nu\alpha\beta} \, R^{\mu\nu\alpha\beta} - 2 R_{\mu\nu}\, R^{\mu\nu} + \frac{1}{3} \, R^2 \right) \, d^4x$$ The Bianchi identity $$\nabla_\nu \left( R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R \right) = 0$$ is lurking around in all this formalism, and with it we can show that the action reduces to the classical conformal gravitational action $$S = 2 \int \!\! \sqrt{-g}\, \left( R_{\mu\nu}\, R^{\mu\nu} - \frac{1}{3} \, R^2 \right) \, d^4x$$ The four-index Riemann curvature tensor is now gone, which considerably simplifies things. However, while the equations of motion are still complicated, they indicate an intriguing possible explanation of dark matter. I suggested long ago that the simpler action $$S = \int \!\! \sqrt{-g}\, R^2 \, d^4x$$ might serve just as well. This action is also conformally invariant provided the divergence of the vector density $$\sqrt{-g}\, g^{\mu\nu} \partial_\mu R$$ vanishes. Indeed, it was Weyl who noticed that $$\sqrt{-g}\, g^{\mu\nu} \partial_\mu R$$ was proportional to the electromagnetic source density in his 1918 theory. Although that theory failed, it remains to be seen if conformal gravity can be quantized. In the above-linked paper, it appears that it might be. At 51 pages, the paper is long and ponderous, but its mathematical content is relatively scant, as it relies on the work of many of its references regarding quantization. What I found intriguing was the author's focus on the $$R^2$$ term, whose action is only "kind of" conformally invariant, hindering the multi-loop quantization effort. But if it can be made to vanish according to the argument I presented above, perhaps quantization can proceed. Most if not all efforts to quantize gravity to date appear to rely purely on the quantum aspects of the proposed theories, not on gravity. This is apparent from the paper's 102 references, of which I've only read a few. Classical conformal gravity is a bit of a one-trick pony, as it relies solely on the Riemann tensor and scalar. Quantum field theory is considerably richer and more complicated, involving quantum fields that may or may not couple to the gravitational field. At any rate, my understanding of QFT is very dated, and at 73 I've got other things on my mind. Perhaps you'll read the above paper and get more out of it than I have.  Believing and Then Seeing — Posted Sunday May 1 2022 I was pleased today when my church's priest talked about the world's common practice of seeing and then believing in his sermon. He turned the subject around by emphasizing the importance of "believing and then seeing," using elementary particles like photons and electrons as examples of things that are not seen but are believed to exist (indeed, no one has ever directly seen a photon or an electron, and no one ever will). He also mentioned Christ's gentle admonition to His disciple Thomas, who refused to believe in the resurrection unless he saw the piercings in the living Christ's hands, feet and side. It was only when Thomas looked that he believed, exclaiming "My Lord and my God!" (John 20:24-28). All of the elementary particles in the Standard Model of Physics are unseen, yet their existence can be felt or indirectly detected, either through their interactions with each other or inferred through mathematical models. My favorite is the photon (light ray), which can act either as a wave or a particle. It moves on what is called a null geodesic, which means that it is subject to neither time nor space, essentially existing at all times and everywhere in space. This seems like a great mystery, but it's just Einstein's Twin paradox taken to the extreme. Christos anesti, alithos anesti (Christ is risen, truly risen).  Sick: Noodles Topped with Gold Leaf — Posted Sunday May 1 2022 I've always liked actor Stanley Tucci, especially his role in the underappreciated 1998 comedy The Impostors. But I do not like Tucci in his current CNN series Stanley Tucci: Searching for Italy, which is nothing but pretentious food porn. I haven't watched the latest episode (and I won't), but I've seen the preview, which features Tucci eating a noodle dish topped with gold leaf. Gold leaf, you understand, is pure gold, hammered to almost transparent thinness. It has been used for many centuries to decorate and embellish works of art, notably paintings and figurines. Sadly, it has also been used by the megarich to garnish their food. Gold leaf is quite safe to eat, as being an inert metal it passes harmlessly through the digestive tract before being pooped out. I suppose it's recoverable as such, but that would have been a thoroughly detestable job for a slave or other underling. My guess is that the ancient Romans topped their flamingo tongues and stuffed dormice with gold leaf, perhaps then losing it all on their trips to the vomitorium. [It's probably not a good idea to consume gold in large quantities. You may have heard of the 16th-century Spanish governor whose lust for gold was rewarded by his Ecuadorian slaves, who supposedly poured molten gold down his throat. The story is nonsense, since molten gold would instantly incinerate the governor's head before going down his throat, but it's a neat story just the same.] Too bad that Tucci has decided to renew this ancient Roman custom of the rich and stupid. In a world of extreme inequality, not to mention poverty and starvation, it's a pity that he even considered doing it.  Artificial Gravity—There Ain't No Such Thing — Posted Sunday May 1 2022 First, an aside—I met my future wife Munira on this date 50 years ago. May God bless and keep you forever, dearest. Back in 1966 I was a 17-year-old high school senior working part time. Friday nights were rough, as all my friends were at home watching Star Trek, and without the benefit of VCRs I missed all the shows. Later on I was able to catch up on the series, although one thing always bothered me: the crew's dependence on artificial gravity. 1968's 2001: A Space Odyssey got it right—director Stanley Kubrick knew from the start that artificial gravity was impossible, so he relied on magnetic shoes and the ship's transverse rotating ring to provide its equivalent. Future space travelers (assuming there are any) will no doubt utilize the same things to avoid muscle deterioration and bone loss. But artificial gravity has long been used in the movies as an artistic license or contrivance, considering the fact that weightless astronauts are hard to simulate. Star Trek was no different. The seemingly endless spinoffs of the original series continues with a new one, Paramount's Star Trek: Strange New Worlds, beginning May 5. The linked article notes that the show's 1960s originator, Gene Roddenberry, was one of the first to realize the importance of gender/racial inclusivity, and this aspect of the new series will likely continue that vision. However, the original series' depiction of Capt. Kirk's interracial kiss with Lt. Uhura upset a lot of people (my guess, mostly from the American South), and this country's persistent adherence to racial division will likely see a continuance of that bigoted reaction with the new show. But I digress. Artificial gravity is impossible because gravity is not a force that can be "shielded," like the use of cavorite in H.G. Wells' 1901 novel The First Men in the Moon. Indeed, gravity's not even a force—it's the warping of spacetime itself, and there's nothing other than massive gravitating bodies or titanic focused energy sources that's going to affect it. I hope the new show is great, although I'm not optimistic. The original series' mission, "To explore strange new worlds, to seek out new life and new civilizations, and to boldly go where no man has gone before" was noble, but its often overlooked corollary was "non-interference," which the show invariably violated according to the concurrent need for Justice and Truth™. Hopefully, the new show will find the appropriate balance.  What Does Putin Really Want? — Posted Wednesday April 27 2022 There's a new post on Daily Kos that was translated from an article by a noted Russian political scientist (Ekaterina Schulmann). It basically asserts that Russian President Vladimir Putin attacked Ukraine not for expanded political power, territory or vainglory but because he wants to destroy the hopes of future Russians, who are increasingly young, optimistic and progressive. I'm still trying to digest the article, and I don't agree with all of what I've read, but one thing rings true: what one might call the Old Guard, consisting of primarily old white men, super rich oligarchs and those in power, are frightened by what they see as a coming world of selflessness, altruism and faith, the very things that stand in the way of limitless wealth, power and domination. It is not difficult to compare Putin with the likes of Donald Trump, Hitler, Mussolini and Stalin, all of whom aspired to power, glory, fame and wealth through lies and abdication of responsibility to the undeserving unwashed masses they view as pawns and cannon fodder. What strikes me odd is the fact that the people of countries harboring these monsters don't resort to more proactive or even drastic measures to get rid of them. Sure, Putin is an expert in martial arts, but he's only one man, and mortal at that. He also has dozens of lackeys supporting him for reasons of benefit like money, property and power, but they too are mortal. Hundreds of millions against dozens seems like a pretty one-sided fight to me. As a Christian, I cannot advocate targeted assassinations to achieve their removal from power, but I'm only human, and wonder how the world might have been much better off if Hitler had been dropped in his tracks back in 1933. Many of Russia's 140 million people probably support Putin to some extent, but only because they live behind a national media firewall of propaganda and laws limiting free speech and expression. Not so in America, where you can pretty much say whatever you please. The difference then is the fact that millions of Americans, who have unlimited access to what's going on in their country, have opted instead to support rightwing monsters like Trump. If there's any truth in Schulmann's article, it's better reserved for America, whose 74 million Trump voters remain willingly ignorant, arrogant and stupid.  I Kinda Wish Dinosaurs Had Survived — Posted Monday April 25 2022 According to Young-Earth creationists, Adam and Eve rode to work on a pet Brontosaurus. Sadly, this one hadn't attended obedience school and was a tad peckish, devouring a member of the ill-fated Carl Denham Expedition. From 1933's King Kong: Former residents of my old California home town, Duarte, may remember the town's original public library, which was situated on Brycedale Avenue about a block from my home on Bloomdale Street. The library's brick building is still there (although the last time I looked it was a Covenant Christian Church), but the houses on the street (where my best friend Dale G. lived) are long gone (along with the orange grove behind it), having made way for an expansion of the local high school's playing field. My father used to take me to that library often, and at the age of four I distinctly remember checking out a book on dinosaurs. I couldn't read yet, but the pictures made a huge impression on me, and it helped foster my life-long fascination with the creatures. Years later, I learned about the K-T event, the near-instant cataclysm some 66 million years ago that wiped out the dinosaurs and many other living species due to the impact of a large comet or asteroid in the region of what is now the Yucatan Peninsula. The story behind the discovery (by a Nobel laureate physicist) of the K-T impact is itself fascinating, but you can read about it on your own. Dating of the K-T event was made possible by various radiometric techniques along with the ubiquitous presence of a thin, worldwide layer of iridium, a rare heavy metal (actually, the densest of all known elements) that was deposited when the comet/asteroid impacted on the Earth and was spread around over subsequent decades (Young-Earth creationists have long rejected the evidence, although the radiometric and fossil evidence is irrefutable). But again I digress. On May 11, 2022, famed naturalist Sir David Attenborough will present Dinosaur Apocalypse, detailing the last days of the dinosaurs along with an amazing recent paleontological discovery which may date to the very day when the disaster struck. I'm looking forward to it. [As a young child, Einstein was presented with a book on elementary geometry, which changed his life. He long lamented having lost it. Meanwhile, I have been unable to locate my childhood dinosaur book, which I also lament.] Here is a preview of the PBS/NOVA program:  News on the March — FROM THE FUTURE! — Posted Monday April 25 2022 API (25 APRIL 2032) — The House Select Committee to Investigate the January 6th 2021 Patriots' Assembly at the United States Capitol, originally formed on January 27 of that year, announced today that it is nearing a final report on its findings, based on over 2,300 interviews of Democratic Congressional members and individuals having information or knowledge of the event. Last year, following an Executive Order by Dictator-for-Life Donald Trump, the Committee replaced the word "Attack" in its title with "Incident," which was again replaced earlier this year with "Patriots' Assembly." The 86-year-old Trump met today with Committee Chairwoman Marjorie Taylor Greene to discuss a preliminary public announcement of the findings, which is said to delete all Congressional testimony along with all historical public records of the event, whether they be published, printed, videotaped, filmed or otherwise recorded. Furthermore, any mention of the event, either publicly or privately, is to be banned in compliance with Mr. Trump's 2025 authorization of the Perpetual Martial Law Act, which criminalizes "negative, detrimental, unfavorable, disparaging or hostile" comments regarding Mr. Trump, his mistresses or his administration. Pending final review and approval of the Committee's report by the Ministry of Truth, Chairwoman Greene assured the press that the report would reflect an "accurate, fair and truthful" summary of the event. Ms. Greene also responded to "unfounded rumors" of summary executions taking place at the Ministry of Love, saying that the rumors were not only untrue but those who spread them are subject to criminal prosecution and summary execution.  "Golly Gee, I Wuz Feeling a Little Fuzzy-Headed, Ya Know?" — Posted Monday April 25 2022 Did you ever wonder why drugs like morphine, benzodiazepines and lidocaine are never advertised on television? They definitely work, and have tons of verified case studies, double-blind tests and pharmacological data to back them up, but their beneficial effects are now just taken for granted. Conversely, many television ads tout the supposed benefits of over-ther-counter and homeopathic medications whose effects have never been verified though any such testing protocols. Sure, aspirin works to relieve minor pain (although it never worked for me), while Tylenol seems to have some benefit, and melatonin may help with sleeping disorders (again, no benefit for me). But now we have any number of costly, over-the-counter, non-FDA approved online medications (all non-prescription) that claim all manner of cures, from restless leg syndrome (what the hell is that?!) and saggy chins to weight-loss wonders. But for me the worst is Prevagen, a very costly dietary food supplement that is supposed to boost brain function and memory. Its main ingredient is a jellyfish protein, and who the heck could ever object to eating that?! You've seen the ads on television—they all feature middle-aged or elderly people (invariably white and financially well-off, judging by their featured homes, belongings and properties) whose sole claim is "Gee, I was feeling a tad fuzzy-headed, you know, but after months of taking Prevagen I seemed to feel, well, you know, a little better off memory-wise. I guess." This is what we call hearsay, in this case unverifiable and untestable claims by companies and their gullible customers. It's also called the placebo effect, but claimants will never admit it. I have a very conservative rural in-law (a Republican, natch) who claims that magnetic bracelets have boosted his overall health and that water dowsing is a sure-fire way to find groundwater (yes, after hundreds of failures, that one success clinches it for him). As a classic example, take homeopathy, which is grounded in the belief that whatever kills you can cure you. Arsenic is a typical toxic elemental material that causes all manner of health problems, even death. But if you take an arsenic salt and dilute it sufficiently with water (such that not a single atom of arsenic is present in a given dose), the water will "remember" the arsenic, and thereby provide a cure for the toxin when taken internally. And whattya know, folks? Not a single person has ever died from arsenic poisoning by taking this miracle concoction! [Republicans living in the South are favorite targets of homeopathy, which likely explains their devotion to former president Donald Trump. Trump is a proven pathological liar, adulterer, business failure, conman and cheat, so hey, he must be an okay guy!] Nevertheless, people will still buy Prevagen, thinking they will eventually become geniuses, although their bank savings will also decrease proportionately, which is the one testable concurrent aspect of the drug they will never observe.  WHEW! — Posted Monday April 25 2022 "Then you will know the truth, and the truth will set you free." — John 8:32 "Then you will believe our lies, and we will enslave you." — America's Republican Party Thank God France's President Emmanuel Macron defeated extreme rightwing nutbar challenger Marine le Pen in that country's election. But America still remains the most dangerous nation in the world, as the crazy conspiratorial and Trump-besotted GOP threatens to dominate the 2022 mid-term and 2024 presidential elections. God save us, save us all.  I Feel Old — Posted Saturday April 23 2022 "I feel old, Starbuck, bowed and humped, as though I were Adam, staggering beneath the pile of centuries since Paradise." — Herman Melville, Moby-Dick In early 1989 I noticed a pronounced ringing in my ears, but I thought it would go away, believing it was just the temporary result of listening to too much music on my old portable Sony cassette player. But it persisted, and it was then joined with periods of dizziness and later vertigo and extreme nausea. In 1996 I had an MRI, and based on the results and my symptoms I was diagnosed with bilateral Meniere's Disease, a non-communicable ailment that is not so much a disease as a condition. For several years I went to the House Ear Institute in Los Angeles for treatment, learning that there was no cure, primarily because its cause is unknown. The symptoms of the condition worsen with stress, although I found that certain medications (notably the benzodiazepines Valium and Ativan) helped lessen the condition's severity (my doctor at the House Ear Institute found this interesting, and these drugs have since been regularly prescribed as a short-term treatment for the condition). But drugs like benzodiazepines are addictive, so I had to resort to other methods of dealing with the condition, mainly salt and coffee avoidance, white-noise generation and meditation. I've never used illegal drugs, but in desperation I once tried eating marijuana cookies (legal in Southern California) in 2018 to see if it would help. But it only made me feel like I was losing my mind, so I never tried it again. With the problem persisting, by the early 2000s I was experiencing severe vertigo and nausea associated with the condition. I took early retirement in February 2002, mainly because my wife had been diagnosed with breast cancer and diabetes, but also because of my problem. I subsequently discovered that there is a very real association of Meniere's with stress levels. However, following her successful surgery and chemo treatments, my Meniere's symptoms decreased substantially. But when my wife died in 2019, the symptoms gradually got worse. They haven't affected my mental alertness, but the vertigo, nausea and garbled hearing have returned, while the tinnitus is worse than ever, requiring my taking the drug Trazodone to sleep. Please pray for me, as I don't know where all of this is going.  On the Persistence of Information — Posted Saturday April 23 2022 Happy blessed Bright Saturday. Following a brief hiatus in which she posted videos on non-physics issues I don't care about, German physicist Sabine Hossenfelder has a new video on the black hole information paradox. Why should anyone care about this at a time of war, rampant insane conspiracy theories and other examples of extreme human stupidity? Because I believe that we've reached a point in human intellectual development that is beginning to focus on the fundamental paradox of our existence—the role of information, its creation and persistence, and its relationship with quantum mechanics and gravitation, arguably the final frontier so far as humans are concerend. Yes, this is a philosophical issue that physics may never resolve, since it appears to be resistant to experiment or observation. Indeed, it's probably more of a religious issue, yet another aspect of human existence that does not lend itself to experiment or observation. I can't help but feel that Hossenfelder, who has given up trying to resolve the information paradox herself, has reached this same conclusion, albeit from a purely non-religious point of view. Dr. Hossenfelder discusses the matter using a thought experiment in which she tosses her notable 2020 book Lost in Math into a black hole. As the book and its informational contents encounter and pass through the hole's event horizon, the hole increases in mass somewhat and perhaps loses a bit of angular momentum. The increase in mass expands the hole's radius a tiny bit, releasing a miniscule amount of gravitational radiation in the process (presumably, this radiation does not counter the hole's mass increase by very much). Later, the black hole undergoes the continuous process of thermal Hawking radiation (in the form of photons and perhaps elementary particles), reducing the hole's mass over eons of time until the entire black hole evaporates entirely. The apparently unassailable feature of quantum unitarity states that the information contained in Hossenfelder's book cannot be destroyed, while the thernal radiation is purely random and thus does not contain any information. So is the information destroyed, thereby violating quantum physics, and if not, where does it go? Hossenfelder points out that hundreds of ideas have been postulated that serve to answer this question, all based on elegant mathematics but without any experimental or observational support. Noting this, and with no workable theory of quantum gravity on the horizon, Hossenfelder believes no reliable answer can be given, and that's why she's given up on the problem. Energy is not conserved in an expanding universe, and if information is just a form of energy, perhaps it is not conserved as well. As a former chemist, engineer, physicist and lay person, I cannot answer this question, but I believe it has something to do with the wisdom of God, which He prefers to keep to Himself for the time being. The human brain is arguably the ultimate repository of information. What happens to it when we die?  COVID and the Sense of Smell — Posted Saturday April 23 2022 Some months before she died in July 2019, my dear wife lost her sense of smell and taste. Could that have been a forewarning of the coming COVID-19 pandemic? I wonder: COVID and Smell.  Jonathan Haidt on Social Media — Posted Friday April 22 2022 The Tower of Babel (Genesis 11:1-9). A multiplicity of regional languages has become a multiplicity of worldwide online conspiracy theories. An article in The Atlantic came out recently that remains the magazine's most-read article. It's by New York University social psychologist Jonathan Haidt, who writes that the past ten years of American life have been uniquely stupid, and not just a passing phase. He blames the rise of social media like Twitter, Facebook and Instagram, which combined have caused America to go from left-right polarization to center-left, center-right demonization. Haidt further notes that social media have demonstrably resulted in increased depression, disaffectation and suicide among the younger generation. Haidt also points out that social media is driven largely by unknown individuals and organizations whose media postings and videos have had an enormous negative impact on both their followers and on naive and gullible viewers and readers who don't know any better (to me, a classic example is the poorly-informed and under-educated individual who once lamented his marginal status in life, but now armed and proud with stupid conspiracy theories that give him a feeling of empowerment, enjoys a renewed sense of importance, purpose and destiny). I have three young grandchildren, and it's just a matter of time before they begin to experience the online world via their own smart phones and other digital devices. I used to worry about their exposure to online pornography (which is now sadly ubiquitous), but now it's also things like online bullying and ridicule, peer pressure and obsession with appearance. And as they get older, that will be joined with a negatively skewed sense of reality via the online world. In the following PBS video, Haidt offers a few possible panaceas, but unless Americans can get off their obsession with celebrity worship and induced self-importance via stupid conspiracy theories, things look pretty hopeless.  Quadratic Gravity — Posted Wednesday April 20 2022 Without the introduction of scalar fields and other extraneous added vector, tensor and spinor quantities, the only possible way to make a gravitational action conformally invariant is through a quadratic Lagrangian, usually involving the square of the Weyl tensor $$C_{\,\,\mu\nu\alpha}^\lambda$$. Conformal invariance usually means invariance with respect to distances and length, but it can also mean time invariance. I see it as a catch-all for a typically ignored symmetry of Nature, which should be added to other symmetries such as displacement, momentum, angular momentum and electric charge. Quadratic gravity has had some success in explaining the dark matter phenomenon, and I tend to attribute its inability to explain dark matter fully to discrepancies in the accuracy or interpretation of cosmological observations. Dark matter is the go-to excuse for our inability to detect what appears to be non-baryonic matter in galaxies and galactic clusters, particularly the missing matter that serves to explain the constant rotational velocities of stars orbiting their host galaxies. Research literature for the past ten years (at least) has shown a consistent interest in quadratic gravity, often in conjunction with efforts to join gravity with quantum mechanics. Indeed, you'll often see the term quantum gravity (the Holy Grail of physics) mentioned in these papers. I think it's due mostly to the fact that quadratic gravity is said to be renormalizable in those theories, although the papers I've seen are just quantum theories with gravity going along for the ride. But problems still exist that appear to be insurmountble, like the negative probabilities and ghost fields that invariably inhabit these quantum theories. At least part of the reasons why gravity is introduced into these theories is because gravity involves only the Riemann curvature tensor $$R_{\,\,\mu\nu\alpha}^\lambda$$ and its two contracted variants, which can be dumped easily into the quantum realm in the hope that something useful will result. Here's just one recent example of modern quadratic gravity research, one in which quantum physics is left out: Dark Matter Production in Weyl $$R^2$$ Inflation.  Penrose and (Ugh) Peterson — Posted Wednesday April 20 2022 Today is the 133rd birthday of Adolf Hitler. I mention this only because you might want to watch out for rightwing violence celebrating his birthday (it was largely responsible for the infamous April 1995 bombing in Oklahoma City and other April atrocities), although with the GOP's current besottedness with Russian President Vladimir Putin and Donald Trump conservatives might now wish to observe October 7 or June 14 instead. But I digress. I find Jordan Peterson to be something between a somewhat okay wannabee philosopher, a conservative jerk and a con man, but he has a large following in academic circles and on YouTube. Here he interviews Sir Roger Penrose, the winner of the 2020 Nobel Prize in Physics and current preeminent expert on black holes. The 90-year-old Penrose is normally nattily dressed and well groomed, but here he appears dishevelled and kind of out of it, perhaps because he's being interviewed by Peterson, who I'm sure really knows nothing about Penrose or his work. Anyway, in the following video Penrose talks about the incompleteness of quantum mechanics, specifically its inability to explain the measurement problem, which has to do with the instantaneous collapse of the wave function $$\Psi(x,t)$$. Penrose notes that while the famous Schrodinger equation $$\hat{H} \Psi(x,t) = i \hbar \frac{\partial \Psi(x,t)}{\partial t}$$ (where $$\hat{H}$$ is the Hamiltonian or energy operator) is perfectly continuous and deterministic, it cannot explain what happens to the wave function when the system it represents is observed by a conscious observer (I'll avoid any philosophical or religious aspects of this for the time being). In the video, Penrose goes on to assert his belief that wave function collapse has something to do with the influence of gravity on the system. You might want to read any of Penrose's great books that touch on this, especially The Road to Reality, which anyone stranded on a desert island might want to have.  Oh Dear—Another "Tension" in Physics — Posted Saturday April 9 2022 As reported in Quanta Magazine, recent experiments at the Collider Detector at Fermilab indicate that the apparent mass of the $$W^{-}$$ boson is about 0.1% higher than it was thought to be. The discrepancy is statistically significant, at roughly 7$$\sigma$$, putting it far above "discovery" status and thereby upsetting the Standard Model of Physics, which predicts a slightly lower mass figure based on rigorous (and presumed correct) calculations. As probably few people know, the neutron (composed of two down quarks and one up quark) is not stable, decaying with a half-life of about 10 minutes to a proton, an electron and an anti-electron neutrino (that's unless the neutron is bound to an atomic nucleus, in which case it is uncommonly stable). Under decay, one of the neutron's down quarks is converted to an up quark, with the emission of a $$W^{-}$$ gauge boson, which then decays after something like $$10^{-25}$$ seconds to the electron and neutrino. The resulting up quark goes on to join the neutron's unaffected up and down partners to become the proton (which, as far as anyone knows, is completely stable). What is 7 sigma, you ask? I've long had trouble dealing with these numbers, as my calculations are invariably off by a factor of two. According to my Mathematica program, 7$$\sigma$$ means that the probability of a difference being due purely to a statistical fluke is about one in a trillion ($$10^{-12}$$): The analysis depends on the correctness of the Gaussian bell curve approach, and I can't help wondering if that isn't always appropriate. There are other probability distributions, and perhaps one of those is the better approach. But assuming it's correct in this case then either the Standard Model needs to be amended, or the calculations used to determine the mass of the $$W^{-}$$ need to be corrected. Those calculations are exceedingly complicated and depend on their own assumptions, like the immutability of the fine structure constant. Ever the optimists, physicists are hoping that the experiments and calculations are valid, and that the discrepancy is due to new physics (like new particles or fields, or low-level side reactions). Meanwhile, there are other "tensions" in physics today, like that involving the Hubble parameter and the muon g-2 problem, both of which are posing truly knotty problems, with differences between calculations and observations off the charts compared with the $$W^{-}$$ issue. Of course, physics will never be "done." There are more discoveries to be made, including the correction of errors and bad assumptions. Lastly, I'll go out on a limb: the Standard Model does not include gravity, and I wonder if quantum-scale gravitational interactions have anything to do with all these tensions.  The Distortion of Reality — Posted Friday April 8 2022 Even worse, the warped public sphere we each inhabit is not random. It is custom-curated to target us with the information that will most likely resonate. This gives most of us an overinflated impression of the prevalence of our own views and values, and an underdeveloped sense of the prevalence of conflicting views and values. This dynamic amplifies extreme perspectives and drives polarization, but even worse, it destroys our collective wisdom as a society. — Louis Rosenberg (my emphasis) Today's Big Think has an article by computer scientist Louis Rosenberg, who writes that the problem with social media is not its content, but how that content is warped and then delivered to its users for profit. That profit can be financial, or it can be the useful promotion of ideologies that benefit the group or groups that promote it. I suppose that in the end, it's financial profit after all, since that's what runs the world today. While many users of social media have been led to believe that it has improved their lives, Rosenberg asserts that social media has instead damaged society. If it had been used solely to dispense actual information, some forms of entertainment, or to promote family connections, that would have been fine. Instead it has also become a means of instantly communicating hateful ideas and nonsensical conspiracy theories, often by individuals who have little or no connection with reality or the truth. Rosenberg concludes his article with possible options to fix the problem, which are either to censor or ban social media through government regulation or through concurrent education of its users. Rightwingers of course hate censoring anything unless it promotes their rightwing views, while leftwingers prefer regulation and/or education. In my view, none of these options will work, particularly because social media is a money-maker and because it is ubiquitous. Banning it altogether might work, but because social media is a worldwide phenomenon it cannot be banned everywhere. The situation is something like nuclear weapons—they can be reduced in number or banned altogether, but the technology behind them cannot be forgotten. With the advent and rise of negative worldwide social media and rightwing ideology, the world might very well be doomed. God save us, save us all.  Republicans: "Putin is Bad, But ..." — Posted Monday April 4 2022 Former President Donald Trump fawned all over Russian President Vladimir Putin, so the Republican Party naturally followed suit, viewing Putin as a great man. Russia's unprovoked invasion of Ukraine didn't change the GOP's attitude toward Putin, but recent evidence of the Russian army's torture and murder of Ukrainian civilians—men, women and children—has required a modification of Republican thinking. Now it's Putin's bad, but ..." Make no mistake, the GOP still loves Putin and Russia, because Trump still adores him, but Russia's inhuman behavior against Ukraine nevertheless has an unpleasant political side, which the GOP wants to avoid in view of the upcoming 2022 mid-term elections and the 2024 presidential contest. I liken the situation to late 1930's Germany, when Germans fell under Hitler's dictatorial spell. Most became Nazi Party members, although many disagreed with the Party's barbarous treatment of Jews and others. Their attitude was "Hitler is bad, but $$\ldots$$" It's history all over again, but it's sadly happening in America today. Meanwhile, my country's unwillingness to prosecute Trump and his minions for their documented criminality and treasonous actions spells disaster for America. I look upon Attorney General Merrick Garland as the shy little guy who scrooches against the back wall at a party so no one will notice him, and to date he has lived up to that description. As the saying goes, "Justice delayed is justice denied," but to willfully ignore criminal behavior is the very definition of injustice. God help this country and this world. I'm not a huge fan of Bill Maher, but his recent show says it all:  Yeah, Too Bad About That Country — Posted Saturday April 2 2022 Another gem from Ruben Bolling: show  Too Many Gravity Theories — Posted Saturday April 2 2022 Einstein's 1915 gravity theory has successfully passed every test thrown at it for the past hundred years, much like quantum theory, which has yet to see an experimental failure. But gravity has one serious problem: it predicts a singularity at the center of a black hole, where spacetime curvature becomes infinite and all known laws of physics break down. Most physicists abhor singularities, primarily because they seem to indicate that if they arise, then the physical model or the mathematics must be wrong. Quantum theory also suffers from a serious problem (wave function collapse), but that problem probably has more to do with philosophical issues deriving from the perceptual foundations of the theory itself. Consequently, quantum physics is likely complete but misunderstood to some extent, while Einstein's theory clearly needs to be modified. Arguably the first serious attempt to modify general relativity was due to the German mathematical physicist Hermann Weyl in early 1918, some two years after Einstein published his theory. Since then, countless attempts have been made to modify gravity theory, mostly centering around its inability to explain dark matter and dark energy (sometimes combined as the dark sector). I haven't seen much come out of Egypt regarding theoretical physics, but last week Alexey Golovnev of the British University of Egypt in Cairo and his colleague Maria-Jose Guzman published an informative (and mostly non-mathematical) paper succinctly summarizing all the important efforts made to date to modify Einstein's gravity theory: This is the only mathematical term in the paper. Entitled Contemplating the Fate of Modified Gravity, the authors note that most of these efforts have been based on seeking the "simplest modification" of Einstein's theory, and that (lamentably) this approach has led to a variety of theories that have produced no real progress. While it's true that superstring theory predicts a massless spin-2 boson believed to be the graviton particle of general relativity, its requirement of 11 spacetime dimensions, the failure of the associated supersymmetry model and the unachievably high energies needed to experimentally test superstring theory have all but doomed the theory. With it likely also goes the present hope for a workable quantum gravity theory. Similar efforts to either quantize gravity or "gravitize" quantum physics have also failed to date. Since general relativity is a classical theory, and one most aptly applied to large-scale, non-quantum phenomena, modifying the theory by similar classical means has proven tantalizing. Such classical methods have included $$f(R)$$ theory, quadratic gravity (which includes Weyl's 1918 attempt), scalar fields, vector fields and combined scalar-vector-tensor fields, all with little or no success. Non-Riemannian attempts have also been explored, like making the metric tensor $$g_{\mu\nu}$$ and the connection $$\Gamma_{\,\mu\nu}^\lambda$$ non-symmetric in their lower indices (a long-time favorite approach of Einstein), leading again to failure. All of these attempts have served in one way or another to introduce additional fundamental quantities into gravity theory that might explain dark matter and dark energy. I still believe that there may be purely geometric quantities embedded in gravity theory that will explain dark matter (dark energy seems to be already explained by the gravitational constant $$\Lambda$$, which Einstein proposed in 1917). For example, Riemannian $$R^2$$ theory introduces an additional constant of integration that appears to be related to dark matter. Lastly, the authors of the paper rightly conclude that given the current bewildering variety of modified gravity theories, some attempt should be made to consolidate or even unify them to prevent researchers from wasting their time on hopeless efforts. Nevertheless, there is also a tinge of hopelessness in the authors' paper itself, given the very real possibility that we'll never truly understand gravity.  Hitting the Jackpot — Posted Wednesday March 30 2022 I mentioned this a few years ago: the world in general—and America in particular—is acting weird, and it's a weirdness that can't be attributed to mental illness. In today's Atlantic Magazine, writer Olga Khazan notes that incidents involving unruly airline passengers, disruptive hospital patients and church members, public drunkenness, violence against women and minorities and related overt racist attacks have gone way beyond their usual levels, and there seems to be no rational basis for it. It began prior to the COVID-19 pandemic, so the resulting social isolation of worldwide populations and health fears that the virus created can't be the cause. It's something else. Khazan's article immediately brought to my mind science fiction writer Robert A. Heinlein's prophetic 1952 short story The Year of the Jackpot, which describes similar irrational human behavior just prior to a world-ending catastrophe. You can read the public-domain story here. Seismic activity is normally preceded by P waves, which are high velocity pressure waves in the Earth that many animals can sense prior to an earthquake. Their behavior appears to be irrational: dogs and cats suddenly acting strangely or running away, birds flying in chaotic formations, and horses bolting out of their stables. But rather than earthquakes and other natural disasters, humans are causing disasters themselves through war, resource waste and depletion, corruption, global inequality and other intentional but stupid actions. The disaster that hits Earth in Heinlein's story is not man-made, but the end result might parallel what's in store for us today. And with 7.8 billion people on the planet, the stakes couldn't be higher.  Purity? — Posted Sunday March 27 2022 In the Gospel of Matthew, Jesus Christ speaks negatively about hypocrites and hypocrisy no fewer than 15 times. Of all the transgressions that plagued mankind in those days, hypocrisy appears to have bothered Jesus greatly. We're all hypocrites to some extent, but the sin of hypocrisy is made worse when we refuse to recognize or acknowledge it. I don't support elective abortion except under certain situations (rape, incest, ectopic pregnancy, severe genetic deformity, mental illness and poverty), so I won't post Ruben Bolling's latest strip here, although I find it tragically appropriate. Despite all those hypocritical Southern purity balls, purity rings and purity pledges, America's South leads in the viewing and downloading of Internet pornography, perhaps the most socially destructive aspect of online technology. There's an old adage that goes "The difference between a sinner and a saint is that the saint knows he's a sinner." We mustn't judge, but we also shouldn't hide our hypocrisy behind pseudo-saintly behavior.  Come and Keep Your Comrade Warm — Posted Sunday March 27 2022 Ukraine girls really knock me out, they leave the West behind $$\ldots$$ — The Beatles, Back in the U.S.S.R. Kind of a follow-up on my post of 24 March—You might have noticed how Ukrainians are not only like us Americans in their appearance and culture (plus most speak English), but those blonde, blue-eyed Ukrainian women are knockouts. It's no wonder that all those phony "Russian women wanna meet American men for romance and marriage" ads on the Internet are so popular. The media (mostly CNN and MSNBC) are also subtly advancing the allure of Ukrainian women by featuring constant interviews with them amid the destruction caused by the now month-long invasion of their country by neighboring Russia, often with equally beautiful young children on their laps for added effect. By contrast, I can't help thinking how none of this occurred when America was bombing Iraqi homes, presumably because Iraqi women were invariably brown, poorly dressed and incapable of conversing in English. But that did not distract from the fact that American soldiers found some very young Iraqi girls attractive. In March 2006 American troops gang-raped and murdered 14-year-old Abeer al-Janabi in the town of Al-Mahmudiyah, Iraq. They also killed the girl's mother, father and 6-year-old sister, then incinerated their corpses to conceal the killings. The killers were convicted and sentenced for the murders, but a number of America's Republican political leaders subsequently expressed outrage over the judgments, saying that the convictions violated the Military Extraterritorial Jurisdiction Act. That's Republican justice for you. It's no wonder then that the Republican Party and its media outlets Fox News and OneAmericaNow have been so quiet concerning the Russian invasion of Ukraine. The American public is currently besotted by all those gorgeous Ukrainian women, which in part has justified Americans' support of the Ukrainian cause. Consequently, Republicans (who love Russia's Vladimir Putin as much as they do Donald Trump) have had to keep their true feelings under wraps.  James Webb Telescope to Earth— Hello? Is Anyone There? — Posted Friday March 25 2022 The James Webb's 18 mirrors are now fully aligned with nanometer precision. Everything's gone well, from its launch three months ago, to its arrival at the L2 orbital point and with final adjustments to its onboard cameras and instruments. A few more finishing touches (taking a few months) will bring the telescope and its unprecented astronomical capabilities to completion, and humankind will have its most detailed and accurate observations of the early universe to date. I've read several notable science fiction stories in the past featuring astronauts who find themselves marooned in space following a nuclear cataclysm on their home planet, rendering them incapable of ever returning home, yet I haven't seen any featuring a hapless, orbiting robotic observatory whose otherwise Earth-shaking discoveries similarly go unanswered because the humans who built it decided to commit global suicide. If everything continues to go well onboard the James Webb Telescope, it will undoubtedly rewrite our understanding of the universe—but only if we're around to appreciate what it finds.  Hypocrisy? Or at Least Double Standards? Nah — Posted Thursday March 24 2022 Few Americans talk nowadays about (or even remember) the horrors that occurred in Iraq's Abu Ghraib ("father of small crows" in Arabic) after we invaded that country in 2003. Well, I remember, to my everlasting shame and disgust. [Funny how fifteen of the nineteen 9/11 hijackers were Saudis, and the attack's Saudi mastermind was found in Pakistan, but George W. Bush insisted on invading Iraq anyway. The invasion was initially called Operation Iraqi Liberation or OIL(!), but it was abruptly changed to Operation Iraqi Freedom, because we gotta have the word "freedom" in there someplace]. No war was declared against Iraq, so accusations of war crimes committed by American forces in Abu Ghraib were rendered moot. It didn't matter anyway, since America was not and is not a signatory to the International Criminal Court (ICC) at the Hague. I see a distinct parallel with what's going on in Ukraine: no war's been declared, and Russia also does not recognize the ICC, and while Putin's forces are not torturing or stacking up and photographing naked Ukrainians like cord wood the way we did Iraqis in Abu Ghraib, Russia's actions are similarly illegal and tragic. But I can't help wondering, though—those Ukrainians are just as white as white Americans, and their culture is nearly identical to ours (most are fluent in English), while Iraqis, Afghanis and Pakistanis are brown, having vastly different ways of life, and their English at best is only passable. Humans are supposed to be good at pattern recognition, but I guess that ability has been lost on Americans. With the war in Ukraine raging, the nearly simultaneous bipartisan confirmation hearing of Judge Ketanji Brown Jackson seems eerily prescient, considering the fact that in spite of her clear overwhelming suitability for the Supreme Court, her judicial record cannot expunge the fact that Jackson is both a woman and a Black. Of course, Republicans on the confirmation panel could not accuse Jackson of being female and Black, so they found a single judicial case that serves as a proxy for their discrimination—a 2013 decision in which Jackson sentenced 18-year-old Wesley Hawkins (found guilty of possession of several child pornography videos) to a three-month prison term, three months of home detention and (because Hawkins was still a minor at the time of sentencing) six years supervision, not probation. The "soft on crime" allegation that Jackson now faces seriously affects her chances of being confirmed, but even if she's not confirmed President Biden has sworn that he will appoint a Black women to the Supreme Court. Stare decisis (meaning that judicial precedents carry weight) seems to be acting in reverse here: Republicans are afraid that the appointment of a Black female to the Court will open the door to future such appointments, and they simply won't stand for that. Yes, I digress. But hypocrisy and prejudice seem to be built into America's genetic code, whether one is talking about foreign wars or Supreme Court candidates. Christian writer, author and former war correspondent Chris Hedges says it better here.  Yet Another Dark Matter Search Bites the Dust — Posted Tuesday March 22 2022 The search for dark matter continues, and a new experimental approach for its detection has appeared in the form of spectral gravitational wave analysis, as reported in this new Quanta Magazine article. The research was carried out by a multi-member team led by Sander Vermeulen from Cardiff University, and their 16 December 2021 Nature paper can be read here. The team assumed that dark matter should couple to electron and electromagnetic fields through a dark-matter scalar field $$\varphi$$, and that evidence of this coupling might be detectable in existing gravitational wave data. The Quanta article straightforwardly reports the results of the search as "a new tool for finding dark matter digs up nothing," but you won't dig that conclusion out of the Nature paper, whose authors prefer to express their null finding in more positive terms. Of the roughly 10,000 statistically significant signals seen in the data, every one was conclusively eliminated as a potential dark matter signal. The authors conclude that their approach nevertheless represents a useful new method for dark matter research, which I suppose it is. But it's still a failure for the dark matter crowd, which stubbornly continues to believe that this non-interacting, undetectable, invisible, tasteless, odorless pixie dust exists.  ELO—"Can't Get It Out Of My Head" — Posted Monday March 21 2022 I'm finally getting back into the gym, but exercising is so boring (and I'm so out of shape now) that I can hardly stand it. Looking at the gym's overhead TV monitors just turns me off, so I listen to music over my Air Pods. But all that interests me now is Jeff Lynne and Electric Light Orchestra, my favorite band of all time. Paul McCartney once admitted that if the Beatles had stayed together, they would have sounded like ELO—rock music mixed with synthesizers and classical orchestral instruments like violins, cellos, brass and piano. Lynne is a true musical genius, and his hundreds of unforgettable songs and many dozens of hits have made his music timeless. It's also decent, with no foul language or overly angry or disturbing lyrics. My kids have always loved ELO, and I hope my grandchildren will also get the chance to learn what great rock music used to be. Even better: Lynne's live performances sound as great as his recordings, and one of the best is his 2018 Wembley, England concert. It's topped only by ELO's 1977 double album, Out of the Blue, arguably the greatest rock music compilation of all time.  Symmetry and Optimization — Posted Saturday March 19 2022 Salon has a neat new article dealing with symmetry in Nature, likening it to the efficiency of living things due to purely evolutionary processes, like the Fibonacci spiral structure of seeds in a sunflower plant. The article's writer calls this the "simplicity bias" of Nature, which I think is mostly correct. However, there are lots of examples where the simplicity of symmetry does not seem to apply, like the placement of the human heart in the thoracic cavity, the appendix, and even the testicles, which are not only not symmetric but are regrettably placed outside a man's body (I know, it's a biological trade-off due to the need for temperature lowering, but it's still regrettable). These are simple examples of form or geometric symmetry, but in physics we have broken symmetry, which is oddly responsible for many of the regular patterns seen in the properties of elementary and composite particles. For whatever reason, Nature wants to keeps things optimized (a better term is extremalized), like the energy of a system in equilibrium or the time it takes to get things done. These turn out to be mathematical symmetries in physics, and they are easily expressible in mathematical terms. Intimately associated with these symmetries are conservation laws, like the conservation of energy, momentum, angular momentum and electric charge. The Salon article doesn't go into it (as it's never been proven), but complex biological systems almost certainly evolved from some kind of symmetry principle, with the result being a consequence of conservation laws. As a rational, curious human being, you've got to ask yourself why in hell Nature operates this way. If the universe popped into being with the Big Bang, there was really no reason why chaos would not have reigned, and such things as symmetries and conservation laws would have been impossible except through random accident (random accidents are the logic behind multiverse and many-worlds theories, if you prefer to go that way). More logically, symmetries and physical laws are the result of extremalization processes, and this requires intelligence (as a simple example, if you set the derivative of a non-monotonic cost function to zero you obtain the optimum value of that function, usually the least cost). As stated, no one yet has been able to figure out how complex biological systems attain optimization, but evolution seems to have worked it out, although it may have taken some time. Why evolution itself is an optimizing process is also an unanswered question.  The Authoritarian Cum Totalitarian Play Book — Posted Saturday March 19 2022 Win elections through right-wing populism that taps into people's outrage over the corruption and inequities wrought by unbridled globalization. Enrich corrupt oligarchs who in turn fund your politics. Create a vast partisan propaganda machine. Redraw parliamentary districts to entrench your party in power. Pack the courts with right-wing judges and erode the independence of the rule of law. Keep big business on your side with low taxes and favorable treatment. Demonize your political opponents through social media disinformation. Attack civil society as a tool of George Soros. Cast yourself as the sole legitimate defender of national security. Wrap the whole project in a Christian nationalist message that taps into the longing for a great past. Offer a sense of belonging for the disaffected masses. Relentlessly attack the Other: immigrants, Muslims, liberal elites. This is from the 2021 book After the Fall - Being American in the World We've Made by Ben Rhodes, former White House aide and confidant of former president Barack Obama. Although the quote pertains to the recently manufactured authoritarian country of Hungary, Rhodes notes that it eerily applies also to the present United States of America, which somehow—perhaps by the grace of God Himself—escaped a narrow brush with authoritarian death due to the unconscionable and inexlicable 2016 election of Donald Trump to the American presidency. Trump—the most virulently anti-Christian, anti-humanitarian, immoral thug to have ever disgraced America—is the very poster boy for Rhodes' comment. Yet despite this, tens of millions of Americans still see Trump as their new Lord and Savior, and they're willing to sacrifice every vestige of their humanity and sanity to re-elect this monster. Rhodes' book should be in every library, but—given recent efforts by Red States to ban any book that dares question the supposed innate godliness of America—it's doubtful that it will be read by anyone needing to learn the book's message: America has fallen, and will continue to fall if its ignorant, arrogant and stupid people will not learn the lessons of history.  Superdeterminism or Free Will? — Posted Friday March 18 2022 Every quantum experiment done to date indicates that quantum states exist in a superposition (linear collection) of possible substates called eigenstates. For example, a state $$|\psi\rangle$$ might exist as a superposition of just four substates: $$|\psi\rangle = a_1 |\psi_1 \rangle + a_2 |\psi_2 \rangle + a_3 |\psi_3 \rangle + a_4 |\psi_4 \rangle = \sum_{n=1}^{n=4} a_n |\psi_n\rangle$$ where the $$a_i$$ are complex coefficients (possibly functions of space and time) and the $$|\psi_i\rangle$$ are eigenstates (also possibly functions of space and time) that represent the only possible results that one can obtain from an observation of the state. The Born rule states that each $$a_i$$ reflects the probability (technically, the probability amplitude) that its associated eigenstate will be observed, and is completely random in nature. (One might even have an infinite set of such quantities, as in $$|\psi\rangle = \sum_{n=1}^{n=\infty} a_n |\psi_n \rangle$$ but the idea is the same.) It is from this view that we derive the notion of randomness in quantum theory, because obtaining any particular $$|\psi_k \rangle$$ is completely probabilistic, like the probability associated with flipping a weighted $$n-$$sided coin or die. Einstein disliked this idea, believing instead that quantum mechanics was incomplete in some way, or that there must be hidden variables in the theory that determine the outcome of any measurement. If we assume that the summation is large but not infinite, there is then a finite number of possible states that any quantum observable can have. Accordingly, a measurement will invariably land on just one of the eigenstates $$|\psi_k \rangle$$, with the probability given mathematically by the square of $$\langle a_k|a_k\rangle$$. Now consider the entire universe, which consists of an enormous (but presumably still finite) number of particles and their associated fields. Then we must accordingly have an enormous (but finite) number of possible eigenstates for any observable. I'm not an expert on this, but my understanding is that this constitutes what is known as quantum superdeterminism, the idea that whatever happens in the universe is fixed or determined not by hidden variables but by the limited possibilities inherent in the entire universe. This unavoidably destroys the notion of free will, because whatever decision or action one takes is just one of a large but limited number of available decisions or actions that one is allowed to take. Most scientists do not believe that the universe is strictly deterministic or superdeterministic (nor do I), and they leave open the likelihood that pure free still exists. Otherwise, one could always appeal to determinism in claiming that their illegal or immoral actions were out of their hands, predetermined by the universe itself. "The devil made me do it" would then give way to a more scientific alibi, assuming a court of law is willing to recognize the argument. Fat chance, I say. But there are notable proponents of superdeterminism and "no free will" out there, one being German physicist Sabine Hossenfelder, one of my favorite scientists. Here's a recent video of hers explaining her point of view (which is mostly semantics, in my opinion):  Putin and His American GOP Worshipers — Posted Friday March 18 2022 Thanks again, Ruben Bolling (aka Tom the Dancing Bug): Disclaimer: I do not support abortion, but leave it to the woman and her God to sort things out. I do not support homosexuality, but leave it to the gays and their God to sort things out. I absolutely detest the Republican Party, and wish it were banned from my country. In other words, death to the GOP.  Where Does Everything Come From? — Posted Tuesday March 15 2022 Everyone knows Einstein's famous $$E= mc^2$$ formula equating energy with mass. In reality, this formula holds only for a particle of mass $$m$$ at rest. For a moving particle, the formula is $$E^2 = m^2 c^4 + c^2 p^2 \tag{1}$$ where $$p$$ is the relativistic momentum. A little algebra shows that the equivalent formula $$E = \frac{mc^2}{\sqrt{1 - v^2/c^2}} \tag{2}$$ also holds, where $$v$$ is the velocity of the particle. By expanding (2) to first order in a Taylor's series with respect to $$v$$, we get $$E = mc^2 + \frac{1}{2}\,mv^2$$ which shows where the classical formula comes from (the constant piece $$mc^2$$ doesn't change anything). Similarly, the relativistic formula for momentum is given by $$p = \frac{m v}{\sqrt{1-v^2/c^2}}$$ which is often (and erroneously) taken to mean that particle mass changes with velocity (no, mass is a true invariant). Energy is conserved (meaning it's invariant with respect to time), right? And it is, even when gravitational, electromagnetic and radiation fields are present. But energy is not conserved when space itself is expanding or contracting. This fact is a consequence of Einstein's gravitational field equations in the presence of mass-energy, which puzzled Einstein for years before he became aware of the expansion of the universe (which the field equations allow for). If inflationary cosmological theory is correct, the Big Bang was followed almost instantaneously by a huge exponenential expansion lasting only about $$10^{-32}$$ second, yet its subsequent decay produced all the mass-energy we observe in the universe today. It's still expanding, and this expansion is producing a much more miniscule amount of energy called dark energy, a kind of energy inherent to empty spacetime. It is this energy that is supposedly causing the universe to expand at an accelerated rate. Much if the foregoing is explained in better and greater detail in astrophysicist Ethan Siegel's latest article. So where does the universe's matter and energy come from? Perhaps a quantum fluctuation, which is the usual explanation given by most scientists today. And if so, where do the laws of Nature come from? A happenstance consequence of such a quantum fluctuation? Oh please, that is hardly an explanation, given the infinite possibilities, and the infinite resulting chaotic nature of those possibilities. I prefer to believe in God, or at least an external entity that has created everything we see. While that does not eliminate the possibility of an infinite multiverse or many-worlds scenario, it's at least as simple an explanation.  No, It's Like Arguing with Pieces of Furniture — Posted Sunday March 13 2022 But given the realities of money and power, in modern America most of the politicization of everything reflects pressures from the right. After all, while there is a philosophical case for a low-tax, minimal government society, modern conservatism relies less on philosophical persuasion than on the fact there are people who would gain a lot personally if we were to retrace our steps toward the Gilded Age. There may not be many of those people, but they're extremely rich. It's very much in their interest to promote the view that moving in their preferred direction would be good for everyone. And monetary support from right-wing billionaires is a powerful force propping up zombie ideas—ideas that should have been killed by contrary evidence, but instead keep shambling along, eating people's brains. — Paul Krugman, Arguing with Zombies, 2021 Beware of false prophets, who come to you in sheep's clothing, but inwardly they are ravening wolves. —Gospel of St. Matthew 7:15 While 2008 Nobel Economist (and self-proclaimed liberal with secular Jewish roots) Paul Krugman's Arguing with Zombies is written for a general audience, its 480 pages is nevertheless a rather daunting read. I struggled with it, but in the end I couldn't help but compare what he says implicitly and explicitly to the teachings of Jesus Christ, in which socialist philosophy is both evident and abundant. America's right wing has successfully managed to equate socialism with godless Communism and Marxism, which are both entirely different. Attendant with their message is the notion that abortion, family planning and contraception, Medicare, Social Security and other social welfare programs somehow run against God's plan for mankind, and that authoritarianism, totalitarianism, deification of the military and prosperity gospel are more in line with what God wants. Krugman has published 27 books, and while I'm sure he's financially well off, his wealth does not begin to approach that of mega-millionaires and billionaires like Sean Hannity, Tucker Carlson, Joel Osteen, Donald Trump and their rotten, pseudo-Christian, media-dominating right-wing ilk.  D'OH! — Posted Saturday March 12 2022 "Who is that feckless orange idiot, Smithers?" "That's Donald Trump, one of your puppets in Economic Sector G7, sir."  The Surprising Antiquity of Fractional Algebra — Posted Thursday March 10 2022 I've known Egyptians, worked with Egyptians, and even married an Egyptian (my late wife of 42 years), and while I've always been fascinated by ancient Egypt, its culture, art, mathematics and language, I was even more impressed reading this new Quanta article on unit fractions, which deal with how sums of inverse integers can be used to represent just about any quantity. The Egyptians were the first to discover unit fractions, which dates back to 1600 BC, some 3,600 years ago. And they must have known about it even earlier, because their methods were recorded on the Rhind papyrus, discovered in 1858 and beautifully preserved in spite of all those millennia: I've often wondered why so much of ancient Egypt's history has been preserved, while that of its neighbor Israel can be summarized by the Old Testament, the Dead Sea Scrolls and a relatively few material odds and ends. On the other hand, the nation of Israel stands strong today, while that of Egypt is little better than a third world country due to overpopulation and economic and political malaise. Even more amazing is the fact that both countries—which share a similar if often contentious history—underwent long-term, multiple occupations by nearby conquering nations. While Jewish accomplishments are replete with the brilliant likes of Albert Einstein and many others, you might want to find out where the words algebra and algorithm come from, and how the mathematics they derive from were discovered by equally brilliant ancient Egyptians.  Trump? What's a Trump? — Posted Saturday March 5 2022 Former U.S. president Donald Trump and his followers continue to praise Russian president Vladimir Putin despite his tragic, inhuman and criminal invasion of Ukraine. Yet while all the media are currently focused on that invasion, people like me are wondering what's happening with the multiple investigations that presumably are still being carried out regarding Trump's bogus business dealings and his attempts to subvert democracy by trying to steal the 2020 presidential election. Writer Jon Skolnik of Salon.com is wondering the same thing. While it's a great read, he neglects to focus adequately on the difference between democracy and totalitarian authoritarianism, something America's rightwing idiots seem to have forgotten. Indeed, in their mouth-foaming adoration of Putin and other egomaniacal, self-absorbed world dictators, their perceptions of democracy, what Jesus Christ taught and the basic dignity of human beings seem to have gotten transformed into a kind of global pyramid scheme involving prosperity gospel and the worship of money and power. If we let Trump and his criminal cabal off the hook, we're saying that it's okay to let a megalomanical, skirt-chasing dictator destroy democracy. Yesterday, South Carolina Republican Senator Lindsey Graham publicly advocated the assassination of Vladimir Putin. Sadly, he neglected to include Donald Trump.  I'm Still Rooting for the Underdog — Posted Monday February 28 2022 Prof. Harold Hill: "Tommy, did you ever experiment with perpetual motion?" Tommy: "Yeah, I nearly had it a couple of times!" The time frame of the 1963 musical The Music Man was 1912, so neither Hill nor Tommy could have known that perpetual motion was impossible. And it was only a decade or so after scientists also realized that the luminiferous aether, which seemed to explain how light could travel through space, was also nonsense. Today we have the notion of dark matter, that undetectable, invisible, tasteless, odorless, non-interacting particle that is assumed to make up over 80% of all the matter in the universe. It has one thing in common with the aether: with several important reservations, it explains the excess velocity of stars orbiting the outskirts of galaxies, where the inverse square law of gravity says they should be much slower. But after decades of search, involving dozens of experiments costing billions of dollars, dark matter particles continue to defy detection. A compact and readable summary of the problem can be read in this new Aeon article by Wired science writer Ramin Skibba, who questions whether it's high time to seriously consider alternatives to dark matter, such as modified gravity and other theories that don't rely on an undetectable particle. The first plausible alternative to Einstein's 1915 general relativity theory was proposed in 1918 by the German mathematical physicist Hermann Weyl, whose work is celebrated on this website. Of course Weyl knew nothing of dark matter, and his work preceded the discovery of the expanding universe and the cosmological work of Alexander Friedmann. But Weyl so early on sought a generalization of Einstein's theory, and in doing so believed it could explain electromagnetism as (like gravity) a purely geometrical construct. Weyl's theory was beautiful, but it failed—just like the modern search for dark matter. Einstein believed his theory was only an approximation, just as Newton's gravity theory proved to be only an approximation. If we take that seriously, it means that we should be looking for generalizations of Einstein's relativity theory that might explain dark matter. I find it ironic that gravity, the first force of Nature that was discovered by mankind (often painfully), appears to also be the most enigmatic. The other known interactions—the electromagnetic, strong and weak nuclear forces—all play out on the background of four-dimensional spacetime, while gravity itself is that spacetime, the stage on which the other forces live, and it is perhaps this fact that accounts for gravity's underlying mystery. To me, there is one glaring flaw in Einstein's theory, which is its noninvariance with respect to conformal tranformations. Weyl also saw this as a flaw, and he showed us a possible way to fix it. His failed 1918 theory was applied a decade later to quantum mechanics, where it stands today as the cornerstone of all modern quantum theory. That should be reason enough to spend more research dollars on fixing up Einstein's theory, and in doing so perhaps the mystery of dark matter will be solved by pencil and paper, not zillions of experimental dollars.  It's October 1962 All Over Again — Posted Sunday February 27 2022 Adolf Hitler killed six million Jews plus millions more, and the USSR's Josef Stalin killed 20 million of his own people, while China's Mao Zedong certainly killed even more. The world has not learned how to deal with rightwing, megalomaniacal mega-murderers, and in Vladimir Putin we now have another in the offing, the biggest difference being that he has control of some 6,100 nuclear weapons. Meanwhile, America has its own brand of rightwing egomaniacs, all of whom are praising the "genius" of Putin and are rooting for Putin's success in Ukraine. In the late 1930s a large number of Americans supported Hitler (forming the American Nazi Party), and thanks to the First Amendment they were tolerated, if despised by most of the American people. But when Hitler invaded Poland in September 1939 they were pretty much silent. Compare that to today, when Trump, Pompeo, Greene and their ilk continue to voice their full support of Putin and their anti-Semitic, anti-democracy garbage here at home, even to the point of advocating all-out war in Europe. Former U.S. president Donald Trump worships Putin, because Putin is worth approximately200 billion and has the power to unleash unimaginable diasater upon the entire world—wealth and power that Trump hopes he can still attain. It's also no wonder that he is ecstatic over the crisis in Ukraine, as it has taken the focus off of his own crimes—and a nuclear conflagation between Russia and America would certainly eliminate any future investigations of Trump and his high crimes. President Biden should immediately banish Trump and his supporters to Russia, where they would be welcome with open arms. And hey, there's also plenty of room there for all of America's Red States.

 The Simulation Hypothesis Again — Posted Saturday February 26 2022 Somehow I missed the 2019 book The Simulation Hypothesis by MIT computer scientist Rizwan Virk, who also has a recent article on the subject in this month's Scientific American. I bought the book, and while it's an interesting read (Virk himself believes we're living in a simulated digital universe), at just three years old it's already somewhat dated in my opinion, as computer technology is progressing rapidly. The major downside to the simulation hypothesis or SH (like string "theory" and many other scientific conjectures) is that it cannot be tested or verified. And unlike string theory, it doesn't have a logical mathematical basis. However, at the same time this is also one of the SH's strengths, given the fact that many scientists (and smart people like Elon Musk) are adherents, despite the lack of supporting mathematics or physical evidence. If string theory were somehow confirmed, or if a workable quantum gravity theory were discovered, scientists would certainly rejoice amid the subsequent brief rash of media reporting. However, positive verification that the universe is a digital simulation would cause immediate worldwide social disruption, with longlasting impacts on all human activities, not to mention the impact on religion. Consequently, the SU is not just another scientific conjecture. Technologically, we already have 2-D computer-generated photos and videos that are indistinguishable from reality, and I'd put money down that within my remaining years we'll have 3-D technology (far surpassing today's virtual reality and augmented reality games) that also will be indistinguishable. The main problem at I see it will be the creation and development of a suitable 3-D projection technology that takes us out of the plane and into the world around us (and it will have to be truly 3-D, not like wearing those colored cardboard glasses that have progressed little since the 1950s). But I think this is possible even with 2-D technology, provided that it can support true binocular, perspective viewing. I like to imagine my house outfitted with windows that incorporate such a technology, so that looking out on a Cretaceous world filled with roaming dinosaurs or outer space vistas would add to my too-humdrum life (I'm 73, so better make that a high-tech nursing home). Depending on your scientific bent, you'll find the simulation hypothesis to be either fascinating to think about or just plain nonsensical, and I unreservedly recommend Virk's book.

 Not to Worry — Posted Friday February 25 2022 C'est une Croix qui de l'enfers nous garde! [Encore] C'est une Croix qui de l'enfer nous garde! [It is a Cross that protects us from hell!] — Gounod, Faust, 1859 I live in Pasadena, California, some 15 miles from the shadow of Russia's nuclear weapons (assuming Los Angeles is ground zero). I'm concerned, but not afraid. As the Scripture says, "Do not let your hearts be troubled, and do not be afraid." — John 14:27. All our angst, fear, anger and wishful retribution and desires for revenge will gain us nothing but ulcers and sleeplessness. Trust in God, and overcome the worries of everyday life, regardless of the potential coming calamity. God save us, save us all. Come, Lord Jesus!

 We Keep Trying — Posted Friday February 25 2022 When one considers the true nature of gravity, one is struck by the simplicity if the Einstein-Hilbert action $$S_{EH}$$ for empty space, which is $$S_{EH} = \int \!\! \sqrt{-g}\, \left(R - 2 \Lambda \right) \, d^4x \tag{1}$$ Extremalizing $$S_{EH}$$ gives the the ten Einstein field equations $$R_{\mu\nu} - \frac{1}{2}\, g_{\mu\nu}\, R + \Lambda g_{\mu\nu} = 0$$ which (where $$\Lambda$$ is the cosmological constant) have withstood every observational test for over 100 years, despite its overall simplicity. As Einstein himself surmised, (1) is just too dang simple (where are the kinetic terms and the potential terms?), and a more accurate theory must surely exist. Einstein thought that a generalization of (1) should incorporate electromagnetism, but all efforts to date in that regard have failed, as well as every attempt to explain quantum mechanics and dark matter (although $$\Lambda$$ almost certainly explains dark energy). To date, any number of generalizations of (1) have been proposed, with some more successful than others. Many have introduced scalar fields, while others have introduced a combination of quadratic, vector, spinor and tensor fields. Still others have restricted the symmetry of the metric tensor $$g_{\mu\nu}$$ and the Ricci tensor $$R_{\mu\nu}$$, all to no avail to date. These efforts all fall under the guise of modified gravity, but with only partial success they have also failed. So what's left? Dear God, reveal to us Your eternal plan, as we have no clue as to what the heck is going on.

 Trumpian Peace-Keeping — Posted Monday February 21 2022 Russia is now moving its troops into the Donetsk and Lukansk regions of eastern Ukraine, which Russia views as pro-Russian separist states longing for "freedom." The move is being called a "peace keeping" mission by Russian President Vladimir Putin. Former U.S. President Donald Trump has long supported Russia's militant policies, including that country's derisive attitude toward NATO. If Trump were still the current president, Putin would have already invaded Ukraine with Trump's blessings, and would have imprisoned or executed all of its anti-Russia leaders, including Ukrainian president Volodymyr Zarensky. Following the possible re-election of Trump in 2024, Putin would then no doubt be invited by Trump to invade the United States on a peace-keeping mission to protect the Trump-supporting Red States from the socialist(!!!) Blue States, which Trump has long wanted to utterly destroy for having voted against him. God save us, save us all. Update: Yesterday, Trump and Trump's former CIA Director and Secretary of State Mike Pompeo praised Putin as being "savvy," "talented" and "a genius." Most Red State political leaders are also praising Putin with similar glowing terms. They'll still be worshipping Putin when Ukrainian deaths go into the tens of thousands.

 Lumpy Universe — Posted Monday February 21 2022 Based on what might be called the ultra-large scale, the distribution of galaxies, matter and radiation in the universe appears to be absolutely homogeneous (the same as viewed from any location) and isotropic (the same as viewed in any direction). This allows the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and the Friedmann equations to be perfectly valid, and to a great extent (based on all observatiosn to date) they are indeed correct. However, on smaller scales (super galactic clusters, clusters, super voids, individual galaxies and certainly solar systems) we observe inhomogeneities in which these equations are either only approximately correct or fail completely. Meanwhile, there is an observed discrepancy (called the Hubble tension in the standard cosmological model relating to the rate of expansion of the universe, with some data indicating an expansion rate of 67 kilometers per second per megaparsec and others indicating an expansion of 73 kilometers/sec/megaparsec. The data sets of both observational methods appear to be consistent and reliable, but their error bars don't overlap. Could the assumed homogeneity and isotropy of the universe account for the discrepancy? There is no question that the FLRW model and the Friedmann equations are invaluable assets to modern cosmology, as we have no hope of modeling the universe on anything approaching a more realistic distribution model on smaller scales. Perhaps the next best approach would be to assume a kind of "lumpiness" in the distribution. Could this be the answer to the Hubble tension issue? A two-part series of new papers has been published that might provide an answer. Research fellow Obinna Umeh of the University of Portsmouth in the United Kingdom approaches the problem here and here. He finds that environmental effects associated with lumpiness (including the tidal deformation effect of local sources) might be contributing to the Hubble tension issue. But whether Hubble rate determinations based on cosmological microwave background data or Type 1a supernovae data definitively favor one or the other methods remains to be seen. I hope this problem is resolved in my lifetime, because it has a huge effect on the true fate of the universe.

 Equal Time! Equal Time! — Posted Friday February 11 2022 I worked in a lab with my future wife Munira from 1972 to 1974, and the lab's radio was mostly always playing rock music (Lord, how I got to hate "Mother and Child Reunion" by Paul Simon and "A Horse With No Name" by America). But our lab director was a classical music afficionado, and he would abruptly change the station to classical music while yelling "Equal time! Equal time!" Well, rock music and classical music both have their benefits, but in the craziness of America today "equal time" has a totally different meaning: Thanks again, Ruben Bolling.

 Enough! Get Serious, News People — Posted Friday February 11 2022 I don't watch much cable news anymore, but when I do it's usually CNN or MSNBC. I'm always amazed at the hosts, commentators and paid contributors who share their views on the latest outrages perpetrated by Donald Trump and his Republican supporters. I simply cannot understand how they can all be smiling and joking while they recount the unending horrors that are unfolding in this country, as if the insanity that's taking over America is somehow worthy only of frivolity, and as if it will go away like any other kind of news. Perhaps they're all taking it lightly because they know they're being highly paid to voice their invariably glib and witty opinions, and that their wealth will buy them comfortable, protected getaways to gated communities if things are really as bad as they are. I always found former conservative politician and current talk show host Joe Walsh to be particularly annoying when he was a Trump worshipper, but he seems to have realized how bad things have really gotten in his party. He explains how the left just doesn't "get it" in this Salon interview, although I still wouldn't put it past him that he too is just looking to capitalize on the madness overtaking America. Bottom line: the minority-hating democratic Dixiecrats of pre-1964 Civil Right Act America were outraged that Blacks, women and other minorities might be given an opportunity to experience the cultural freedoms and economic benefits of equality, and they abruptly switched over to the Republican Party when Richard Nixon and other Republican leaders successfully enacted the Southern Strategy, designed to reclaim total white rule in America. And for the past fifty years, it has not only worked, it has gotten much worse, worse to the point of outright insanity. While I admire and respect MSNBC's Rachel Maddow for her in-depth analytical ability and delivery, she may be the worst when it comes to her unintentional trivializing of the greatest-ever threat to American democracy. Just once, I'd like to see her and her colleagues sternly look into the camera with a straight face and say, "Americans, this is freaking serious business. If we don't stop it, it's the end of Amerca as we know it." But I'll tell you that my biggest fear, admittedly as selfish as it is, is that should he be re-elected in 2024, Trump—being the revenge-filled monster he is—will seek to punish the blue states, which provide far more to the federal budget than their red state counterparts. My federal taxes are already high enough, but one way Trump can punish us is to enact a new tax code that hits us even harder. Have a care!

 On Zeno's Paradox — Posted Thursday February 10 2022 Perhaps the first truly interesting puzzle the first-year calculus student encounters is the one known as Gabriel's Horn, because it has two unambiguous but mutually conflicting solutions. Consider the simple expression $$y = \frac{1}{x}$$ (Both the $$y$$ and $$x$$ axes go asymptotically to infinity, so consider the $$x$$-axis starting at 1.) If you rotate the curve around the $$x$$-axis, you get what looks like a horn: Now ask yourself what the surface area of the horn is. If $$x$$ extends from 1 out to infinity, some basic calculus shows that the surface area is infinite. Alternatively, imagine now that you fill this infinite horn with paint. You'll now find that the volume of the horn is a finite number. This is not too puzzling, but if you then pour the paint out of the horn, leaving a thin layer of paint around the horn's inside, you'll see that a finite amount of paint covers the horn's surface area. How can a finite amount of paint yield an infinite surface area? Only if the paint layer is infinitesimally thin, and that's the solution as I see it. A similar problem arises from one of Zeno's paradoxes: Hercules (or Atalanta) is racing against a turtle across a finite path, but because Hercules is much faster, the turtle is given a head start, beginning halfway through the course. By the time Hercules reaches the turtle's starting point, the turtle has moved on some distance away. By the time Hercules reaches that point, the turtle has moved on even farther. The paradox says that no matter how fast Hercules runs, he'll always be behind the turtle, assuming an infinite number of such steps. Of course, it's not a paradox at all, since the associated infinite series converges, and Hercules always wins. But in his latest article, physicist Ethan Siegel says hold on a second (so to speak). Although the decreasing distances in the paradox converge to zero, he argues that the sum of the times between each step might not converge. Siegel then goes into a discussion involving the so-called quantum Zeno effect, quantum tunneling and wave function collapse, which I find difficult to follow. Instead, I see distance and time connected through the conjugate variables $$x$$ and $$p$$ (momentum, or velocity) and $$E$$ and $$t$$ (energy and time), with momentum $$p$$ and energy $$E$$ related via special relativity. I can't quantify that, but maybe you have a better idea.

 Still Gorgeous After 3,350 Years — Posted Wednesday February 9 2022 The bust of the ancient Egyptian queen Nefertiti ("the beautiful one has come," ca. 1350 BC) continues to amaze and confound admirers, art critics and legal experts, ever since its discovery in December 1912. Meanwhile, archeologists are still looking for the great queen's mummy. My dentist (who's also an MD) is a native Egyptian who happens to be an expert art historian and researcher. He has personally examined the famed Nefertiti bust (now held at the Neues Museum in Berlin) in detail, and is familiar with all the physical, chemical and other forensic analyses that have been done to date on the antiquity. His verdict—it's just too perfect to be authentic, and he believes it's a clever forgery made by the bust's discoverer. On the other hand, he has also inspected the Shroud of Turin in Turin, Italy, which he believes is an authentic image of the crucified Christ. That's something that I, even as a Christian, find hard to accept, given the fact that individual snippets of the shroud have been carbon-dated to between the 13th and 14th century. I've been to the Neues Museum and to the Museum of Antiquities in Cairo, Egypt, and as a total layman I have to admit that the Nefertiti bust outshines everything else I've seen in terms of quality, artistry and preservation. I too am amazed that it supposedly withstood millennia on the floor of the ancient artist Thutmoses' ruined workshop in Amarna, middle Egypt, while dozens of other artifacts found near it were much worse off for wear. What's far more interesting, perhaps, is the journey the bust has made since its discovery and transport to Berlin, followed by two world wars (during which the bust was secreted in various safe locations), and efforts by Egyptian authorities to repatriate the antiquity back to its homeland, a story that is recounted in this fascinating Aeon article.

 McConnell's Nazi Ruse — Posted Wednesday February 9 2022 Amanda Carpenter is a political columnist for The Bulwark, author (Gaslighting America - Why We Love It When Trump Lies To Us) and frequent CNN contributor. I saw her this morning on CNN, where she was addressing Republican Senator Mitch McConnell's recent remarks regarding the censuring of two Republican Trump critics and the RNC's claim that the January 6 2021 Capitol insurrection by thousands of rabid Trump supporters was "legitimate political discourse," despite the fact that police officers were killed and injured, the building damaged and defaced, and that then-President Donald Trump had personally ordered the insurrection the morning of the attack. While McConnell admitted that the attack was a bloody, violent insurrection, Carpenter noted that it really made no difference as far as Republican policies are concerned. Consequently, Trump supporters can breathe easy again—the Republican insanity will continue on unabated, as if McConnell had said nothing. When I first heard McConnell's statement, I got the distinct impression that it was only a carefully worded attempt to give cooler heads the impression that the Republican Party is not completely insane after all. More importantly, even his tossing moderates a bone was countered by McConnell assuring the Trump base that nothing was really going to change, as he still believes the January 6 investigation is an overreaction to the event, that Trump might very well have won the 2020 presidential election due to voter fraud, and that he still plans to vote for Trump in the 2024 election. By mildly denouncing those Republicans who believe the insurrection was legitimate, in my opinion McConnell was resurrecting the old Nazi trick of killing your own to garner support for your cause. Thank you, Ms. Carpenter, for bringing this falsehood into the light of day.

 Rogue Black Hole in Earth's Back Yard — Posted Tuesday February 8 2022 Black holes seem to be everywhere today, but to date they've all been members of galaxies and other large multi-star systems. But as reported in this recent article in Scientific American, a rogue, solitary 7-solar mass black hole has been spotted roaming our Milky Way galaxy. Unambiguously detected by a large, diverse group of astronomers that had long suspected such rogues existed, there's no cause for alarm, as it's some 5,000 light-years away from Earth. The associated arXiv paper can be read here.

 America, the Waste Land — Posted Tuesday February 8 2022 April is the cruellest month, breeding Lilacs out of the dead land, mixing Memory and desire, stirring Dull roots with spring rain. Winter kept us warm, covering Earth in forgetful snow, feeding A little life with dried tubers. T.S. Eliot's famous poem The Waste Land is now 100 years old, and I can only wonder if it will survive the current rash of literature bannings and book burnings now being perpetrated upon America by Republican conservatives. After all, it deals subtly and not-so-subtly with death, despair, lust and sex (even abortion) and the futility, isolation and alienation of modern life. The poem was way over my head when I first read it in high school, although I recall it being something of a real downer. The poem is a difficult read even today given its confusing mix of historical, literary and cultural allusions and allegory, all set against the disillusionment that Eliot felt in the years immediately following World War I, "The War to End all Wars." I still struggle to comprehend the poem, even with the many analyses available on the Internet, but the overall feeling of inutterable despair tainted with a dash of hope is obvious. The poem also alludes to both the cruelty and pleasantness of memories, with our past lives (good or bad) being unattainable yet unforgettable at the same time. My wife's passing in 2019 makes my memories of the 42 years we had together both painful and enjoyable as well as inescapable. As whatever remaining months or years stretch before me, I am filled with despair for this world. My death will be a welcome end.

 I Just Don't Understand — Posted Monday February 7 2022 Does anyone remember former FBI Director Robert Mueller? Of course you don't, but after leaving the FBI he was appointed Special Counsel in the 2017-2019 investigation of former President Donald Trump and his alleged illegal ties with Russia. The allegations appeared to be based solidly on evidence that Trump conspired with Russia to personally denigrate 2016 presidential candidate Hillary Clinton and ruin her chances for election, among many other allegations based on phones calls that Trump made with Russian leaders, including obstruction of justice, money laundering, violations of unregistered foreign agent laws, false statements by Trump and his handlers to the FBI and Department of Justice, and widespread dissemination of Russian propaganda leading up to and beyond the 2016 election. While the evidence seemed overwhelming that Trump had broken numerous impeachable laws, and despite numerous indictments and convictions of Trump counsel members, Mueller was forced to concede that a U.S. President could not be charged with any crimes while in office. In short, Trump escaped justice. Do you also remember Democrats and progressive groups salivating over the seemingly imminent removal of Trump from office and his imprisonment? Of course you don't, either. But I see the same thing happening now regarding the January 6 2021 insurgency that took place at the Capitol, which resulted in four deaths and hundreds of federal officers injured and the desecration of the Capitol building itself. And despite video evidence of Trump ordering thousands of his supporters to attack the Capitol, criminal investigations have so far failed to convict Trump of any crimes (including incitement to commit crimes, sedition and treason). While a number of attackers have received what might be viewed as relatively minor punishments for their crimes to date, Trump has vowed to pardon anyone arrested in the Capitol attack should he return to office in 2024. People, we live in a different time in the country's history today, when an armed mob can kill and injure federal officers, construct a gallows on the steps of the Capitol building, openly threaten murder, destroy property and smear excrement on the building's inner walls, while the Republican National Committee declares the attack to be LEGITIMATE POLITICAL DISCOURSE. Dear God in Heaven, please save us from this insane Republican Party.

 Sometimes I Just Don't Get It — Posted Sunday February 6 2022 Maybe I'm just stupid (people keep telling me that), but aren't the mice in Maus supposed to be the victims of the Nazi cats? It's like the cats are the good guys trying to cope with the Capitol-attacking, anti-vaxxer mice: Oh, I get it now—it's the "alternative" Republican version.

 The True Tragedy of COVID — Posted Thursday February 3 2022 As of today, over 895,000 Americans have died from COVID-19 in less than two years, far in excess of the estimated 675,000 who died in the Great Influenza pandemic of 1918. It's now almost certain that the number will easily exceed one million before (and if) COVID ends. But just like the pandemic that swept the world a hundred years ago, it will likely be quickly forgotten, again assuming it ends. The comparisons between the 1918 and 2020 pandemics are never ending, but perhaps the most notable is the significant percentage of Americans who refused to take precautions (like wearing masks) or take available medications for reasons of denial, conservative politics or "personal freedom." Another popular comparison of COVID's impact involves American war deaths. The Congressional Research Service has estimated that the total number of war-related deaths (not just direct battle deaths) for the Revolutionary War, the War of 1812, the Mexican War, the Civil War, the Spanish-American War, World War I, World War II, the Korean War and the Vietnam war comes to about 1.26 million (including an estimate for Civil War Confederate casualties but not including much smaller numbers from 9/11, the Middle East and other hostilities). I don't know about everyone else, but it boggles my mind to realize that COVID deaths are comparable with all the war deaths that America has ever incurred throughout its history, yet there is a sizable percentage of Americans (I estimate 20%) that are willingly in denial over the disease, thinking that it either doesn't exist or that it is being confused with the flu or other common illnesses. I also contend that it's these same Americans who are the conservative Republicans that have fallen under the spell of former president Donald Trump, who infamously claimed that COVID was a "Democrat hoax." Sadly, that claim stuck with them, and now here we are today.

 "Pain and the Knife Are Inseparable" — Posted Wednesday February 2 2022 This morning, President Biden recommitted to his 2016 pledge for a cancer moonshot, a renewed effort to reduce American deaths by cancer by 50% over the next 25 years and to provide more resources for cancer victims and their families. America's original 1960s moonshot was the dream of President Kennedy to put a man on the moon by the end of that decade, which famously came to fruition in July 1969. In 2020 dollars, the cost of the Apollo program totalled some $25 billion, while the overall moonshot through that decade cost some$200 billion. Was it worth it? Well, we got some moon rocks to study (which showed exact similarity to those on Earth), we got the sugary orange drink Tang, which the astronauts supposedly consumed during their journeys, and a slew of other minor spin-offs in the engineering and technology fields. So no, it really wasn't worth it. It was just a consequence of the space race with the USSR and a chance to strut our stuff around the world. Eliminating or significantly reducing the incidence of cancer would be a much greater accomplishment, assuming it can be done at a cost that won't break the bank. President Biden has been encouraged by the results to date of genetically-based progress in the development of COVID-19 vaccines, and he has expressed hope that the same approach might be effective in eradicating or reducing cancer. However, to date some 20-30% of the American public has vowed not to take available COVID vaccines, either for themselves or their children, primarily because the vaccines have fallen victim to political hyperpolarization. Again, thanks to Mr. Trump and the Republican Party. You might remember the outbreak of HIV/AIDs in the early 1980s, which predominantly affected the gay population. Conservatives saw the disease as a punishment from God, who was responding to America's permissive attitude towards homosexuality. Many conservative groups actively opposed efforts to find effective treatments for the disease, even hoping that a cure would never be found. Before the advent of anesthesia in the mid-1800s, it was widely believed that the pain of life-saving surgery would permanently afflict mankind. "Pain and the knife are inseparable" was the call word in the 1958 Boris Karloff film Corridors of Blood. Again, disease and death were widely seen to be the consequence of a sin-ridden, fallen world. I believe that same attitude still exists within conservative groups in America today. While I haven't seen a formal response from the Republican Party regarding Biden's moonshot plan, it is still notable that the White House is only asking for an initial outlay of one billion dollars, no doubt due to fears of GOP opposition (which is probably waiting for approval by their de facto messiah, Mr. Trump). My wife passed away in 2019 after a lengthy bout with breast cancer. Biden's plan will come too late for her, but I hope it will not be too late for women living today, of whom some 300,000 will be diagnosed each year, with 50,000 dying of the disease. May God speed the moonshot.

 Nice Try — Posted Wednesday February 2 2022 Isaac Newton (1642 - 1726) is revered the world over as perhaps the greatest mathematical physicist of all time, but few people know that he was also a devout Christian who probably spent more of his time studying the Bible and writing Christian articles and tracts. An article in today's Big Think reminded me of a science fiction story I read many years ago. It told how a scientist, despondent over how much time Newton had supposedly wasted exercising his long-held Christian faith, thought Newton would have been much more productive in science if he'd had access to something as simple as a pocket calculator. So the scientist uses his time machine to travel back to 1660s England, and he presents Newton with the calculator. "What's this thing?" asks Newton, and the scientist tells him it's a device that will allow Newton to do complex mathematical calculations instantly, thereby giving Newton the ability to greatly expand his discoveries in math and physics. "Let me show you an example," the scientist says. He punches in a bunch of long random numbers, doing a variety of complex multiplications and divisions. The calculator's output then displays the answer, which unfortunately is 666. Horrified by this apparent evidence that the scientist is Satan himself, Newton kicks him out of his laboratory and resolves to devote much more of his time to his Christian faith. I can't remember where I saw this story, but it might have been an early issue of the now-defunct magazine Omni from the 1970s.

 Does Spacetime Emerge From a Deeper Reality? — Posted Monday January 31 2022 The February 2022 issue of Scientific American has a lengthy article on how spacetime—that apparently smooth, continuous 4-dimensional network of time coupled with the three dimensions of length, width and height—might be an emergent phenomenon that springs from some physical process that is deeper and more fundamental than quantum physics and general relativity. The article describes in some detail how one particular version of string theory (the so-called AdS/CFT correspondence) might provide the necessary link to that emergence. Modern string theory posits many additional space dimensions to the usual three, and while none of those dimensions have been observed it brushes that away by claiming that those extra dimensions are "compactified," or curled up in sizes akin to the Planck length (roughly $$10^{-35}$$ meter), making them impossible to detect. Also, string theory demands that the theory known as supersymmetry is real, which itself requires "mirror" particles to those already in existence. But a few of those mirror particles have predicted energies well within the detection range of the Large Hadron Collider, which to date has definitively not seen them. While many physicists have given up on string theory, many more have simply moved the goalposts, thinking that since the theory must be true the estimates for mirror particle energies must have been underestimated. String theory is one example of an extra-dimensional theory known as Kaluza-Klein theory, first postulated by the Prussian physicist Theodor Kaluza in 1919. Kaluza wondered how Einstein's general theory of relativity might change if there was a single extra space dimension, thus bringing the total to five dimensions. He was able to show that the fifth dimension could incorporate all of Maxwellian electrodynamics, and for a brief time Kaluza's idea seemed to be the answer to the hoped-for unification of gravity and electromagnetism. The mathematics of Kaluza's theory is fairly understandable, and seems to miraculously explain electrodynamics as a consequence of Einstein's gravity theory, but it too requires some lucky guesswork that cannot be proved. Specifically, the $$4 \times 4$$ symmetric matrix associated with the fundamental metric tensor $$g_{\mu\nu}$$ of general relativity is expanded to the $$5 \times 5$$ matrix $$\bar{g}_{\mu\nu}$$, with the lower row and righthand column of the matrix containing elements of the electromagnetic 4-vector $$A_\mu$$ (which is also sprinkled among the other components of $$\bar{g}_{\mu\nu}$$). The theory lucks out because this expanded tensor seems to be unique, has the required property that $$\bar{g}_{\mu\nu}\, \bar{g}^{\mu\lambda} = \delta_{\,\nu}^\lambda$$, and that no other combination seems to work. While the extra dimensions of the AdS/CFT model provide a convenient way of "enclosing" all the gravity in the universe (thus making the universe finite), it also has the disadvantage that it holds only in anti-de Sitter space. This is totally unlike our universe, which is nearly de Sitter now and is approaching a pure de Sitter description as the universe expands. This and other disadvantages in current string theory models make them appear to be purely mathematical with either unphysical or unprovable aspects. Noted Columbia University physicist Peter Woit is perhaps the most vocal opponent of string theory, and he often posts his views on his longtime website Not Even Wrong. The Scientific American article also addresses loop quantum gravity (LQG) as one notable rival to string theory. LQG has provided its supporters with a few correct calculations involving the thermodynamic properties of black holes, but little else beyond what might be generously called beautiful mathematics.

 For Brilliant Four-Year-Olds — Posted Friday January 28 2022 Why, a four-year-old child could understand this report! (Run out and find me a four-year-old child. I can't make head or tail out of it.) — Groucho Marx in Duck Soup, 1933 In all graduate-level textbooks on general relativity, the quantitative analysis of gravitational waves depends on assuming a weak-field metric $$g_{\mu\nu}$$ of the form $$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$$, where $$\eta_{\mu\nu}$$ is the flat-space Minkowski tensor and $$h_{\mu\nu}$$ is a weak perturbation. This allows Einstein's field equations to be linearized, vastly simplifying the analysis. It never once occurred to me that someone would attempt to do an analysis using the full, non-linearized field equations, which I assumed was impossible. In this new arXiv paper by a group at the Institute for Theoretical Physics in Zurich, the impossible has apparently been done. However, the authors state that "these notes provide a student-friendly introduction to the theory of gravitational waves," but at 120 pages the paper is hardly a collection of "notes," nor is it "student-friendly," as like Groucho I can't make head or tail out of it. Maybe you can.

 Can America Do "The Splits"? — Posted Thursday January 27 2022 With Justice Stephen Breyer formally announcing his retirement today, President Biden will get his chance to appoint a black female to the Supreme Court. CNN is predicting that the forthcoming event will be a "titanic battle" between Democrats and Republicans, which it probably will be. While I can't see Senate Minority Leader Mitch McConnell pulling another "Let's wait for the election" stunt like he did before with former President Obama (which deprived Obama of the Merrick Garland appointment), I still see it as an opportunity for the GOP to go all out on its present course of getting all it can while the getting's good. And with the upcoming midterm elections looking like a Republican takeover of the Senate and House, it looks increasingly likely that Biden's appointment will be met with a stone wall. Meanwhile, you might have noticed that the Red States are abandoning the Constitution and federal laws in favor of a renewed "states rights" approach to state legislation, including the banning of books, family planning, voting rights, minority rights and even the teaching of history in public schools. A number of these states have even proposed secession from the Union, and as doubtful as that might be it appears they are moving in the direction of the medieval "city-states" Balkanization approach to self-governance. Indeed, Texas is already commandeering national guard troops to its southern border (a blatent political stunt by Texas Governor Greg Abbott to bolster his re-election chances), much to the delight of minority-hating conservative Texans. Secession or city-state governance might sound great if yer a librel-hatin', freedom-luvin' patriot, but the reality is that the Red States collectively take a lot more than they give to the federal budget, and they would collapse overnight if federal funds were to be taken away. But as the article in the above Atlantic link notes, it appears highly unlikely that the Red State drive toward self-governance can be reversed. President Biden has little ability to enforce federal-level legislation on these states (it also appears that he won't be around after 2024), and the Democratic Party (with its tenuous current hold on the Senate and House) is both too weak and too spineless to do anything about it.

 On Hyperpolarization — Posted Wednesday January 26 2022 New York Times contributing writer Thomas Edsall claims that "America is split", hardly news when the evidence has been around for at least a decade now. But Edsall points out a range of issues and conditions that have led America to where it is today, also referencing the views of others that support his claims from a number of psychological and cognitive interpretations. Issues that normally would bring the country together are now lacking—we have no external threat to rally and unite the left and the right (even the threats posed by Russia, China and North Korea have been marginalized to a great extent, thanks to former President Trump's habit of praising their leaders). Meanwhile, identity politics, the diversity of races and ethnicities and the perceived threat of women and minorities usurping the privileges of what had once been centuries-long advantages of white men in America are what's really driving the wedge between the right and the left. Edsall also notes that extreme monetary and cultural inequality are also to blame. In the scant two years of the COVID pandemic, American billionaires more than doubled their fortunes—an increase representing in excess of a 100% profit on their investments, with little to no risk—which compares with the paltry average of 0.3% interest that 99% of Americans earned in their savings during the same period. Still, conservative Americans are led to believe that their time will come, if they only adhere to and approve of the outright greed and avarice of the super-rich. So what's to be done? I myself think that America will never be truly united anymore, given the extent of the hyperpolarization that exists and the rightwing media lies that are fueling it. I'm reminded of an old Outer Limits episode from 1963 that offers a possible cure for our polarization ailment. In The Architects of Fear, scientists genetically alter a human to become the represntative of an invading malevolent extraterrestial species, in the hope that the threat of an invasion from space would unite the world and avoid nuclear war. Spoiler: It didn't work, and it wouldn't work today.

 On Symmetry and Stuff — Posted Tuesday January 25 2022 Ethan Siegel's latest Starts with a Bang post talks about symmetries in physics, how they work and how they sometimes fail. Mathematical symmetries play a huge role in the principle of least action that I talked about in my blog of January 22, but symmetry as an unfailing guiding principle seems to not always work. German physicist Sabine Hossenfelder's excellent 2020 book Lost in Math - How Beauty Leads Physics Astray analyzes a number of symmetry principles (which are often referred to as beautiful) and how and why they fail. Perhaps the most persistent mathematical symmetry is that of time invariance, which explains why physical laws do not change with time. According to Noether's theorem, time invariance is responsible for the conservation of energy, a physical law that has served physicists well for hundreds of years. But Siegel points out that this law fails when one is dealing with an expanding universe—as spacetime expands, photons of light get stretched, with the result that their longer wavelengths lead to lower energies according to $$E = h c/\lambda$$. So where does that energy go? Apparently, it goes nowhere, because energy is simply not conserved. I always believed that the lost energy of stretched photons was somehow "absorbed" into the spacetime bulk, which in turn gives rise to dark energy. This makes perfect sense to me, but my discussions with Caltech physicists have botched the idea for various reasons. But I'm still not convinced. Strictly speaking, conservation of energy can be traced to ordinary partial derivatives. But in general relativity, partial derivatives are not covariant; instead, one uses covariant derivatives. The covariant differentiation operator is usually expressed as $$\nabla$$, but I prefer double subscripted bars, with a single subscripted bar representing ordinary differentiation. In Einstein's gravity theory, energy is represented by the energy-momentum tensor $$T^{\mu\nu}$$, whose covariant derivative vanishes according to $$\nabla_{\nu} T^{\mu\nu} = T_{\,\,\,\, ||\nu}^{\mu\nu} = T_{\,\,\,\,|\nu}^{\mu\nu} + T^{\mu\lambda} \, \Gamma_{\,\lambda \nu}^{\nu} + T^{\lambda\nu} \, \Gamma_{\,\lambda \nu}^{\mu} = 0$$ where the $$\Gamma$$ terms have components associated with the gravitational field. There's simply no way to make them vanish without removing gravity (as in flat spacetime), and so energy is not conserved in Einstein's gravity in the usual sense. However, in de Sitter spacetime (which our universe appears to be turning into) there's no matter or radiation, just dark energy. If we were to introduce a single photon, the exponential expansion of de Sitter space would also stretch it out. This makes me think that either dark energy is indeed the repository of lost photon energy, or that the $$\Gamma$$ terms include the parameter $$\Lambda$$ usually associated with dark energy. So I'm still stumped.

 Oh, the Poor Fly — Posted Monday January 24 2022 One of my favorite stories involving the drop-dead brilliant Hungarian-American mathematical physicist John von Neumann (1903-1957) is this one, told in the latest Quanta article. While von Neumann instantly solved the puzzle in his head (it involves a converging infinite series), he apparently didn't notice the obvious solution. I first saw this puzzle around 1968, when I was studying infinite series in calculus. I didn't see the obvious solution either, and it took me hours to figure it out. Oh, if I only had a brain.

 Is Gravity Quantum in Nature? — Posted Monday January 24 2022 The Aharonov-Bohm effect refers to the quantum-mechanical phase shift of a charged particle in the complete absence of an external magnetic field $$\mathbf{B}$$. The phase shift is due solely to the non-zero vector potential field $$\mathbf{A}$$ associated with the internal magnetic field of a solenoid via the Maxwell relation $$\mathbf{B} = \mathbf{\nabla} \times \mathbf{A}$$. Even with $$\mathbf{B} = 0$$ outside of the solenoid, the potential field persists. The effect was first described in a famous 1959 paper by the physicists Y. Aharonov and D. Bohm, which demonstrated that $$\mathbf{A}$$ was a real field, and not just a convenient mathematical trick used to calculate the magnetic field $$\mathbf{B}$$. Recently, a similar experiment by Stanford physicist Chris Overstreet and colleagues was performed in which a non-uniform gravitational field induced a quantum-mechanical phase shift in pairs of rubidium atoms, demonstrating for the first time that gravity might have a quantum foundation. Classically, gravitational and electromagnetic forces are very similar, varying with respect to the product of their masses (charges) and the inverse square of the distance between them, respectively. The scalar electric potential $$V$$ is also very similar to the scalar gravitational potential $$\Phi$$, with each varying with respect to the inverse of distance. However, electromagnetism is different in the sense that electric charge can be positive or negative, while a gravitating mass has only a single "charge." In addition, electromagnetism also involves the 3-vector potential $$\mathbf{A}$$, whereas gravity has no such similar quantity. Nevertheless, before the advent of the strong and weak nuclear forces, gravity and electromagnetism were the only forces of Nature known, and many attempts were made to link the two through some fundamental unifying theory. However, when quantum theory came along it was found that electromagnetism could easily be incorporated into the theory, but gravity remained aloof and uncooperative, a situation that persists to this day as arguably the greatest problem in physics. The magnetic field is related to the vector potential via $$\mathbf{B} = \mathbf{\nabla} \times \mathbf{A}$$, but experimental detection of the vector potential was always deemed impossible, and it was considered only a mathematical artifice that could be used to simplify calculations of $$\mathbf{B}$$. Indeed, $$\mathbf{A}$$ was considered a "hidden" quantity that for some reason Nature had chosen to keep secret. In 1986, the Aharonov-Bohm effect was quantified in a brilliant experiment by Tonomura et al. using a microscopic iron filament as a solenoid. Still, there are signficant differences between the Tonomura and Overstreet experiments. Electromagnetism is not gravity, and there is no gravitational analog of the $$\mathbf{B} = \mathbf{\nabla} \times \mathbf{A}$$ relation, just as there are no true analogs of $$\mathbf{E}$$ and $$\mathbf{B}$$ for gravity. But for the first time scientists have an intriguing connection between the gravitational constant $$G$$ and Planck's constant $$\hbar$$, and future research bears watching. [The Overstreet paper appears in the January 14 2022 issue of Science magazine, and is available online but behind a paywall. For an explanation of the Aharonov-Bohm effect using a simplified path-integral approach, see this.]

 Pandemic Amnesia — Posted Sunday January 23 2022 As of today, some 860,000 Americans have died from COVID-19 and its delta and omicron variants out of a total of some 69.3 million infected people. With 330 million Americans, that comes out to a death rate of some 1.24% of those infected with the virus, or about 0.26% of the total population. By comparison, the Centers for Disease Control and Prevention (CDC) in Atlanta reports that the death rate due to influenza is about 16.3 per 100,000 population, or roughly 0.016%. That makes COVID 0.26/0.016 = 16 times deadlier than the flu. Yet despite the evidence there are millions of rightwing Americans who believe COVID should be accepted as nothing worse than the flu or a cold, no doubt a result of President Trump's early 2020 proclamation that COVID was a "Democrat hoax." Nevertheless, attitudes toward pandemics like COVID have been similarly marginalized in the past. The great influenza pandemic of 1918 killed an estimated 50 million people worldwide, but when it abated two years later its memory was all but forgotten. Of the several books I've read about that pandemic, the best by far is the best-selling 2018 book Pale Rider - The Spanish Flu of 1918 by Laura Spinney, who also noted a tendency on the part of people to forget the disaster that befell the world. Before that was Laurie Garrett's also excellent The Coming Plague, which in many ways predicted a COVID-like pandemic when the book was published in 1995. It too noted that the 1918 influenza pandemic was quickly forgotten. It is probably a stretch to state that the Black Death of 1348—which killed upwards of half of Europe—was also quickly forgotten, but the tendency for impacted populations to try to put world-changing disasters behind them is likely a truism. But what's changed from then to now is the impact of instant mass communication and social media on the public's understanding, perception and reaction to the current COVID outbreak. I'm guessing, but I would estimate that 20% of Americans either do not believe COVID exists or that it poses only a minor threat to their health; consequently, they refuse to get vaccinated, wear masks or avoid crowds. These are the people who are responsible for America's sluggish vaccination rate, which remains below 65% despite the rates of other advanced nations, which are at or greater than the herd immunity level. This is not "pandemic amnesia," but a willful, ignorant or arrogant attempt to circumvent accepted or mandated public health policy designed to protect not only their lives but those around them. The attitude of many of the 20% is that if they get sick, so what—they'll either get better, end up in the hospital or die. This ignores the fact that America's hospitals are already overwhelmed with patients in varying degrees of sickness, and it also overlooks the excessive costs to society to treat them: The nation of Israel is already mandating a second booster shot, with the effort seeming to be to provide an end to the virus once and for all. Epidemiological evidence indicates that it provides limited additional protection, although there has been a five-fold increase in the level of COVID antibodies. It's no wonder that America remains the laughing stock of the world (the former ultra-conservative pollster Mr. Luntz now refers to America as a "s**tshow"). Thank you, Mr. Trump.

 Why Believe in a Creator? — Posted Saturday January 22 2022 Did the universe come into existence on its own (like a random quantum fluctuation that got out of control) or was there a Creator behind it all? Modern physics and cosmology has considered both arguments in detail, with the general consensus that however the universe came into being, no Creator was needed. Most scientists tned towards this view, while most theologians believe God did it. Proof of the existence or non-existence of God is probably impossible, so both sides continue to promote their positins. For me, there are two primary reasons for believing in a Creator, both of which are grounded in rational scientific thinking. The weaker argument is the so-called fine tuning argument, which states that if any one or several of the twenty fundamental constants of Nature (like the speed of light, the fine-structure constant, electric charge and electron mass) were different by more than a fraction of a percent, then the formation of the universe as we know it would have been impossible, not to mention the formation and propagation of complex life forms. But this argument can be negated by the multiple-universe or many-worlds theories of modern cosmology and quantum physics, in which bubble universes or parallel worlds might spontaneously occur due to quantum fluctuations and/or wave-function collapse scenarios. Either of these theories could give rise to universes having vastly different physical constants than our own, with some being stable or unstable. If an infinite number of such universes were possible, then it is statistically certain that at least one would be our universe. The fine-tuning argument is presented in countless philosophical papers and YouTube videos, the most recent being this discussion between Robert Lawrence Kuhn of Closer to Truth and the noted Jesuit priest and philosopher Robert Spitzer: But to me the most convincing evidence of a creator God is the stationary-action principle, better known as the principle of least action. "Action" in physics is a quantity having the units of angular momentum (energy $$\times$$ time, or equivalently momentum $$\times$$ position). It's invariably presented as an integral over all applicable levels $$n$$ of space and time, $$S = \int \! \mathcal{L} \, d^n x$$ where $$\mathcal{L}$$ is a scalar Lagrangian density that incorporates various combinations of classical and quantum quantities, which usually can be broken down into potential and kinetic energy parts. The action $$S$$ is just a number, but that number has a unique minimum that corresponds to a particular physical law of Nature. For example, the minimum of the exceedingly simple action $$S = \int \! \frac{1}{2}\,m \dot{x}^2 \, dt$$ gives the Newtonian law of motion for a free particle, $$\frac{d(mv)}{dt} = 0$$ More complicated actions have been identified for any number of physical applications. The Standard Model of physics is described by perhaps the most complicated action known, and to date it has never failed to correctly predict countless classical and quantum experiments. The minimum of any action can be obtained by the equally amazing variational principle, which is roughly akin to taking the derivative of the action and setting the result to zero. Even given the possibility of an infinite number of possible universes, I can see no logical reason to believe that the action principle would result as well. It beautifully describes Nature at its most efficient level while, by comparison, a universe popping up out of a random quantum fluctuation or wave-function collapse would at best be chaotic and incapable of displaying such beauty and order. Furthermore, although beauty is admittedly a subjective human notion, only a beneficent Creator would conceive of a universe whose physical laws are grounded on such precise mathematical harmony and order.

 Friedmann — Posted Saturday January 22 2022 Alexander Friedmann (1888-1925) was a Russian cosmologist who is credited with the mathematical discovery of the expanding universe, a concept that was proven observationally by the American astronomer Edwin Hubble in 1929. Today there is no question that the universe is expanding, but its rate of expansion and its ultimate fate are still open to question. Most cosmologists believe that the expansion rate is actually increasing due to dark energy based on (to me, somewhat questionable) observations of Type 1a supernovae, but a minority of researchers feels that the expansion may eventually halt and reverse, leading to a collapse in the far distant future. Einstein famously believed in a static universe, and in 1917 he introduced the cosmological constant $$\Lambda$$ into his gravitational field equations, which provided the universe with a fixed constant radius. But Friedmann's analysis showed Einstein was unequivocably wrong—the bare field equations led to a universe that had to be either expanding or collapsing, and even with a finite $$\Lambda$$ the universe would be unstable, again leading to expansion or collapse. Friedmann's 1922 work resulted in two fundamental equations that today form the foundation of much of modern cosmology. They each involve the Hubble parameter, which is primarily responsible for the fate of the universe. The equations take into account all forms of matter and radiation (including light, dark energy, dark matter and neutrinos, as well as the curvature of the universe). The derivation of the Friedmann equations from Einstein's 1915 gravity theory is not too difficult, but you can skip the derivation and just consider the inherent meaning of the equations, which will give you an good idea of what's likely going to happen to our universe. While stopping for a bite to eat at a railway station in late 1925, Friedmann unfortunately ate a contaminated pear and died from a bout of typhus at the young age of 37. But perhaps he was spared from the great Stalinist Purge of a decade later, when hundreds of Russian astronomers and cosmologists were executed either because of their anti-Marxist views or even their scientific discoveries (for one notorious and tragic example, read the story of Matvei Bronstein). Note: Since publication of the equations, the time-dependent radius of the universe has been expressed as $$a(t), S(t)$$ and $$R(t)$$, the latter often being confused with the Ricci scalar $$R$$ (so don't let the above article confuse you). It can be shown that if the Ricci scalar is a constant, the universe will expand exponentially forever. However, if dark energy is quintessent (that is, dependent on time). the universe might indeed recollapse.

 Glad and Sad — Posted Wednesday January 19 2022 Following my wife's death two and a half years ago, I converted what I thought were all our 8mm video cassettes to digital format (over 150 hours of video). But yesterday I came across two more that were buried in a box in the garage. One shows my wife teaching beginning Arabic to our younger son, dated August 10, 1999. It's two hours long, and I've been watching it all afternoon. I'm happy to see and hear my beautiful wife again (four years before her breast cancer diagnosis), but at the same time it's another stark reminder of what I lost. God bless and keep you always, dearest Munira.

 ArXiv or ViXra? — Posted Friday January 14 2022 I'm a big fan of modified gravity (MG) theories, and I regularly read new technical articles dealing with MG as a viable alternative to dark matter and dark energy. But it seems most everything to date has been explored, from MOND, to Weyl $$R^2$$ theory, to scalar-vector-tensor theory, to string theory and beyond. Nothing has worked, but there's one thing left: letting the Newtonian constant $$G$$ be a function of time, $$G(t)$$. This idea is considered in a new paper available on the free repository website arXiv.org. Years ago, when I wanted to read a new research paper on some subject, I would got to Caltech's Milliken Library, which has just about everything. Then in 1991 arXiv came along, courtesy of Cornell University, which today posts preprints online of new, recent and old papers on most scientific and mathematical subjects of interest. But the sheer popularity of the site has presented problems with respect to its paper review and acceptance protocols, not to mention the ability of its limited staff to handle the volume of material being submitted to it. This recent Scientific American article discusses these problems in detail. Legitimate researchers who have experienced frustration with arXiv have chosen to submit their work to its evil twin viXra.org (as I have done), despite viXra's reputation (often earned) of being a repository for crackpots. But arXiv's authors have often been just as crackpottery, given the number of papers lacking data or evidence of any kind to back up their authors' conjectures. Still, arXiv is the place to go if you want to know what's happening research-wise, or if you don't have access to paid sites such as Nature or Physical Review.

 Just Don't Look Up, and Everything Will Be Okay — Posted Friday January 14 2022 There's an old The Simpsons episode (I forget which one) where Homer Simpson, having created some fresh new disaster, hides in the closet, waiting for his wife to fix everything so he can come out again. This is essentially the plot of the Netflix movie Don't Look Up, which is now the most viewed Netflix movie ever. I watched the film late last year, and on December 30 I posted a few thoughts on it. While the film deals with the imminent destruction of Earth due to a planet-destroying comet, the film is in reality an allegory of humankind's collective denial of global climate change. The film's title is cleverly appropriate, as it encapsulates much of what is wrong with conservative reactionaries in this country today: if you stay ignorant of the facts, all your problems will somehow magically go away. This month's Scientific American addresses the issue by presenting five myths, all of which deal with the ignorance or rejection of scientific truth. My favorite is Myth # 1: If science isn't 100% certain, then you can choose to simply ignore it. Nothing is absolutely certain, but when something is 99.78% certain (as in the movie scientists' prediction of the comet destroying the Earth), it should at least provide reason for pause. But no: in the film, that 0.22% uncertainty provides a plausible reason to first deny what's happening, then to see the event as an economic opportunity, then to make a half-assed effort to deal with it, and finally as something that will hopefully just go away. Spoiler: at the end of the film, the Earth is destroyed, at which point 99.78% becomes 100%. In the book of Genesis, God promised never to destroy the Earth again with water, but He hedged that promise by leaving open pretty much everything else. At this time there doesn't seem to be a horrific comet or asteroid headed our way, but climate change, thermonuclear war and even fact-denying stupidity and authoritarianism remain in the offing.

 Medicinal Cannibalism, or Hey, Who's the Barber Here? — Posted Monday January 10 2022 Noted YouTuber Joe Scott talks about everything, from string theory to quantum mechanics and beyond, but he also addresses more mundane topics, like human ignorance. In this video, Scott shows us the dangers of ignorance that were common in the Victorian era, mostly dealing with radium-infused health drinks, opium-soaked tampons, morphine-laced soothers for cranky babies and other miracles of that time, including the health benefits of grinding up ancient Egyptian mummies for human consumption. It's nice to know that the current Republican Party does not wish to take us back to those days; instead, they plan to take us back to the 13th century, when a scientist could be burned at the stake for heresy.

 Ted, You're Back in the Fold — Posted Friday January 7 2022 Senator Ted Cruz (R-Texas) was recently under attack by his fellow Republicans for calling the January 6 2021 insurrection on the Capitol a "violent terrorist attack." But he quickly realized his mistake when he was corrected by Fox News media god Tucker Carlson and so he backtracked, calling his remarks "dumb" and taken out of context. What Cruz really meant to say was that the event was either A mass hallucination A happenstance occurrance involving peaceful Trumpian patriots who just happened to be gathered near the Capitol A large mob of armed, minority Black Lives Matter insurgents dressed in white-face An army of thousands of Antifa fanatics disguised as Republicans A large disorderly crowd of Biden-led Democrats seeking the blood and adrenochrome of children they heard were touring the building Heroic Trump supporters seeking to stop a wild child sex-ring party being conducted by Nancy Pelosi, Hillary Clinton and other Satan-worshipping Democratic leaders It was a close call, to be sure, but Cruz has now been fully brought back into good standing with the GOP.

 Can You Imagine — Posted Sunday January 2 2022 Is an American right-wing dictatorship possible in the foreseeable future of this country? Some credible people believe it is indeed not only possible, but even probable. The American electorate—mostly the liberals—has largely chosen to ignore what's going on politically, provided their creature comforts are being met, while current Democratic leaders seem to be shell-shocked into catatonic inaction by the ongoing god-like popularity of Donald Trump, the seemingly perpetual COVID pandemic, inflation, the rise of worldwide authoritarianism and other problems. Consequently, there's little doubt that Biden and his team will not survive the 2022 and 2024 elections. Meanwhile, Georgia Congresswoman Margerie Taylor Greene has called for a "national divorce" of the Red and Blue states (which I kind of agree with), and her likening of Democrats to "termites" suitable only for eradication and her misinformation campaign regarding the COVID pandemic has resulted in Twitter permanently suspending her account. But can you imagine Donald Trump being re-elected in 2024 and, like China's Xi Jinping, proclaiming the end of term limits and himself dictator for life? And can you imagine Rep. Greene being elected Vice President or appointed Secretary of State? I sure can, and if you can't then you're no better than the Democrats who also cannot imagine the end of American democracy.

 Unforgettable — Posted Friday December 31 2021 With little to do today (because the local streets are crowding up with Rose Parade visitors), I watched the otherwise forgettable 1933 film Flying Down to Rio, memorable only for two reasons. One, it's the first screen teaming of dancers Fred Astaire and Ginger Rogers; and two, it features a bit part played by silent-era Our Gang's Mary Kornman (1915-1973), who innocently utters the deathless line What do these South American girls have below the equator that we haven't got? I have most of the old Our Gang films, and Mary's wonderful in all of them, but this always cracks me up. As for the dancing, I've always wondered why it was so darn entertaining in those days. To me, dancing is a complete waste of energy and time.

 A Geeky New Year's Physics Puzzle — Posted Friday December 31 2021 I received an email recently regarding an old paper I posted here some time ago, demonstrating that the special theory of relativity is responsible for inducing a fictitious magnetic field around a thin current-carrying wire. While the paper is technically correct, it assumes a highly idealized wire that is carrying identical negative and positive currents in opposite directions. This is the standard picture in which relativity is explained as the reason for the apparent magnetic field around the wire. The emailer noted that a real wire consists of a fixed lattice of positive ions (copper, for example) surrounded by valence electrons that are free to move about. When the wire is connected to a battery, the electrons then move in the direction of the battery's positive end, but the positive ions remain fixed in the lattice. The question is then: if a stationary positive charge is introduced near the wire, why doesn't it see the charge density of the moving electrons increased due to the Lorentz-Fitzgerald contraction, with the charge then moving toward the increased electric charge of the wire? The situation addressed in the email is as shown here: where the positive charge $$q$$ is stationary with respect to the wire, which is carrying an electric current to the right. Although the moving electrons are moving at a velocity $$v$$, the velocity of any single electron (called the drift velocity) is actually very small (typically 0.001 cm/s) due to the thermal energy of the electrons and the wire's resistance, which bounce randomly all over the place, even glancing off and even interacting with the fixed positive ions. But there is a net velocity to the right as shown, and even if this velocity is small the Lorentz-Fitzgerald contraction will reduce the size of the electron field, increasing their negative charge density. But experiment shows that the charge $$q$$ doesn't move, although it should react to the increased electric charge of the wire. Now consider the positive charge $$q$$ moving to the right with the same velocity as the electrons: This is the lab frame, the point of view of the experimenter, and she now sees the charge moving away from the wire, as if the wire had somehow acquired a net positive charge due to the electric current. The experimenter is then led to believe that a magnetic field B exists around the wire, and the motion of the charge $$q$$ causes it to be repelled due to the Lorentz force law $$F = q v \times B$$. But now consider the point of view of the charge (the charge frame), which moves to the right at the same velocity as the electrons: Now the charge and the electrons appear to be stationary, but the positive ions now appear to be moving to the left at the same velocity. Now the charge sees a Lorentz-Fitzgerald contraction of the positive ion field, with a corresponding increase in the ions' charge density. The charge now should move away from the wire, since like charges repel. This is precisely what happens in every given experiment. So we seem to have two possible situations, with the charge $$q$$ moving both toward and away from the wire depending on one's point of view. But special relativity says that all reference frames are equivalent, so therein lies the problem: which is the correct explanation? Like I did, you can check any physics book you like (even Feynman's), and it will invariably assume the same idealized case of two oppositely charged currents flowing in the wire as I assumed. You can also look at any number of YouTube videos that address the problem, and you'll see the same thing. There are a few videos that try to explain away the issue with a single current, but they seem to be grasping at straws (this one uses a "golf course" analogy, which I find ridiculous). For the life of me, I could not answer the question posed by the emailer. Since electrons are elementary particles, maybe there's some quantum physics involved. Or maybe it's just the fact that the electrons in the wire are free to bounce all over the place (while the positive ions are fixed in their lattice), so that some combination of thermal effects and special relativity is involved. Or maybe there really is a magnetic field that does not spring solely from the relativistic effect. Comment: After thinking it over, I've realized that this problem is way too simplistic—it isn't even classical electrodynamics. It says nothing about the Poynting vector, about electrical energy or anything remotely having to do with electromagnetism. It's really just a mechanical model, and the application of special relativity seems out of place.

 Don't Look Up — Posted Thursday December 30 2021 I saw the new film Don't Look Up yesterday, and while it has been touted as a parody of climate change denialism, I found it to be more closely aligned with the 2006 Mike Judge film Idiocracy, which deals with a future America in which total morons have taken over. In Don't Look Up we have both intelligent and cartoonishly idiotic players who exhibit one form of weakness or another, although the scientists generally come out on top of things. The film's parody of nonsensical and morally unconscious media lords (Elon Musk-types and Paris Hilton-types) abounds, but in the end it's all about human beings in total denial about their mutual total annihilation by an Earth-impacting comet. As the Scientific American article notes, a life-ending comet strike would be much quicker than the life-ending effects of climate change, but the same denialism aspect is present, down to the Fox News-like commentator who notes that the biggest news story of the day is "topless urgent care nurses." More humorous than disturbing, Don't Look Up (a sly reference to Nancy Reagan's pathetic Just Say No mantra or Fox News' "Just ignore the facts" approach to everything), the film will likely be filed alongside disaster flicks like 2004's The Day After Tomorrow and 2012's 2012.

 Some Graphs — Posted Thursday December 30 2021 One item I forgot to include in yesterday's snarky post was the fact that the 20% I referred to generally are unable to interpret a simple graph. This is why back in 2016 Fox News aired a column graph comparing the four deaths that occurred in Benghazi under then Secretary of State Hillary Clinton with other secretaries. While the other death figures were much higher, the column height for Clinton soared above those of its counterparts, making Clinton look much worse (Fox News has since eliminated all references to that graph). But here's a newer and much more detailed graph showing COVID-19 vaccination rates for all 3,144 U.S. counties whose residents voted for or against Donald Trump in the 2020 presidential election: (The graph's compiler has attempted a least-squares linear correlation of the data, but the trend of the data is what stands out.) But wait! You say so what, the graph shows Trump's influence on the vaccination rate alright, but does that necessarily mean that more unvaccinated people died as compared with those who were vaccinated? The answer is yes: This graph shows that to date, the death rate was roughly five times higher for the unvaccinated population. With over 820,000 U.S. deaths due to COVID-19 having been reported to date, this can easily be interpreted as meaning that somewhere around 150,000 to 200,000 unnecessary deaths occurred due to people who refused to get vaccinated. Is former president Donald Trump responsible for these excess deaths? I believe he is, but those who stormed the Capitol building and who resolutely stand by him will never be convinced.

 Basic Scientific Literacy — Posted Wednesday December 29 2021 Most of what you listen to or watch is noise. Most of the media you consume is noise. And much of what you can find on the Internet, particularly if you're having that information curated to you through social media, is not just noise, but actively misinforming you in a way that's designed to play to your preconceived biases. — Astrophysicist Ethan Siegel Many years ago I occasionally gave public talks on a variety of water quality and supply issues. When trace levels of suspected carcinogenic volatile organic contaminants were discovered in drinking water supplies in Southern California in 1980, various treatment options were available at the time, including aeration and activated carbon filtration. In my presentations I tried to alleviate the public's concerns regarding the effectiveness of these treatment methods in removing the contaminants (typically, one or two passes would remove roughly 90% to 95% of the contaminants). The State Environmental Protection Agency at the time had established a maximum allowable limit of 5 parts per billion for these contaminants (roughly one drop in 13,000 gallons or a standard swimming pool), which correlated to a cancer risk of one in a million, based on a healthy indivudual drinking two liters of the water a day over a lifetime of 70 years. I invariably ran into the same two concerns from the public: Why not design treatment systems that will remove 100% of the contaminants? A cancer risk of one in a million is unacceptable if I am the one who gets the cancer! My explaining that 100% efficiency is either unachievable or cost prohibitive was unacceptable to a small but significant number of people, while any non-zero risk of contracting cancer was unacceptable to those same people. Because of this experience and others I've encountered over the past 40 years, I am convinced that something like 20% of Americans fit the following character traits: They do not believe or trust experts (especially those in science and government), preferring to believe in their gut instincts or their peers They are undereducated, especially where basic scientific issues are involved They crave absolute certainty in alleviating their fears They crave Big Brother-type autocratic leaders, even when those leaders prove to be cravenly immoral and unfit for office They cannot distinguish theories from conjectures and opinions/hearsay from facts Hundreds of millions of guns and tens of thousands of deliverable nuclear warheads make them feel safe They tend to be white, conservative, evangelical and Republican As noted in Dr. Siegel's recent Big Think article, getting the general public educated to the point of basic scientific literacy is going to be difficult. But I see the problem being one of just getting that 20% educated, because right now they represent the tail wagging the country's political dog. The quiet words of the wise are more to be heeded than the shouts of a ruler of fools. Wisdom is better than weapons of war, but one sinner destroys much good. — Ecclesiastes 9:17-18

 One Hundred Years — Posted Tuesday December 20 2021 "Put 'em both up, insect, before I comb your hair with lead!" This month marks the 100th anniversary of the first film appearance of Stan Laurel with Oliver Hardy, although they wouldn't be an official team until 1927. My all-time favorite comedy pair.

 Yet Another Delay — Posted Monday December 20 2021 Waiting for the $10 billion James Webb Space Telescope to launch is like waiting for ex-president Donald Trump to be rightfully put in prison. After innumerable launch delays, the scheduled December 22 launch has been delayed again. Still, considering the literal cosmic importance of this new astronomical space telescope, it's best to be as sure as possible that all things go right. Even after an uneventful launch, the spacecraft still has to unfurl its gigantic solar screen and become operational without a hitch. If unsuccessful, the telescope will be just so much space junk, as it will be too far away to be repaired. If successful, it will provide answers to many of mankind's fundamental questions about the universe. My fingers are still crossed.  Laws Don't Apply to Those at the Top — Posted Monday December 20 2021 As a fairly conservative Coptic Orthodox Christian I have many disagreements with Dr. PZ Myers, an atheist biology professor at Morris State University in Minnesota. But his recent article on the American legal system and other matters has me in full agreement. "Burn it all down," he says. I say yes indeed, and let's start all over again.  David Brooks on Conservatism — Posted Sunday December 19 2021 Conservative New York Times writer and author David Brooks has infuriated me and many other progressive types with his articles and comments over the past 15 years, but the sheer insanity of the current Republican Party seems to be causing a sea change in his thinking, at least with respect to how he views conservatism in America today. Consequently, his December 8 article in the Atlantic is a refreshing change for me. You should read the article, although typical of most Atlantic articles it is overly long. My biggest argument with Brooks was always what I viewed as his "they all do it" approach to Republican crimes and misdemeanors, which he would casually tack onto Democratic actions and policies as well, therefore making GOP crimes somehow more acceptable—after all, if they're all doing it, why get too upset with the GOP? Brooks' attitude seems to have changed in his Atlantic article, although some of his earlier views still leak through (he implies that Reagan's ridiculous 1983 Star Wars defense plan was technically brilliant). So I've warmed up to Brooks a bit, but I'm waiting to see how he deals with le déluge—the imminent day when the GOP utterly destroys American democracy through rightwing lies and voter suppression, the very Republican diseases that Brooks bases his article on.  Merry Early Christmas, GOP — Posted Saturday December 18 2021 Three U.S. generals are warning of a potential civil war in America if the results of the 2024 presidential election are disputed by political factions in the U.S. military. In particular, they warn that if the Republican Party should suffer a defeat similar to that of the 2016 election, military leaders and troops sympathic to the Republican cause might break ranks and stage a coup attempt, potentially leading to civil war or a "shadow government." I seriously doubt that this will happen, but if high ranking military leaders are concerned, I think we should all be concerned. Meanwhile, the GOP and Russia must be thanking their lucky stars.  New JFK Assassination Evidence — Posted Wednesday December 15 2021 Over the past 20 years or so I've read I don't know how many books and articles on the 1963 JFK assassination. My overall takeaway: the assassination was due to a conspiracy involving not only Lee Harvey Oswald but other participants acting either passively or actively in the killing. The so-called Frame 313 "head shot" of the Zapruder film and subsequent frames irrefutably show Kennedy's head being thrown backward and to the left, indicating JFK was shot from the front and the right, presumably from the "grassy knoll." Several professed experts, including Nobel Laureate physicist Luis Alvarez, have claimed that Kennedy's reaction to the fatal shot was due to an autonomic physiological reaction, but the underlying physics disproves such claims (Alvarez was later shown to be a paid government employee and confidante of the FBI and CIA, which themselves promoted the "one assassin" theory). The final report of the Warren Commission confirmed the one-assassin theory, but today we know it was heavily influenced by the government's need to avoid conflict or even war with the Soviet Union, which was earlier believed to have played a part in the assassination. Despite the many books and studies that have come out since November 1963, no definitive answer has emerged regarding who was responsible. Oswald was no doubt a participant in the killing, but his supposed culpability ranges from naive patsy to "lone gunman." Forensic data are extensive, but much of it is still being kept hidden from the public, presumably because of national security concerns. Even the Kennedy family itself is suppressing detailed forensic material, such as autopsy information on the precise track of the fatal bullet through JFK's skull. However, the Biden Administration has promised to release some of its classified information on the assassination, and today marks the deadline for its release. Even so, those hopeful for revelation of "smoking gun" evidence will almost certainly be disappointed. In the meantime, you can watch a new, interesting documentary on the subject, osted by ABC here (the entire documentary can be viewed here). Much of the video is based on research by Josiah Thompson, whose groundbreaking 1967 book Six Seconds in Dallas has since been updated by the author in Last Second in Dallas, which claims that the fatal head shot was followed less than a second later by the bullet that passed through Kennedy's neck (I haven't read the book yet, but I intend to order it when it's available next month). But based on the video, the argument that Kennedy was killed in a crossfire by at least two snipers seems plausible. If true, then the assassination was indeed carried out by a conspiracy of more than one individual. To me, the "lone gunman" explanation is too pat, and the suppression of evidence to date seems unjustifiable given the historical nature of the killing and its repercussions. Before his death, Kennedy had laid plans to get America out of Vietnam, an effort that would have cost American military manufacturers billions of dollars in profits. His decision to not follow up on the disastrous Bay of Pigs invasion of Cuba was also seen by important military leaders as a "weak sister" decision that led directly or indirectly to the near-apocalyptic confrontation with the Soviet Union in October 1982. This is just my view of things, but it is supported by many others. If true, then American military right-wingers killed Kennedy, and I don't see the subsequent assassinations of Robert Kennedy and Martin Luther King Jr. to be mere coincidences, either. Of all the references available on the subject, my favorite to date is the concise 2014 book 22 Noverber 1963 - A Brief Guide to the JFK Assassination by Jeremy Bojczuk. One can only wonder if Thompson's new book will shed any more light on the assassination, or if the American people will ever learn what really happened. My personal view is that this confusion is exactly what the American govenment wants, and that it will forever suppress any definitive evidence outside of the lone gunman theory. How's that for paranoia, folks?  Where's the Beef? — Posted Tuesday December 14 2021 I'm a fan of old Westerns, movies and TV shows alike, with the 1957-1962 series Maverick being my favorite. But I can't help but be offended by the Wild West culture as America has grown to know and love, which is usually completely wrong, both historically and morally. Everything is scrubbed clean, with the men wearing nice clean clothes and sporting expensive haircuts, while the women are invariably beautiful, with perfect teeth, hairdos, makeup and figures. The Calamity Jane of old in reality was a dirty, spittin', cussin', fartin' tomboy, and not the demure, refined young lady that Doris Day portrayed her to be after she'd been tamed by her true love. I won't go into the way Mexicans and American Indians were portrayed, but it was pretty awful as well. I recently caught the 1948 John Wayne classic Red River, which at times I found almost unbearable to watch. Early in the film, Wayne and his team are driving a herd of cattle to market over Mexican territory when they are confronted by a Mexican representative of the region's land owner, Don Diego. Claiming that all of Diego's land is too much for one man to possess, Wayne shoots the agent and promptly declares it his land, then has the Mexican buried while reading the Bible over the grave, giving the dead man a good Christian send-off. Oh, the hypocrisy! But the real zinger for me is when Wayne, in his usual growling, authoritative voice, pontificates over his noble goal in life: The "Beef to make 'em strong, make 'em grow" line has me abolutely convinced that the National Cattlemen's Association paid the film's producers plenty to have that bit of script included in the film, much as how the country's cigarette makers paid to have everyone in 1940s and 1950s films to be smoking constantly ("Would you like a cigarette?" was a superfluous question back then, as everyone wanted a cigarette, including kids). Ironically, John Wayne himself died from lung cancer, which he attributed to a lifelong habit of cigarette smoking. (No, it wasn't from consuming red meat all his life, but that's another story.) More recently, we're experiencing the Critical Race Theory argument, which is intended to educate Americans about issues like slavery, Jim Crow and other unpleasant aspects of the country's history. Republicans claim that the theory's real purpose is to make children feel guilty and ashamed about America, but America's guilt is a fact of life, not a illusory political hoax. It's reality, the same reality that modern Germans have come to acknowledge and accept regarding their Nazi past. America's children can do the same—acknowledge and accept our country's historical faults, then move on to build a more just and lasting democracy. But no, Republicans want us to think we've always been the shining City of Light, as professed by Saint Ronald Reagan, and that if mistakes were made, it wasn't our fault.  Is the Cosmological Principle Strictly Valid? — Posted Tuesday December 14 2021 It's a bit like computing the volume of the Earth: You could fret over every mountain and ravine, or you could assume the planet is a sphere and call it a day. — Charlie Wood, staff writer, Quanta Magazine The Cosmological Principle states that on very large scales the distribution of matter and radiation is perfectly uniform. It is both homogeneous (the universe looks the same no matter where you are) and isotropic (the universe looks the same in any direction). Of course, the principle does not apply to local regions—Earth looks very different compared with any other region of the Solar System—but on truly cosmological scales it is assumed to be true. This assumption allows for a general-relativistic description of the universe, which to date has survived all observational tests. Einstein's relativity theory leads to two important equations known as the Friedmann equations, which describe the effects of matter and radiation on the evolution of the universe as as a whole, including its observed expansion. These equations include the effects of large-scale curvature, dark matter and dark energy. Indeed, the noted astrophysicist Ethan Siegel has stated that the Friedmann expressions are his favorite equations, as they accurately describe the history and evolution of the universe. But what if the cosmological principle is not quite correct? I've often wondered what effect the possible non-uniformity of the universe would have on the Friedmann equations, and if that non-uniformity could be built into the Friedmann model—kind of like having a small standard deviation or "fuzziness" built into the equations to account for some slight non-homogeneity or non-isotropy. Would this have a small effect, or would it make a huge difference in how the universe is currently described? As noted in the Quanta article, University of Geneva cosmologist Ruth Durrer is asking this same question. Granted, the Friedmann equations have had remarkable success to date in explaining the large-scale universe, but are they too simplistic? Like Quanta writer Wood wonders, would some tiny discrepancies make any difference? The question might be moot, as any attempt to build non-uniformity into general relativity would seem a hopeless task. But given the enormous size of the universe and the something like 3 trillion galaxies inhabiting it, might it be possible to contruct a Friedmann-like universe based on a purely statistical distribution of matter and energy against a general relativistic background? If current assumptions about dark energy are true, then it's entirely possible that such an effort may be a waste of time, since dark energy is assumed to be both perfectly uniform, and the assumption that it is now rapidly taking over the universe. Again, if true, then the future of the universe will be totally de Sitter in nature, completely dominated in its evolution by exponential expansion into near nothingness. What a great time to be alive!  Compound Pulleys Are Very Efficient — Posted Tuesday December 14 2021 Here's cartoonist Gary Larson again:  Yeah, Let's Call It Quits — Posted Monday December 13 2021 When fascism comes to America, it will be wrapped in the flag and carrying a cross. — Nobel Laureate Sinclair Lewis The prestigious Proceedings of the National Academy of Sciences (PNAS) has just released a study of America's political and ideological differences, and the results of the study indicate that America may have reached a tipping point with regard to the country's ability to resolve its differences. While similar earlier studies have shown that America's right and left have successfully united in the past when faced with various serious or existential threats (the attack on Pearl Harbor and 9/11, etc.), the current COVID pandemic, which has so far claimed over 800,000 American lives, has shown no similar unifying effect. Indeed, the right wing's continued focus on gun rights, abortion, socialism, minority rights, vaccination and even mask wearing have made the pandemic almost a non-issue. My only problem with the study report is that it uses language and terminology that only graduate students are likely to fully comprehend. Given the right wing's already distainful attitude toward "experts" and science in general, this will drive the right even further away from the study's conclusions, compounding the divisiveness that now exists. Terms like bimodal polarization, homophily, dimensional attribute space, exogenous shock and many others will not only drive the average reader away, but the study's mathematical model is likely to make even a liberal like me weep in frustration. Still, the study's results are disturbing and, if verified by calls for further study and confirmation, serve to call into question the country's ability to remain a democratic republic. A new Civil War? I doubt it. But the Democratic Party's continued refusal to impose the powers it already has in hand will likely result in a GOP victory in the 2020 mid-term elections and the 2024 presidential election, and it's doubtful democrats will do anything but shrug their collective shoulders. As for me, I prefer a divorce, not a civil war, but I have no idea how to achieve it.  Collapse and Overshoot — Posted Saturday December 11 2021 Progressive Christian minister, author and eco-awareness guru Michael Dowd recently posted two half-hour videos in which he discusses the state of Earth's ecosystem. It's not good news, and rather than post the videos here I'll just supply the links. The first is called Collapse in a Nutshell, while the other is its companion video Overshoot in a Nutshell. I watched the first, but got so downhearted that I couldn't bear to watch the second. Dowd notes that the word "denial" is overused, so he prefers to call it "adaptive inattention" instead, which I fully support. When faced with a calamity of the magnitude of worldwide ecological collapse and the attendant destruction of modern human civilization, Dowd notes that it's easier to get up in the morning and focus on our families, jobs and day-to-day lives—a mental attitude that I liken to the knowledge of one's unavoidable death, which the human mind cannot fully comprehend or accept. Yes, we'll all die "someday," but it's so far in the future that we can safely ignore it. Or, as many Christian fundamentalists believe, Jesus Christ will return while they are still alive, obviating the necessity of their deaths. Any barely rational person realizes that the continued growth of the human population, attended by the loss of habitat for farming and industrial use, the alarming rise in atmospheric green house gases like CO$$_2$$ and methane and the irreversible depletion of limited and/or non-renewable resources simply cannot be continued indefinitely. While Dowd argues that collapse is uncomfortably near, he also acknowledges that little will be seriously done to mitigate it. Indeed, Dowd notes that while "problems" are subject to solutions, "predicaments" are only subject to forced adaptation. But like the sometime nagging awareness of our own certain mortality, we're likely to go on with our lives and hope for the best. After all, we have lives to live, right?  Chief Justice Roberts is a Phony — Posted Saturday December 11 2021 As a Christian I don't believe in abortion, but I leave it up to the woman to decide. If it's a sin, it's between her and her God. If it's a crime, then we have the situation that's rapidly spiraling out of control in America today. Recent efforts in Texas, Mississippi and other Red States are underway to bypass federal abortion laws and the nearly 50-year-old Roe v. Wade decision by making certain abortions illegal under any circumstances, including rape, incest and the age of the victims. That said, I do think that a 15-week limit is appropriate, although I recognize that in many cases a woman won't even know she's pregnant as she approaches the end of her second trimester, due to a concurrent medical condition, obesity or just plain ignorance. But what really bothers me is the Supreme Court's obvious effort to let the states effectively overturn a longstanding federal law. This would set a precedent, allowing other federal laws to be overturned based solely on the political and religious biases of the states' individual legislatures, or the disgruntlement of their electorates over the results of presidential and/or congressional elections. With the Supreme Court now standing firmly 5-4 on the wishes and desires of conservative Red States, the Court is no longer a judicial body, but a sociopolitical arm of the Republican Party. Chief Justice John Roberts is well aware of this bias, and he has repeatedly gone on record saying he'd like to make the Court more sensitive to purely judicial matters. But I see Roberts playing a good-cop/bad-cop game with the other justices, since he knows that by voting along with the three more liberal justices he can appear to look fair and reasonable, knowing full well that the five conservative justices will always carry the day for the GOP (remember that the Justices are appointed for life). For this reason, I believe that President Biden should expand the Court by two Justices. By appointing two members who are more moderate or liberal leaning, Biden would not only make future Court rulings fairer but force Roberts to take a more decisive role in those rulings. Case in point: if the Court were split 5-5 on an issue of national importance, it would force Roberts to show his true political side, which I believe today is just as conservative as any of the others.  Farmelo on Numbers — Posted Friday December 10 2021 UK Cambridge physicist and writer Graham Farmelo is the author of The Strangest Man, by far the best biography of the great British mathematical physicist Paul Dirac. Read it and you'll understand why Farmelo uses the word "strangest," although I think "most brilliantly eccentric" would have been better. In my opinion, Dirac stands high above all others in physics, including Newton and Einstein. Farmelo's latest book is The Universe Speaks in Numbers which, while I haven't quite finished reading the book, I highly recommend it. In the book Farmelo recounts a story that every physicist is aware of, while others should know of it nonetheless. As Einstein was feverishly completing his theory of general relativity (gravitation) in late 1915, the great German mathematician David Hilbert was hot on his heels. In November of that year Einstein finally got his theory right, and he managed to publish it just days before Hilbert discovered a far better and easier derivation of the field equations of gravitation. Hilbert's approach was to extremalize the quantity $$S = \int \!\!\sqrt{-g}\, R \,d^4x \tag{1}$$ which results in the field equations for empty space $$R_{\mu\nu} - \frac{1}{2}\, R \,g_{\mu\nu} = 0$$ (Hilbert's method can be done in less than a minute; it took Einstein months). Einstein barely managed to squeak out the same field equations by a much more complicated and circuitous approach, but he did indeed scoop Hilbert. Hilbert recanted, although today (1) is called the Einstein-Hilbert gravitational action. Farmelo's book also has a nice tribute to the German mathematical physicist Hermann Weyl, whose mentor and advisor was Hilbert at the University of Göttingen. Weyl was also a colleague and close friend of Einstein, and Weyl was instrumental in explaining and popularizing Einstein's theory to the world.  The Antimatter Anomaly — Posted Sunday December 5 2021 In classical physics, the energy $$E$$ of a particle with mass $$m$$ in a potential field $$V(x)$$ is given by $$E = \frac{p^2}{2m}\, + V$$ where $$p$$ is the particle's momentum. But in Einstein's special theory of relativity, the energy is more correctly given by $$E^2 = m^2 c^4 + c^2 p^2 + V$$ where $$V$$ is the potential energy (I suppose it should be $$V^2$$) and $$c$$ is the speed of light. This presents a problem: to obtain $$E$$, do we take the positive or the negative square root? In 1928, the 25-year-old British physicist Paul Dirac solved the problem. He postulated that positive $$E$$ referred to ordinary particles, while negative $$E$$ referred to the antimatter variant of the particle. Since then, Dirac's interpretation has held up perfectly, and we now know that antimatter is a fundamental constiuent of the matter in the universe. But bad things happen when matter and antimatter interact—they annihilate each other, resulting in a burst of light (photons). All things being equal, the Big Bang should have created equal amounts of matter and antimatter, which would have resulted in a universe of only radiation, not matter. So there must have been a slight preference of matter over antimatter when the universe was created, with matter winning out. Physicists have estimated that given the amount of radiation and observed matter in the universe, the initial ratio of matter to antimatter was something like 10 billion to ten billion minus 1. In her latest video, German physicist Sabine Hossenfelder addresses this ratio, which she revises down to about a million to a million minus 1. That doesn't seem to be a huge difference, but it allows for a universe in which antimatter stars and galaxies can exist within and outside our own Milky Way. Gravitational accretion of matter particles to these antigravity bodies would give off a particular kind of radiation, but such radiation has not yet been seen or confirmed. A preponderance of matter over antimatter on the order of a part per million or billion would seem to mean that the total amount of matter created in the Big Bang would have been truly enormous, given the amount of ordinary matter already observed or estimated. The presumed matter/antimatter anomaly puzzle seems to to be indicative of slight but important irregularities in the universe. One example is the the cosmological background radiation, whose density difference amounts to one part in 100,000. Another is the Higgs mechanism, which arises from a seemingly innocent ccordinate change in the standard Lagrangian of particle physics. I personally see all kinds of philosophical and religious implications in these imperfections. Bottom line: the universe is very slightly imperfect, but its imperfections have made all the difference to us humans. Here's Hossenfelder's views on the subject:  The Webb Space Telescope — Posted Sunday December 5 2021 My first telescope was a pathetic 3-inch reflector, which my father bought for me when I was eight years old. I was able to make out the craters on the moon, four moons of Jupiter, the rings of Saturn, and not much else. Much later, I built 4-inch, 8-inch, 10-inch and 12.5-inch reflecting telescopes, and in doing so I made a great discovery—I enjoyed designing, grinding the mirrors and building the telescopes a lot more than actually using them. Today, the newest telescope to catch my attention is the orbiting$10 billion James Webb Space telescope, which will (hopefully) be launched later this month. Far larger than the Hubble telescope, the Webb telescope will operate in the mostly-infrared range but will provide unprecedented views of the universe. If successful, it should also provide details on the nature of dark matter, dark energy and the origin of the universe itself. There is at least one hitch—unlike the Hubble space telescope (whose optics were flawed but subsequently repaired thanks to a series of servicing missions by American astronauts), the Webb telescope will be too far away for any such repair missions. If the folded mirrors and sunlight shields fail to deploy properly, the telescope and its onboard instruments will become nothing more than a pile of useless, orbiting space junk, too far away for any repair missions. I'm crossing my fingers.

 What's Wrong With Gravity? — Posted Sunday November 14 2021 PBS Spacetime's latest video questions our basic understanding of gravity, a force that was known to mankind ever since the first Homo erectus fell off a cliff. It wasn't known mathematically until Isaac Newton formalized his theory of gravity in 1687, which itself was largely based on Newtonian mechanics. That theory stood the test of time until around 1830, when astronomers noticed that the theory did not correctly describe the orbit of the planet Mercury. Unwilling to consider the possibility that Newton's theory was wrong, astronomers believed that Mercury was being grqvitationally shifted due to another planet (dubbed Vulcan) on the other side of Mercury's orbit, hidden from view because it was always behind the Sun. The Vulcan idea persisted until early 1916, when Einstein used his new theory of general relativity to precisely calculate Mercury's orbit (Einstein was delirious with joy for days following his discovery, since he knew then that Newtonian gravity was only an approximation to the truth). Then in the 1930s astronomers noticed that stars rotating around galaxies were moving too fast based on the amount of measured galactic mass. In order to preserve Einstein's theory, astronomers assumed there had to be extra mass hidden mass in and around galaxies, causing their stars to rotate faster. Thus was born the notion of dark matter, said to be "dark" because it couldn;t be seen and because it didn't seem to interact with anything (except gravity), including itself. But unlike the Vulcan theory, dark matter is today part of the Standard Model of Cosmology, in spite of the fact that for decades billions of dollars have been spent worldwide by experimentalists trying to detect the stuff, all to no avail. By comparison, little effort has been expended looking for a theoretical alternative to dark matter, an effort akin to the replacement of Newtonian gravity with that of Einstein's. The leading contenders to date have been modified Newtonian gravity (MOND) and its relativistic cousin tensor-vector-scalar (TeVeS), which despite some successes have failed to equal the explanatory power of dark matter. It seems to me that the current game plan for modifying Einsteinian gravity is to take the original theory and add various vector and scalar fields to it in the hope that something works. This appears to be something like curve fitting, since the addition of parameters to the theory is being done simply to match observation without a sound theoretical justification. Dark matter skirts this problem by simply adding more dark matter here and there until things jive. Consequently, dark matter is essentially non-predictive, since one can always cheat by tossing in more or less dark matter. Here's one other thought: any theory of gravity shou;d include one or more of the Riemann geometrical trio $$R, R_{\mu\nu}$$ and $$R_{\mu\nu\alpha\beta}$$. In some TeVeS theories, none of these are apparent, while scalar and vector quantities dominate. Here's the video, and you can decide for yourself where all this might be going:

 Our Wallflower Attorney General — Posted Tuesday November 9 2021 Showing my age here, but older people will remember Warner Brothers' Droopy Dog character from the 1940s and 1950s. Slow and methodical to the point of being completely uninteresting and ineffectual, the character reminds me of current Attorney General Merrick Garland. You may recall that Garland was President Obama's pick to replace Antonin Scalia on the Supreme Court, but his nomination was effectively cancelled by Senator Mitch McConnell. Democrats cried foul, saying that Garland wuz robbed. But instead of fighting for Garland, Obama decided that he'd let it go, likely not wanting to appear as an uppity black man. Of course, once Obama was out of office the Republican Senate immediately approved President Trump's rightwing selection, Neil Gorsuch. That may be water under the bridge now, but President Biden's selection of Garland for Attorney General went ahead unimpeded, since it was only a consolation prize anyway (Supreme Court justices have lifelong appointments, whereas Attorney Generals come and go with presidential terms). Garland now has the unprecedented opportunity to bring Trump and Friends to justice for their traitorous attempt to overthrow the government of the United States, but Garland is nowhere to be seen. As I've noted before, Garland is like the timid party attendee who's always scrooching to the back wall trying not to be noticed. This is a heck of a way for an Attorney General to behave, given the fact that our country's very existence is at stake today. As Droopy would say, "Oh, dear!"

 Speaking About Time $$\ldots$$ and 1963 in Particular — Posted Saturday November 6 2021 The Moving Finger writes; and, having writ, Moves on: nor all thy Piety, nor thy Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it. — The Rubayat of Omar Khayyam You see, the past doesn't want to be changed. — Al Templeton, 11.22.63 In early 1963 I was a 13-year-old 8th grade student in Mrs. Daphne Cunningham's English class. The class had been studying The Rubayat, and for the life of me I had no idea what it was all about. One day Mrs. Cunningham kept me after class, and we sat together to discuss the problems I was having with the poem. I remember the occasion distinctly, as all I could think about were my teacher's beautiful face and shapely legs dangling before me, physical aspects of womanly beauty that were only then becoming aware to me. Because of my stupidity she had to explain the poem to me, along with its underlying notions of love, death and the meaning of life, but it really made no differance, as all I could think about was that gorgeous woman sitting in front of me. Thinking back, maybe that was what the poem was all about. While the future holds promise (and fear) for many people, few wish to travel into the distant future to find out what happens, assuming the return trip is impossible. But traveling to the past is something entirely different. We all would like to go back into the past, primarily for two reasons. One, to find out what really happened, to recover information that we believe has been lost forever, like who really killed JFK. The other is to relive the past in some sense, like correcting our mistakes, marrying the girl we truly loved, or to redirect our lives into more productive avenues. But the past is past, and nothing can change it, while the scary and unknowable but otherwise uninteresting future is all that's left for us. Speaking about time (and JFK), you may want to watch the excellent 2016 mini-series 11.22.63, an eight-part television series adapted from Stephen King's overly long novel of the same name. Yes, it's all about preventing the assassination of JFK in 1963, and while the time-travel technology involved is rather nonsensical, it's entertaining just the same. Like many older people like me, I personally will never forget that day when as a freshman high school student I learned about the assassination. Awareness of girls, entry into high school (which I detested), and the JFK murder. Yes, 1963 was a heck of a year, but one I wouldn't want to revisit.

 The Future is Quantum Physics, the Past is Classical Physics — Posted Saturday November 6 2021 I think it was Socrates or Augustine or one of those ancient guys who said that he understood what time was but then didn't know whenever he was asked what it was. That seems to be just as relevant today as it was ages ago. In this new video from technologist Arvin Ash, the concept of time is raised for the umpteenth time in history. He doesn't get too far with it either, but he does bring up a few interesting points, motivated by this recent paper by noted physicist Lee Smolin. In a nutshell, Smolin says the past and future are respectively definite and indefinite, connected by the instantaneous and infinitesimally ephemeral present. This observation reminds us of the Copenhagen interpretation of quantum mechanics, which asserts that a quantum state is inherently unknowable and complex-valued until a physical measurement or observation is made, at which time the state's associated wave function collapses instantaneously to a single eigenstate, which is unique, single-valued and real. Wave function collapse is assumed to be instantaneous, and in that regard it resembles the present that Smolin discusses in his paper. Similaarly, the future represents the infinite multitude of uncollapsed wave functions in the universe, while the past represents the infinite multitude of fixed, knowable eigenstates. Ash ties all this in with the notion of entropy, itself a topic that is subject to many interpretations. States with high entropy may be highly ordered (e.g., a small box of compressed gas molecules) but unknowable (the positions and momenta of the individual molecules are probabilistic but cannot be known with any precision), while systems with low entropy are highly disordered but can be known to high precision (the gas molecules slow down to a crawl or halt entirely). Ash points out that this characteristic of entropy is similar to that of wave functions and eigenstates, or the future and the past. But where does the present fit into all this? However, all this talk about quantum states and entropy doesn't tell us what time is. And like the nature or purpose of human consciousness, we may never know.

 Air Taxis Are Coming — Posted Friday November 5 2021 I've been following the all-electric vertical take-off and landing (eVTOL) airplane technology for several years now, mainly as something that I might want to invest in. It's definitely coming along, and the technology might be sufficiently robust within five years or so, at least for the high-end air taxi service sector. Here's a reliable update on the possibility of near-term eVTOL aircraft, which seems well within technological capability provided that the energy capacity of on-board batteries will be substantially improved in the next few years. My only criticism is that it doesn't adequately address the redundancy issue, which has to do with mid-air battery or propulsion failure, bird strikes or similar mishaps. The article is based in part on this recent paper by researchers at Carnegie Mellon University. Companies such as German-based Lilium are heavily invested in eVTOL aircraft with significant redundancy. Recognizing that a major percentage of energy expenditure occurs during take-off and landing, the company seeks to minimize energy loss during horizontal flying (cruising) using what is known as boundary-layer air ingestion (also the Coanda effect) of its electric ducted fans (see this YouTube video for details).

 American Insanity is Thriving — Posted Thursday November 4 2021 When I received my third and final Moderna COVID vaccination yesterday, all I ended up with was a slightly sore right arm. I didn't glow in the dark. But when the respected science journal Bulletin of the Atomic Scientists reports that the lunatic conspiracy group QAnon claims that scientists have put the bioluminscent chemical luciferase into the vaccine supply so that the federal government could track commie-loving leftists around the country, I took notice. QAnon is the same outfit that (among other outrageous claims) published the claim that John F. Kennedy and his son John Jr. would show up alive in Texas, thus disproving their reported deaths (which of course was just another government conspiracy). Consider this: all it takes to cause a nationwide disaster is for one lunatic with a "God-given" 100-round assault rifle to slaughter dozens of innocent people, although he may represent only a tiny fraction of the total population. Consider also that some 30-40% of American voters believe that Donald Trump won the 2020 presidential election, and that this same electorate believes a monomaniacal sexual predator and pathological liar should be restored to the presidency—by insurrection, if necessary—and be made Dictator-for-Life. Finally, consider the fact that if only several percent of Americans truly believe QAnon's lies (a figure that the polls support), then American democracy surely has no chance of surviving.

 On Optimization — Posted Tuesday November 2 2021 Roughly three millenia ago, the Iron Age ushered in a revolution in tool and weapons manufacture. Iron ore was plentiful and cheap, but iron was expensive to produce, requiring vast reserves of wood to burn to create the high temperatures needed to refine the ore. Very early on iron was forged into nails for building, and due to their high cost they were routinely reused (there is evidence that nails used in crucifixions were recovered for future use). Because of their value, nail dimensions underwent great refinement through trial and error. Too long or too thin, and nails would bend or break when hammered into wood; too short or too thick meant a waste of material. With the advent of calculus, it was a simple matter to to employ even the early rudimentary science of strength of materials to calculate the optimum dimensions of nails and other metallic fastening materials, such as rivets, bars and beams. The mathematics of optimization is used everywhere today, from packaging, scheduling and shipping to structural design and building. At the most fundamental level, optimization seems to have been built into Nature herself—the mathematical quantity known as action has the units of energy times time (or equivalently momentum times distance), and Nature seeks to extremalize (and usually minimize) the amount of energy, time, momentum or distance that some activity requires for completion (indeed, when the calculus of variations was discovered in the late 1600s, the power and inherent beauty of the action principle were collectively considered proof of the existence of God). Is any physical process subject to optimization? Apparently not. The traveling salesperson problem is a famous example of an optimization problem that continues to elude an exact mathematical solution. And according to this recent Quanta Magazine article, there are likely many such problems whose solutions are intractable. Optimization has led to great discoveries in the efficient use of resources, but it is useless when those resources disappear. One of those resources is fossil fuels, whose extraction from the ground, refinement, distribution and use have been continually optimized since their discovery. But mathematical optimization should also include the costs of future consequences, such as environmental degradation and climate disruption. To date, humankind has intentionally chosen to ignore these costs, mainly because we are a short-term thinking species that believes getting rich first is all that matters.

 Script Writers and TV Viewers, Please Learn a Little Science — Posted Tuesday November 2 2021 My late wife and I were fans of the otherwise excellent mystery series Monk starring the Lebanese actor Tony Shalhoub. But on occasion the plots (like those of many other shows) were so patently ridiculous that we eventually lost interest. Case in point: in the second season's "Mr. Monk Gets Married," a writer has hidden a fortune in gold with the single clue "It's in my journals." Turns out it really was—the writer melted his gold, mixed it with black ink and used the mixture to pen the pages of a thousand bound journals, so the entire fortune was hidden in plain sight on his bookshelves. Trouble is, gold melts at around 1,100 degrees Fahrenheit, while ink is carbon-based and would be instantly destroyed. Furthermore, the mixture couldn't be used to write anything anyway, as the gold would solidify and be useless as a writing material. I recently saw this episode again, and the stupidity of the plot ruined it once more for me. So long, Mr. Monk.

 Neutrino Oscillation — Posted Frdiay October 29 2021 Neutrinos—chargeless elementary particles of spin 1/2 and very small mass, first postulated in 1930 and then experimentally verified in 1956—are known to come in three types, the electron neutrino $$\nu_e$$, the muon neutrino $$\nu_\mu$$ and the tau neutrino $$\nu_\tau$$. For several decades they have been known to oscillate into one another, so that an electron neutrino created in the Sun can become one of the others when it arrives on Earth. As late as the 1980s it was hoped that neutrinos might account for the existence of dark matter, assuming that their mass was sufficiently large. But that mass has since been estimated to be thousands of times less than the mass of the electron. In addition, such a small mass would give neutrinos relativisitic velocities upon their creation, making them difficult to accumulate around galaxies under gravitational attraction. The assumed tiny mass of neutrinos is what has prevented them from being identified with dark matter. There has also been the possibility of one or more much more massive neutrinos, including the hypothetical sterile neutrino, also chargeless and of spin 1/2. Is it possible, I've often wondered, if neutrino oscillation can account for the creation of the sterile neutrino as a fourth member of the known three? After all, a composite of three neutrinos would still have a spin of 1/2 while remaining chargeless, and the binding energy might result in a much more massive particle. Recently, the presumed even distribution of neutrino oscillations has come into question, lending this possibility some credence. A new article in Quanta Magazine doesn't exactly address this possibility, but it does question the distribution issue. As a Christian, I've also wondered about the seeming oddity of God the Father, the Son and the Holy Spirit being one and the same. The neutrino was my answer to this, along with the unity of the electric and magnetic fields being one and the same due to special relativity. But I'll admit that's probably all wrong! There's still much more to be learned about neutrinos, which I see as the last remaining possible answer to dark matter.

 My Biggest Fear — Posted Monday October 25 2021 Yale philosophy professor Jason Stanley talks about ten aspects of fascism in this new Big Think video. It's all so obviously true, but the allure of fascist leaders and strongmen never goes away in spite of all the education and intelligence of their deluded followers. Former President Donald Trump and most of his sycophants and enablers exhibit all of these traits, yet fully 74 million Americans voted for him in his failed bid for re-election in November 2020. We've had nearly a year since that time to discover, review, digest and analyze all the lies that came out of the man before and during his reign of terror, and yet there's a real chance that he'll return in 2024. And one thing seems certain to me—once the Republican Party gains control again over this country, they'll never let it go. Aside: At the video's 8:12 mark, you'll see the Arbeit Macht Frei ("Work shall set you free") sign that greeted doomed Jewish prisoners upon their arrival at the Auschwitz death camp of World War II. The sign was fabricated and erected by Jewish prisoners, but they had one opportunity to show their resistance—they intentionally set the letter "B" upside down. Their German overseers apparently didn't notice, but we can see it today as a subtle form of defiance. When fascism takes over Amerika, how will such defiance be demonstrated when every form of communication has been subdued by the GOP?

 Stupidity — Posted Thursday October 21 2021 If someone were to call you stupid, how would you feel? The same as me: either angry, ready for a fight, or willing to walk away. Unless one is truly mentally impaired, I prefer the definition of stupidity as a learned cultural, emotional or political resistance to generally accepted facts and evidence. It has nothing to do with intelligence, but everything with one's cultural conditioning. Here's a new video on "stupidity theory," which despite my objections to the definition of stupidity seems quite accurate: If 51% of the population were homicidal, would you feel secure wandering out in public? Certainly not! How about 49%? Again, certainly not. But what only 0.01%, a figure that might represent the actual population? You'd venture out, but you might want to be cautious—but not paranoid. But now consider the fact that some 47% of the American population believes that Trump won the 2020 presidential election, that COVID vaccine is to be avoided at all cost, and that (to an admittedly much lesser extent) Democratic Party leaders are drinking the blood of children to obtain the supposed life-extending benefits of the blood marker hemochrome? Sure, such people represent a minority of the American electorate, but are you comfortable with that? And are you also comfortable with the probabilty that this minority is currently driving American politics toward another Trump presidency? CNN's Don Lemon is despairing over the Democratic Party's seeming inability or unwillingness to deal with the stupidity of American voters, despite the fact that most Americans agree with President Biden's efforts to alleviate the negative impacts of homelessness, poverty, climate change and dwindling energy resources. But the polls say otherwise: the stupidity of Republican Party leaders is leading the way toward another Trumpian era. The Republicans seem to be saying that an immoral, pussy-grabbing monster is okay with them because "he gets things done." If Democrats can't get things done in spite of their majority in the executive and congressional branches, then all is lost.

 A Different Approach to Modified Gravity — Posted Thursday October 21 2021 The current issue of the British science magazine New Scientist has an article by the American astrophysicist Paul M. Sutter entitled "Gravity, With a Twist." The title is appropriate, as it describes a theory of gravity that includes something called "torsion," or more generally teleparallelism. (I had a friend in high school who had to have a testicle removed because of torsion, but that's a different use of the word.) In Einstein's general relativity, there are two fundamental quantities that describe all of what we currently know about gravity. One is the metric tensor $$g_{\mu\nu}$$ (which also has the upper-index form $$g^{\mu\nu}$$), which itself is the most fundamental of all tensors. It's assumed to be symmetric, so that $$g_{\mu\nu} = g_{\nu\mu}$$. The other is the non-tensor connection $$\Gamma_{\,\mu\nu}^\lambda$$, so-called because it "connects" vectors undergoing parallel transport and because it (and its first derivatives) make up what is known as the Riemann curvature tensor $$R_{\,\,\mu\nu\alpha}^\lambda$$, which vanishes in the absence matter in space but is non-zero whenever there's a massive object nearby. The connection is also assumed to be symmetric in it lower indices, so $$\Gamma_{\,\mu\nu}^\lambda = \Gamma_{\,\nu\mu}^\lambda$$. In Einsteinian gravity, the metric tensor and connection are related by the rather complicated expression $$\Gamma_{\,\mu\nu}^\lambda = \frac{1}{2}\, g^{\lambda\alpha} \left( \partial_\mu g_{\alpha\nu} + \partial_\nu g_{\alpha\mu} - \partial_\alpha g_{\mu\nu} \right)$$ With these quantities, Einstein's gravity theory has passed every test ever made since its publication in November 1915, and its predictive power far exceeds that of the more familiar Newtonian theory of gravitation. In the 1920s, Einstein (and many others) tried to generalize the theory to incorporate a purely geometric provenance for electromagnetism. Einstein's idea was to abandon the notion that the metric tensor and connection were symmetric, and he hoped that the contracted quantity $$\Gamma_{\,\mu\lambda}^\lambda - \Gamma_{\,\lambda\mu}^\lambda$$ might represent the electromagnetic source vector $$S_\mu$$ (the connection is not a tensor, although the difference is a true tensor). But I digress. Sutter's New Scientist article describes how torsion might be able to account for a number of perplexing problems in cosmology, including the nature of dark matter, dark energy and the Hubble tension, and that torsion might also be able to connect grqvity with quantum mechanics via string theory. But adding torsion to general relativity is exceedingly complicated, as all of the theory's resulting equations have to be resolved in a way that it still accounts for terrestrial and cosmological observations. I've never been tempted to explore torsion for this very reason, but then I'm a lay idiot. One of the oldest books on my bookshelves is Einstein's The Meaning of Relativity, published in 1955 (the same year as his death). It's a fairly readable (if mathematical) account of general relativity, but it includes a chapter called "Relativistic Theory of the Non-Symmetric Field," which is essentially the theory of torsion. Completed in the late 1940s, Einstein thought he had finally achieved a consistent version of the theory, although it didn't have any predictive power. Upon Einstein's 70th birthday on March 14, 1949, his colleagues at Princeton's Institute for Advanced Study (which included Hermann Weyl, himself an early researcher into gravity theory) threw Einstein a party. His long-time secretary, Helen Dukas, baked him a cake whose icing summarized the key equations of his non-symmetric theory: When Einstein died of a ruptured abdominal aneurism in Jume 1955, the attending nurse found several pages of calculations lying on the floor next to his hospital bed. They described more generalizations of his non-symmetric connection term, so we know that Einstein was at it right up to the very end. If he made it to Heaven, I can almost hear him saying to God "I never would have guessed the answer was so simple!"

 An Old Man's Memory — Posted Thursday October 21 2021 It just dawned on me that in two months (appropriately, the first day of winter) I'll turn 73. Oh Lord, take me now. As I've noted many times before, I'm a complete idiot but I do have a great long-term memory. I can recall my mother bathing me in the kitchen sink at the age of two (me, not her), and spotting a mouse in the kitchen around the same time. But my most enduring memory is when my maternal grandmother came to visit from Illinois in the summer of 1952. I was only three, but already a dedicated fan of the early TV show Time for Beany (I didn't know it then, but Einstein was also a regular watcher of the show!) My grandmother once caught me talking with two of my own imaginary finger characters, "BiBi" and "Saucer" (no doubt my take on Beany and Cecil), and I recall wondering how in hell she knew about them. Time for Beany (not to be mistaken for the much later stupid cartoon show of the 1960s) first aired in 1949. It was a puppet show, featuring many characters from the minds of Stan Freeberg and Daws Butler, the show's creators (I remember always being scared when Dishonest John would show up). I distinctly recall one of the puppets, which at the age of three I presumed was a black crow: Now I realize it was intended as an African native, its stereotypical features being an artifact of the racist attitudes of the early 1950s. (I also remember my parents watching Amos and Andy, an even worse exemplar of racist 1950s America. Many Time for Beany episodes can be viewed on YouTube, and they're of historical interest only. Don't worry, I've moved on.

 Apparently, Even Tiny Sizes Matter — Posted Wednesday October 20 2021 Some 2,700 years ago, the value of the transcendental number $$\pi$$ (pi) was known to be roughly 3, and that was good enough for most purposes back then: And he made a molten sea, ten cubits from one brim to the other. It was round all about, and its height was five cubits; and a line of thirty cubits did compass it round about. — 1 Kings 7:23 Millennia later, pi got to be better known, first 22/7, then 355/113 (try it!), then to hundreds of digits, and today to trillions of digits. According to Einstein's general relativity theory, clocks tick faster the farther they are from a gravitating mass. This has been proven experimentally many times for clocks, astronauts and satellites in Earth orbit; the time difference between terrestrial clocks and those orbiting above amounts to merely milliseconds, but the calculated differences agree perfectly with those observed. Amazingly, the clock difference has now been measured to within a height of one millimeter from Earth's surface, according to this paper. A more readable version can be had here. Although a millimeter is still huge compared with quantum scales, it makes me wonder how time might vary at the subatomic level, where tiny but possibly important massive particles quickly pop into and out of existence due to quantum fluctations and the Heisenberg uncertainty principle. This could not have been surmised over a hundred years ago, when the German mathematical physicist Hermann Weyl (who's still my hero) proposed that time might vary from one point to another depending on the path taken between the points. On the basis of a purely classical argument, Einstein nullified Weyl's idea, but today things look a lot better for Weylian theory, particularly as it applies to gravity and cosmology. See many of the articles I have posted on my weylmann.com site for further details.

 Metropolis — Posted Wednesday October 20 2021 As a silent film buff, one of my favorite movies is 1927's Metropolis, produced in Germany over the period 1925-1927 and directed by the great Austrian-German film maker Fritz Lang. Various grainy versions of the film can be found on YouTube, but a fantastic, nearly complete remastered version is available at Amazon. It's a first in many respects—a gorgeous humanoid robot, tricky special effects, a huge cast and filmed at enormous expense at the time despite Germany's not-yet recovered economy from its World War I drubbing—but its socialist message did not sit well with the coming Nazi regime, which viewed underclasses with scorn. (Another great Lang film, 1931's M, also was not popular with the Nazis, due to the film's seemingly kindly attitude towards the mentally ill.) Here's a recent video that talks about some of Metropolis' lesser known facts. I found it informative and interesting.

 And On It Goes — Posted Tuesday October 19 2021 This is the first time I've come across these folks, who in this video discuss the ongoing battle between dark matter and modified gravity (MG). They also address the possibility that cold neutrinos (which would fit nicely into Einsteinian gravity with no modification) may be responsible for what otherwise appears to be dark matter, but such neutrinos have not yet been seen (they probably don't exist). I remain hopeful that dark matter is a myth, and that a modification of general relativity (Einstein's gravity) will eventually explain the mystery of dark matter. Based on this 1989 paper by Mannheim and Kazanas, I always felt sure that MG was the answer, but then this paper by Hobson and Lasenby came along this year that made me question everything. I try to explain the issue in this paper, but now I'm truly clueless about what the real truth might be. Dark matter remains what is arguably the most pressing problem in cosmology today.

 Colin Powell — Posted Monday October 18 2021 General Colin Powell, ex-Secretary of State under George W. Bush, has died at the age of 84 due to COVID-related complications. My last full-time job was as Assistant Executive Officer in an engineering group oddly dominated by mostly pro-Bush Republicans. On the day that Powell gave his ill-fated May 27, 2003 address to the UN Security Council on the dangers of Saddam Hussein's supposed weapons of mass destruction, my office rolled out a television into the conference room, where the staff (but not me) gleefully listened to Powell's carefully orchestrated presentation, complete with exhibits, photographs, video and other evidence that Iraq had amassed nuclear and biochemical weapons scheduled to be unleashed upon Hussein's Middle East enemies (namely Israel). All hell would break loose unless the United States and her (reluctant and largely unconvinced) allies stopped Hussein in his tracks. It was all a sham, as the world was to learn later. The mobile biological weapons turned out to be weather balloons, and the aerial photos of amassed nuclear bombs turned out to be domestic and military equipment misread by American "intelligence" agencies. Powell subsequently apologized for letting the Bush Administration abuse his personal and military credibility, but it did not prevent the slaughter of hundreds of thousands of Iraqi civilians, the expenditure of some three trillion dollars worth of American treasure, the loss of tens of thousands of US troops due to war death and injury, and the attendant loss of America's credibility around the world. Meanwhile, American citizens yawned. They're still yawning. But the airwaves are now full of nothing but praise for Powell, despite his having misled the country into the most tragic military disaster since Vietnam. One might be willing to forgive Powell, as misled as he was himself by Bush and Bush's pro-war cronies, but it's doubtful that nothing but glory will now be heaped upon Powell's memory. Meanwhile, George W. Bush continues to paint and tend his garden. His record as former President of the United States is also doing well, because the collective memory of Americans citizens is short-lived at best, while their stupidity and willful gullibility persist unhindered. After all, they elected Trump.

 On Not Thinking — Posted Monday October 18 2021 This a kind of follow-up on my last post, which had to do with the lure of authoritarianism for people in difficult times. It's also a follow-up to a post from long ago in which I discussed Nobel Laureate Daniel Kahneman's best-selling 2013 book Thinking, Fast and Slow, which asserts (among other things) that stessed people tend to rely on gut feelings and emotions rather than logic, facts and evidence. In short, when you're frightened you don't think, and that's when authoritarian leaders jump in and take advantage of things. Along this same line of thought is this new video from Big Think: Dang it all, God gave us humans the ability to think, reason and analyze, and He gave us the ability to use science as a defense against the hardships of disease, injury and tough times. When we resort to fear-based, emotional, gut-level actions (like electing amoral demagogues like Donald Trump), we're essentially telling God that we don't need the brains He gave us after all.

 Applebaum on Authoritarianism — Posted Sunday October 17 2021 Political writer Anne Applebaum on conservative media commentator Laura Ingraham [my emphasis]: The America of the present is a dark, nightmarish place where God speaks to only a tiny number of people; where idealism is dead; where civil war and violence are approaching; where democratically elected politicians are no better than foreign dictators and mass murderers; where the "elite" is wallowing in decadence, disarray, death. The America of the present, as she sees it, and so many others see it, is a place where universities teach people to hate their country, where victims are more celebrated than heroes, where older values have been discarded. Any price should be paid, any crime should be forgiven, any outrage should be ignored if that's what it takes to get the real America, the old America, back. — Anne Applebaum, Twilight of Democracy: The Seductive Lure of Authoritarianism, 2020 You might want to pick up Applebaum's short (120 pages) book to get an idea of how authoritarianism seems to be the go-to political ideology when regional and world affairs go awry and when frightened people look for any semblance of order despite its tragic cost. My only disagreement with Applebaum is her repeated use of the word "unity" when she really means the collective obedience, conformity and loyalty of ill-informed and scared people to those in power regardless of how immoral, craven and power-hungry they are proven to be. Some 74 million Americans voted for Donald Trump in the 2020 presidential election. Although Joe Biden won the election with seven million more votes, Trump's tally is a truly frightening harbinger of what America has become.

 Holy Authoritarian Takeover, Batman! — Posted Friday October 15 2021 Wow! At only $1.75, cartoonist Ruben Bolling's domestic insurgent set is a fantastic bargain with over 5,000 pieces. The Donald Trump action figure is sold separately, but the set does include the Insane Pillow Man figure, a true collectible that's sure to increase in value when the country's democracy is overturned in 2024 by America's Republican traitors. President Biden, we hardly knew ye.  Unfinished Business — Posted Sunday October 10 2021 It's now been 115 weeks since the worst day of my life, and I'm far from over it. Hmmm, I had this grave marker installed over a year ago, but one of the dates seems to be unfinished. Hopefully that will be corrected before too long.  Going Strong — Posted Sunday October 10 2021 Indeed, politics since 2000 has been marked by the rise of populists—politicians who spurn "out-of-touch experts" and who claim to speak on behalf of millions of people with whom they in fact have no authentic connection, and in whom they have no genuine interest beyond securing votes to support their own often very personal agendas. — Fiona Hill, There's Nothing For You Here, October 2021 Yes, America, your favorite pussy-grabbing, pathologically lying, narcissistic sexual pervert Donald J. Trump is not only still around, but now fully in charge of the Republican Party. Noted political authors have repeatedly warned us of this, notably Alvin Toffler, Naomi Wolf and others. But most recently we have Fiona Hill, whose semi-autobiographical 2021 book There's Nothing For You Here explains the political and cultural crises America is now experiencing. It's all about populism and authoritarianism, which invariantly arise whenever civilization undergoes an overwhelming shock or change of some kind. For America, it came with the 9/11 attacks, then the financial crisis of 2008, followed by the demanded rights of minorities and a twice-elected black President, all of which ushered in a panic on the part of undereducated (I mean stupid) white evangelical Americans, whose longing for the mythic 1950s days of Leave It To Beaver and Father Knows Best has diseased their minds into thinking that a thrice-married sexual predator (Republicans: I'm talking about Herr Trump) should be the glorious leader of our country (aside: in Shakespeare's Hamlet, the word "country" is really meant as cuntry). Meanwhile, the Democratic Party is viewed not only as the inverse of a desired perpetual Trumpian dictatorship by right-wingers but a bunch of wusses and wimps on the part of everyone else. President Joe Biden (the so-called adult in the room) appears glaringly boring and near-senile, while much of his administration is viewed as ineffective. We all remember the days with then-Attorney General William Barr, whose obvious criminal support of Trump kept the media dancing, but whose replacement by shoulda-been-Supreme Court Justice Merrick Garland has resulted in what can only be described as a quantum-mechanical human vacuum state. He reminds me of the perpetual loser who somehow finds himself at a party, constantly scrooching himself against a back wall so no one will notice him. (Wait a minute—I was that loser in high school). I don't watch much television these days, but on CNN today it was revealed that the media and its listeners only want negative news, as it's much more interesting than positive news. This is nothing more than a reflection of what American viewers want as entertainment, which is why we're hearing so much about Gabby Petito, Kim Kardasian and all those other jerks. Will Trump run in 2024? I'd bet on it, and I'd also lay odds on his winning. America is truly a pathetic joke.  Batteries Have Come a Long Way — Posted Sunday October 10 2021 We will not get serious about alternative energy and climate change until the last drop of oil on earth is burned. — My suggested mission statement for the American Petroleum Institute For the past year I've been watching YouTuber Dave Borlace's Just Have a Think site, in which the technology expert addresses mostly issues involving climate change and emerging energy technologies, especially high energy-density battery technology. The latter is especially interesting, as companies such as Tesla, Litton and others are making significant improvements to existing battery chemistry (both liquid and solid state), and it appears that within five to ten years the world will have low-mass batteries that can not only power automobiles over 1,000 miles on a single charge, but limited taxi-like electric airplanes as well. [Borlace is a hard guy to track down. He's a highly informed and interesting technical commentator, but my efforts to find out more about him have proved useless. The most I could find about him is this brief Medium.com article.] At any rate, Borlace's latest video talks about the advantages (and serious challenges) of lithium-sulfur batteries versus the now-standard and pervasive lithium-ion technology. Tesla is currently making great improvements to the latter (which power the Tesla series of electric automobiles), but the technology will likely hit a plateau at some point in terms of energy density, fire safety and recharge cycles and recharge time. Meanwhile, efforts to surpass lithium-ion are being made for various alternative lithium applications, including lithium-iron and lithium-aluminum, and the advantages of these technologies will only improve with time. Even if some of these can never be utilized in automobiles or aircraft, the promise of large, fixed-site power generating facilities utilizing these technologies looks expremely good. I'm now looking into investment opportunities for the coming wave of high energy-density battery technology, as their future looks very bright. You might want to watch Borlace's latest video, which will give you an idea of how far research and development of battery technology is moving:  Speaking of the End of the World $$\ldots$$ — Posted Tuesday October 5 2021  The End is Nearer Than We Think — Posted Monday October 4 2021 "Truly I tell you, this generation will certainly not pass away until all these things have happened. Heaven and earth will pass away, but My words will never pass away." — Mark 13:30-31 The noted Christian writer and book author C.S. Lewis once referred to this passage as "the most embarrassing" verse of the New Testament, as we all know that when Jesus of Nazareth uttered it (roughly around 30 A.D.) the end of the world didn't come to pass. Christian apologists have written books on the passage in an attempt to make Jesus's words true, even though the fabled "End Times" definitely did not occur within the lifetimes of the disciples he addressed it to (Mark tells us that Peter, James, John and Andrew were present, but the full complement of disciples may have also attended as well). Yet, some 40 years after Jesus's crucifixion the Roman army under Vespasian and his son Titus burned Jerusalem and the Jews' holy Temple to the ground, carting away its treasures and slaughtering hundreds of thousands of Jews in the process. This event certainly occurred within the lifetimes of most of Christ's disciples and followers. The word "generation" might refer to the expected lifetime of someone living in 1st century A.D. (my interpretation), although it could also refer to a host of other meanings depending on the exact nature of the Greek word $$\gamma\epsilon\nu\epsilon\alpha$$. Many modern theologians believe that Jesus was just an itinerant apocalyptic preacher whose prediction of the fall of Jerusalem in 70 A.D. was either a lucky guess or an after-the-fact postscript of the early Gospel writers. But we also know that several of Christ's disciples were martyred in Rome around 64 A.D., less than 40 years after the passage of Mark 13:30, so whatever is the true meaning of the verse remains open to debate. In the Coptic Orthodox Church (my church), the word "generation" refers to all believers at all times, which is as good as any other interpretation. But regardless of all this, Christians today remain hopeful that Christ will indeed return in the End Days, although that time will most probably occur sometime long after we die. This is the primary hope of all Christians, yet it would seem that physicists are also falling under the sway of a similar hope, at least when it comes to their ultimate fate. Last month's edition of the Scientific American included this article by science writer John Horgan. who contends that the teleological matter of "what's the point of it all" weighs very much on the minds of many scientists today, whose theories to date have taken them about as far as experimentally possible. In his article, Horgan also raises the issue of terror management theory, which has to do with how we sentient humans have learned to cope with the knowledge of our imminent demise. At its extreme, the theory says that all human endeavor—getting educated, making money, developing hobbies, having children and whatever—is nothing more than our subconscious efforts to distract us from the fear of death, a fear that only we humans seem to be acutely aware of. Horgan's article touches upon an issue that to my knowledge was first raised by noted physicist Frank Tipler, whose 1997 book$$^{**}$$ The Physics of Immortality: Cosmology, God and the Resurrection of the Dead says that we'll all come back again at the "Omega Point," a time in the unimaginably distant future after the universe has undergone complete heat death. But it ain't heat you should be worried about, but the time when the universe has achieved maximum entropy through the dissolution and decay of all the matter, stars, galaxies and black holes, leaving nothing but a thin fog of stray photons. And it is this fate, Horgan writes—this unimaginably boring, bland, seemingly pointless fate—that is now keeping many physicists up at night. The good news—if you are capable of accepting it—is that you and I will never have to worry about this fate of the universe (which modern cosmology says is certain and unavoidable), as we'll all be dead long before it takes place. And that's the entire point of what I'm saying here. The end is nearer than we think—we should be ever ready for the return of Jesus Christ, because the End Times comes when we draw our last breath. Maybe that was what Christ was getting at all along. $$^{**}$$ Tipler's book opens with this moving dedication: Dedicated to the grandparents of my wife, the great-grandparents of my children Jozefa Basarewska and Adam Rokicki Shot to death by the Nazis in 1939, for the crime of being Poles Jozef Basarewska Tortured by the Gestapo, and died shortly thereafter All three being citizens of Torun, Poland, the birthplace of Copernicus, Who died in the hope of the Universal Resurrection And whose hope, as I shall show in this book, Will be fulfilled near the End of Time  Free Speech? — Posted Sunday October 3 2021 Felicia Hofner is a young native German from Munich currently living in Cincinnati, Ohio. Her popular YouTube site German Girl in America deals with cultural and political differences between Germany and America. Her latest video addresses a number of actions that are surprisingly illegal in Germany. My first visit to Berlin and Munich impressed me with how open and sincerely apologetic Germans are regarding the Holocaust. Despite the ongoing presence of neo-Nazis and a pervasive distrust of immigrants (albeit by a tiny minority of Germans), laws have been enacted in Germany designed to both secure the dignity of all persons living there and to fix Germany's responsibility for the horrors of World War II. I already knew that it is illegal to say "Heil Hitler" or "Sieg Heil" in Germany, but according to Ms. Hofner it is also unlawful to publicly deny the Holocaust, whatever one's opinions might be on the subject. She explains that this is not a violation of free speech per se, but an acknowledgment of the inherent dignity of those living and dead who suffered as a consequence of Germany's past persecution of the Jews. I could not help but compare the situation in Germany with that here in my country, where one can pretty much say anything in public, in the social media or anywhere else, regardless of how preposterously wrong, stupid or hurtful it might be. I am reminded of the American ignoramuses (almost solely white evangelicals from Red States) who openly denigrate minorities, the incidence of mass shootings, climate change and vaccination efficacy, often with horrendous consequences. This is "free speech" in America. However, the state of Wisconsin recently did formally ban certain forms of speech, albeit applying to critical race theory and historical slavery. "Multiculturalism, equity, racial bias, social justice" and other terms are now banned from official state legislative language, school districts and other public agencies. Of course, the bill was passed by a predominance of Republican legislators in that state. God help this country.  Dark Energy Again — Posted Thursday September 30 2021 Astrophysicist Ethan Siegel's latest article discusses the nature of dark energy, which scientists believe accounts for some 68% of all the energy in the universe. Ordinary matter and radiation (protons, neutrons, electrons, neutrinos and photons) contribute only 5%, while the remaining 27% is thought to be dark matter, a strange variant of ordinary matter that is non-interacting with anything except gravity. Over the past three decades billions of dollars have been spent looking for experimental evidence of dark matter, but to date all efforts have come up empty. Siegel posits the possibility that dark energy is just a property of spacetime itself, and is not a particle or a field. Basic cosmological theory says that the universe is not expanding into anything (like a surrounding empty space), but that the expansion itself creates space, and this space may contain a constant energy density that happens to be dark energy. The few reliable estimates we have indicate that this energy density is very small but non-zero, and that it is positive and so results in a kind of antigravity field that tends to push ordinary matter away. This would explain the observations of Perlmutter, Riess and Schmidt, who jointly won the 2011 Nobel Prize in Physics for their 1998 discovery of the accelerating expansion of the universe. I once thought that the energy lost by photons (via the red shift) as they are stretched by expanding space might account for dark energy, but this idea has been discounted. Others have thought that the zero-point energy of the vacuum might be dark energy, but the nature of vacuum energy to date does not have a sound theoretical basis. Einstein himself proposed the cosmological constant $$\Lambda$$ in 1917, which (when added to the gravitational field equations) fully explains dark energy, but this too lacks a firm experimental basis. Meanwhile, Einstein's gravity theory itself holds that mass-energy is not strictly conserved, which violates the once-traditional law of mass and energy conservation. So what is dark energy, and where does it come from?  Stop Looking for Superman — Posted Thursday September 23 2021 Oh Superman where are you now When everything's gone wrong somehow The men of steel, the men of power Are losing control by the hour. — Genesis, Land of Confusion (1986) Just months into his administration, President Biden is being blamed for all of America's faults, not only from conservatives but from his own party as well. Meanwhile, hideous moral monsters like Donald Trump cruise along, supported by willfully ignorant and stupid conservative fawns who've led us once again into another COVID-19 disaster: Meanwhile, COVID deaths are now averaging 2,000 a day. Great job, morons. Case in point: former Trump national security advisor Michael Flynn is now claiming that Biden operatives are putting COVID vaccine into salad dressing, and Trumpists are swallowing the lie whole hog. God help us. As the Genesis song indicates, the human race has too many people doing too many wrong things. That was 35 years ago, but it applies even more today. With some 7.8 billion people on the planet now, all it takes is a tiny minority to ruin everything.  Racist Hypocrisy — Posted Thursday September 23 2021 Gabby Petito—so young, so beautiful, so white$$\ldots$$so much more interesting and important than missing women of color. This happens on a regular basis—a beautiful, young white woman goes missing or is found murdered, and all the news networks drop everything to focus on her. Police, volunteers, helicopters, surveillance aircraft and all manner of other resources combine forces to solve the mystery, and Americans are glued to their television sets waiting for the latest news. Meanwhile, many more women of color undergo the same fate, but are ignored completely by the media. Yet Americans pride themselves as being beyond racism. It's all because of ratings, and the media know perfectly well that viewership depends heavily on the color of the unfortunates. Shame on us.  Turtles — Posted Wednesday September 22 2021 And then, a sail appeared; it was The Rachel. The Rachel, who in her long melancholy search for her missing children found $$\ldots$$ another orphan. — Herman Melville, Moby-Dick Today I watched 1999's The Thirteenth Floor again for the first time since my wife passed away. It's based on the possibility that we're living in a computer simulation, programmed and run by future programmers (human or otherwise), and I still believe the concept has some merit, although I don't truly think it describes the reality of our world. The concept has some religious aspects I won't go into here, except to say that some fellow members of my church also believe it's at least possible. The 1999 film is based broadly on the 1964 story Simulacron-3 by American science fiction writer Daniel F. Galouye. It concerns the near future in which some computer programmers develop an artificial world inhabited by sentient people of their own design, all unaware that they're simulated. In the movie, one of the simulated characters discovers "it ain't real": Later, "real-world" programmer Douglas Hall takes his own trip and makes a similar disturbing discovery: Many philosophical articles have been written about the simulation hypothesis, including the possibility that it's not only just turtles all the way down but turtles all the way up as well. I've sometimes pondered the possibility that the linkage is somehow circular, so that the simulations all derive from one another, and that nothing is either real or unreal.  Coincidence? — Posted Thursday September 16 2021 Once is happenstance, and twice is coincidence, but three times is enemy action. — Auric Goldfinger In quantum mechanics, anything that is allowed to happen, no matter how improbable, will happen. This is encapsulated in the Quantum Totalitarian Principle of Murray Gell-Mann, the late Caltech physicist and winner of the 1969 Nobel Prize in Physics, which states that "Everything that is not expressly forbidden is compulsory." And according to the so-called Law of Truly Large Numbers, even the most outrageously improbable event imaginable is likely to occur at some time. For example, over the complete history of our race some 110 billion human beings have lived out their lives and, with the countless events they've witnessed, at least a few seemingly impossible events will have taken place. Barring acts of God or clever tricks by humans, they can all be dismissed as coincidences. Some forty years ago, the Japanese particle physicist Yoshio Koide discovered a formula that many scientists believe simply must have a scientific explanation. Given the currently known masses of the electron $$m_e$$ and its identical (with the exception of mass) cousins the muon $$m_\mu$$ and the tau $$m_\tau$$, Koide's formula is $$\frac{m_e + m_\mu + m_\tau}{\left( \sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_\tau} \right)^2} = 0.666661\ldots \approx \frac{2}{3}$$ The slight difference from the exact 2/3 figure can be completely attributed to the uncertainties in the known masses. These uncertainties were larger when Koide first made his observation, but the formula has continued to converge on 2/3 since that time. It is entirely possible that with more accurate mass measurements, the formula will indeed be precisely 2/3. The formula may still be just a coincidence, but if improved measurements of the masses of these particles are able to add two or three more 6's to the formula, then physicists will likely have to accept the fact that new physics is involved. This is the take according to astrophysicst Ethan Siegel, who discusses the formula in his latest online article. But I have an even bigger question: how in the world did Koide come up with this crazy formula in the first place?!  What an Age — Posted Monday September 13 2021 My father was born in Illinois on January 8 1905, four years after the Victorian Period officially ended. That era governed England during the reign of Queen Victoria from her coronation in 1837 to her death in 1901, but its influences in terms of culture, politics and technology spread all the way to America. One of those influences had to do with the dressing of young boys as girls; here is my father in mid-1908 with long blonde locks, looking rather like a girlish Buster Brown, a popular comic strip character of the time: The life expectancy in America when my father was born was only 49 years, so people had to grow up quickly compared to now. Education was still hit and miss—if you managed to graduate from high school, that was great, but college was a distant hope for most. Articles from my father's high school yearbooks (1919-1924) reflect the need for most kids to leave school, get a job, make money, get married, have a family, and hope for the best. Oddly enough, germ theory was well established when my father was born, but routine chlorination of drinking water didn't arrive until 1906. Prior to that time, people died in droves due to water-borne typhoid and cholera, due mostly to contamination of the drinking water supply. Case in point: my father had three brothers, all of whom lived to old age except for Russell (born 1896), who unexpectedly fell dead on the floor in 1902, presumably because of cholera. I have an original page of his Kindergarten scribbles, a rare artifact preserved by my late sister. This and other issues are addressed by Joe Scott, an afficionado of the Victorian Period, although he generally confines himself to science issues. In the following video he discusses the Victoria era in some detail, and it's amazing how many of its cultural and technological issues compare with those of America: My late wife and I were big fans of British television shows and movies, and one thing that always stood out for us was the strict formality that invariably existed between parents and their children in Victorian times (and even much later). Mr. Scott explains why this is so: the child death rate was about 60% before the age of ten, so parents were apparently reluctant regarding getting too personally close to their kids, knowing that their suvival into adulthood was very doubtful. With the advent of photography in Victoria's time, it became common to have a dead child or relative photographed to preserve their memory. Photographic memento mori (remembrance of the dead) dates back to the 1840s, but it achieved its heyday in the 1850-1880 period. YouTube is replete with such photographs, which range from the serenely beautiful to the macabre.  Pretty Neat — Posted Friday September 10 2021 The Pasadena area experienced a great lightning and thunderstorm last night, sadly without much of the rain we so desperately need. But on my walk this morning I was pleasantly greeted with this sight, something I haven't seen in ages. It's no big deal in many parts of the country, but rare around here.  The Night of the Hunter (1955) Documentary — Posted Wednesday September 8 2021 The acclaimed actor Charles Laughton directed only one film, which was 1955's The Night of the Hunter starring Robert Mitchum, Shelley Winters, Lillian Gish, Peter Graves and James Gleason. The movie was not a financial success when it was first released, but it has since become a classic noir-ish film with subtle sexual and religious motifs and overtones. The plight of the two children, desperately fleeing a homicidal maniac played brilliantly by Mitchum (in his favorite role of all time), underscores the recurrent theme of innocence fighting off the evil of the world while surrounded by hapless adults who are either unaware of the evil or are unable to recognize what is going on around them. This morning my older son alerted me to this recent 2 hour, 40 minute YouTube documentary, in which Laughton is depicted discussing the film and directing the actors during various outtakes and scenes. It's brilliant, and I'm so grateful that it's now available for viewing. (Thanks, Kristofer!) At one point in the film, an exhausted, sleep-deprived John (played by Billy Chapin) is awakened in the dead of night by the idle singing of the pursuing killer, who always seems to be just one step behind John and his younger sister Pearl. "Don't he never sleep?!" he intones to himself, which to me represents the constant threat of unrelenting evil that pervades our world. Mitchum's repeated rendition of the old Gospel hymn "Leaning on the Everlasting Arms" is both charming and malevolent at the same time, and once you've seen the film the hymn will never sound the same again. Don't miss the film or the video.  Nuts on the Proof of the Gatic Theorem — Posted Saturday September 4 2021 The late cartoonist Gahan Wilson was a favorite of mine in the 1970s, and his NUTS series was a great take-off on the Peanuts strip. I remember this one, as it reminds me of Miss Woods' high school geometry class. I was never sick in high school, but I swear every day in her class was like this one.  Hossenfelder Again — Posted Saturday September 4 2021 I apologize for posting yet another of German physicist Sabine Hossenfelder's videos, but she addresses an issue that many cosmologists have been questioning for the past few decades, which concerns the validity of the Cosmological Principle. In short, the principle states that if one looks out at great distances, the universe appears to be both isotropic and homogeneous—that is, wherever one looks, the density of matter and radiation appears to be uniform. The Cosmological Principle is a bedrock assumption in standard cosmology, because it's really the only way the dynamics of the universe can be understood analytically. For example, the Friedmann equations (which to date have been remarkably accurate in describing the dynamical universe) could not be derived from Einstein's general relativity theory without the simplications that the Cosmological Principle provides. As Hossenfelder points out in the video, recent research has shown that if the Cosmological Principle does not hold absolutely, then the assumed existence of dark energy (and possibly dark matter) might be invalid. A universe completely devoid of dark energy and dark matter would most likely halt its observed expansion and recollapse in the distant future, possibly resulting in a new Big Bang. I've always wondered if the Cosmological Principle might be made more realistic if some kind of clumpiness or non-uniformity could be embedded in the formalism, perhaps by introducing some sort of random "fuzziness" in the large-scale distribution of matter and radiation. Maybe this kind of adjustment would explain the divergence seen in Type 1a supernovae data, which seems to imply that the universe is expanding at an accelerated rate. Indeed, the following graph published in 1999 won its researchers the 2011 Nobel Prize in Physics. Just wondering.  A Discovered Notebook — Posted Wednesday September 1 2021 I met my future wife Munira when she joined our laboratory in May 1972. She would usually sit alone eating her lunch and reading the Bible, but on occasion she would read from an old, tiny book that had wood covers. Later I learned that the book was The Imitation of Christ, written anonymously in the 15th century but usually attributed to one Thomas à Kempis. It was originally published in Latin, but has since been translated into many other languages. During lunch I would occasionally sit and chat with Munira in the little garden outside the lab. One day she loaned me the book, although at the time I could hardly consider myself to be a devout Christian. But I did read it, and returned the book to her in late 1972. I honestly didn't give it much thought at the time. When Munira died in July 2019 I found the book in her handbag, where without my knowledge she had carried it throughout our 42 years of marriage. Then yesterday, while going though some of her things in the garage, I found a copy of the Imitation of Christ that Munira had laboriously handwritten into one half of a notebook from her first year at the University of Cairo, Egypt in late 1963 (which is ironic—she started college the same year I started high school). She wrote it in English, her second language, and with some amusement I spotted a few grammatical errors that she made, although the context was correct. The other half of her notebook contained detailed notes she transcribed from lectures she had taken in her first year at university. Amazingly (to me), those notes were from her first physics course, which included elementary atomic physics. So there was my future wife, studying calculus-based physics when I was just getting comfortable with Algebra I in high school. In fact, I never took physics in high school, despite being fascinated with the subject from an early age. I now treasure these notes from my dear late wife, who went on to earn a Master's Degree in chemical engineering while maintaining her Christian faith throughout her life. And I consider the juxtaposition of her physics notes with The Imitation of Christ to be a moving and very profound message to me from her spirit, and I am deeply moved. Three months ago I was ordained a deacon in the Coptic Orthodox Church, the same church my wife grew up with in her native Egypt. During our marriage we attended the church only infrequently, but now it's a lifeline for me as well as an ongoing connection with her and with the Christ she loved. With God's help I hope to join her again someday in the Kingdom of Heaven.  The Chandrasekhar Limit — Posted Monday August 30 2021 In 1930, the brilliant Indian physicist Subrahmanyan Chandrasekhar derived the theoretical limit of how massive a star can be without collapsing into a white dwarf, a neutron star or a black hole. That limit today is about 1.44 solar masses, and of the hundreds of white dwarfs and neutron stars observed to date, none have exceeded the limit, confirming Chandrasekhar's work. I lost interest in stellar physics years ago, mostly because Chandrasekhar's mathematics was just too daunting. But here's a wonderful new YouTube video on the derivation of a decent estimate of the Chandrasekhar limit involving mostly just algebra: I find it interesting that Chandrasekhar's limit was ignored for decades, mostly because of the refusal of colleagues to believe it was valid. But in time they did, and in 1983 Chandrasekhar was awarded the Nobel Prize in Physics for his work. I can't help but feel that at least some of the difficulties he faced had to do with the same racist attitudes the similarly gifted Indian mathematician Srinivasa Ramanujan had to deal with. On the basis of a series of brilliant but unsolicited calculations he sent to the noted Cambridge mathematician Godfrey Hardy, and almost out of curiosity Ramanujan was invited to England by Hardy. Hardy became Ramanujan's mentor, but the racist attitudes and cultural differences Ramanujan had to endure in England were profoundly difficult for the young man, and he died at the young age of 32. A decent overview of Ramanujan's life can be glimpsed in the 2015 film The Man Who Knew Infinity.  Gone 25 Months — Posted Saturday August 28 2021 And now I'm lost, so gone and lost Not even God can find me. — They Call the Wind Maria  Siegel on Dark Energy — Posted Thursday August 26 2021 This recent Medium article by astrophysicist Ethan Siegel deals with the nature of dark energy and its possible effects on the future of the universe. Dark energy is represented by the cosmological constant $$\Lambda$$ in Einstein's gravitational field equations, given by $$R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu} \tag{1}$$ The standard model of cosmology says that as the universe expands, ordinary matter (including dark matter) and radiation get diluted, but dark energy is actually created with constant density $$\rho_\Lambda$$. Dark energy has a kind of antigravity effect, so as the universe gets bigger the antigravity effect grows, resulting in the runaway, accelerated expansion of the universe. If the standard model is correct, and if $$\Lambda$$ is truly a constant, then the universe will definitely expand without bounds forever. Consequently, matter and radiation will become so diluted that the universe in effect will simply disappear into a bleak nothingness. But Siegel raises the possibility that $$\Lambda$$ may not be a true constant—it may increase in strength or grow weaker with time, with vastly different effects on the fate of the universe. I've always felt that the $$\Lambda g^{\mu\nu}$$ term in Einstein's field equations was an easy plug-in, since the covariant divergence of (1) (which implies a kind of mass-energy conservation) is assumed to vanish. The metric tensor $$g^{\mu\nu}$$ is a constant under covariant differentiation, but if $$\Lambda$$ is not a constant but a differentiable scalar then all bets are off with respect to the model. Similarly, it is also possible that the metric tensor does not vanish under covariant differentiation. This is called non-metricity, and the concept has been around almost since the dawn of Einstein's general relativity theory. Even if the combination $$\Lambda(x) g^{\mu\nu}(x)$$ is somehow covariantly constant, the cosmological consequences of Einstein's equations would be radically different and far-reaching. Many theories have been proposed to date that examine these consequences, but as yet they have not agreed with observation. As the early 20th century astrophysicist Arthur S. Eddington once noted, "The universe is not only stranger than we imagine, it is stranger than we can imagine."  Yes, Everything Vibrates — Posted Monday August 23 2021 German physicist Sabine Hossenfelder's latest blog was inspired by "two lovely ladies" who expressed their belief that they wouldn't contract COVID-19 because their personal "vibrational frequencies" are out of sync with that of the virus. I've heard of crazy beliefs like magnet therapy, homeopathic medicine, vaccine magnetization, astrological forecasting and other nonsense, but this one takes the cake. Hossenfelder's opinion mirrors mine, but she notes that there is some truth to the notion that "everything vibrates." This is true even at a temperature of absolute zero (0 Kelvin)—a particle at that temperature jiggles a tiny bit, due to the Heisenberg unceertainty principle. But I fear that Hossenefelder's guarded admission will be taken completely out of context by the women appearing in her video, assuming they bother to watch something on the Internet that does not feature the American flag, guns, Trump and competitive Krispy Kreme doughnut eating. Back in the late 1960s we had harmless hippie behavior like love-ins and navel gazing, but modern pseudoscience like vaccine avoidance and willful stupidity can have truly tragic consequences. If the estimated 30% or so of Americans opt not to get vaccinated (out of allegiance to Trump or preferences for hydroxychloroquine, Clorox injections or veterinary drugs), then the current and projected variants of COVID-19 will be with us forever.  Airliner Disaster Over Duarte, or When World Lines Intersect — Posted Monday August 23 2021 I had long forgotten this event when I stumbled across this YouTube video, which describes an airline disaster that I witnessed back in June 1971. I left this comment on the YouTube site: I had just graduated from college, and was walking home to my parent's house in Duarte, California from the Alpha Beta supermarket when I heard a distant explosion. Looking east, I saw something plummet straight down from the sky. After dropping off my groceries, I drove to the Fish Canyon area of Duarte only to find that the roads had been blocked off by police cars. I returned home, turned on the TV and learned that it had been an in-flight collison between a commercial passenger jet and a military aircraft. Later, there were rumors that the military jet had been doing a victory roll just prior to the collision, but it was subsequently judged to be an evasive maneuver by the pilot. God save the souls of those who perished. In physics, a world line is the trace of one's life sequence through space and time. I find it tragically coincidental that the world lines of two aircraft might find themselves at the same point in spacetime. Since that day fifty years ago I have flown many times, but because of this event I still do not like flying.  The Horror! The Horror! — Posted Friday August 20 2021 As a junior at Duarte High School in 1966 I saw a film screened in the school's auditorium on the dangers of premarital sex. A U.S. Army film made back in 1944 to warn overseas soldiers on the hazards of venereal disease, the film traces the sad tale of one unlucky soldier who discovers he's contracted a "fine dose" of VD. Just before announcing his discovery to a pal, his buddy asks "What's eating you?" I didn't see the unintended humor in that remark in 1966, but it's all too obvious to me today! While walking out of the auditorium that day, I recall one girl saying to her friend "Did you see that chancre sore? Ugh!" I remember it distinctly because I had a fatal crush on that girl at the time. I suppose the film had its intended effect on her, but the message was largely lost on me, as I had no chance of having even a date in high school, much less experiencing sex. Back in those days kids talked about getting the "clap" (gonorrhea), which was easily treated with penicillin, while syphillis was another matter entirely. There was a widespread rumor in high school back then that the cafeteria workers were putting saltpeter (potassium nitrate) in the food to counteract the raging hormones thought to be prevalent in boys at the time. I'm still not sure if that rumor was true, nor if saltpeter had such an effect. You can watch the 30-minute film at this YouTube site. Meanwhile, the ultimate venereal disease remains the one depicted in the critically-acclaimed 2014 horror film, It Follows. It's recommended watching, and it might just change your mind about illicit sexual conduct.  The Kal-Els at Home — Posted Tuesday August 10 2021 I fell in love with science (especially physics and chemistry) while reading comic books as a child in the late 1950s and early 1960s. Staple fare then was Superman, Superboy, Action Comics, Adventure Comics and World's Finest Comics. "Kal-El" was Superman's name on his home planet Krypton, which exploded due to an instability of the planet's core, minutes after Kal-El was saved by his parents Jor-El and Lara by shooting their young son into space via rocket. Kryptonians had no super powers because their sun was red, but when Kal-El landed on Earth he attained super powers due to our sun's yellow color. The remnants of Krypton were highly radioactive due to their conversion to kryptonite, but it was toxic only to Kryptonians. Pieces of Krypton occasionally found their way to Earth, providing many plot lines for the comic books. I never questioned the existence of a radioactive element such as kryptonite, although in 1962 I knew there were only 106 known chemical elements at the time. My 8th grade science teacher at the time was Mrs. Wilson, a real battle ax you really didn't want to mess with. She caught me talking in class one day, and demanded that I give her the number of chemical elements. To her surprise I answered correctly, but she told me never to speak in class again while she was talking. Mrs. Wilson was probably around 40 years old then. She had a big impact on my life, and I wonder what happened to her. By the way, names with "el" often have religious significance. It's related to the God of Judaism and Christianity, with Michael, Gabriel and Raphael being the principle angels of orthodox Christianity. Conversely, names with "bel" are often related to wicked paople, due to its connection to Baal, the pagan god of the ancient Canaanites and others. For example, Israel's 9th century BC King Ahab was seduced by Jezebel, who was ignomiously pushed out of a window, with her body eaten by dogs. Meanwhile, my name is Bill, and I can only wonder what disaster awaits me.  Cuomo Resigns — Posted Tuesday August 10 2021 With some eleven women testifying that New York Governor Andrew Cuomo sexually harrassed them, Cuomo has resigned. Meanwhile, former President Donald Trump, accused by fifteen women of sexual harrassment and molestation, skates off unblemished. Something's wrong here, but the worshipers of Trump could care less.  Learning Can Be Fun When You're Miserable — Posted Friday August 6 2021 First there was the COVID-19 alpha ($$\alpha$$) variant. Then the beta ($$\beta$$) and gamma ($$\gamma$$) variants came along, but they were minor players, as far as viruses are concerned. The delta ($$\delta$$) variant then came along, and it's currently all the rage (literally). Now there's news of the epsilon ($$\epsilon$$) variant, and even a lambda ($$\lambda$$) variant. It appears that America is gonna have to learn the entire Greek alphabet before (or if) this thing is over. If it doesn't end, I hope we'll start learning the Arabic alphabet, as I need the practice.  Merritt's MOND Book — Posted Monday July 26 2021 I received my copy of David Merritt's 2020 book A Philosophical Approach to MOND (MOdified Newtonian Dynamics). At only 250 pages, it's a fairly quick and easy read (provided you have at least an undergraduate degree in physics and you skip over the book's preliminary philosophical stuff). I found that it deserves all the praise it has received from Germany's Sabine Hossenfelder and many others, although I don't think it will soon overturn the conventional Standard Model of Cosmology, which asserts that dark matter exists. MOND basically says that gravity acts a little differently than what's taught from the usual $$F = ma$$ point of view, with the gravitational force falling off as $$1/r$$ rather than $$1/r^2$$ at galactic distances. This means that at great distances stars will orbit their galactic centers at roughly constant speeds, which is what is observed for nearly every galaxy. Dark matter, on the other hand, accounts for these constant velocities by assuming the presence of dark matter "haloes" surrounding the galaxies, which preserves the usual Newtonian $$F= ma$$ force law. First proposed by Israeli physicist Mordehai Milgrom in 1983, MOND received aparse attention despite its ability to accurately predict stellar motions and other cosmological phenomena discovered in subsequent years. Its main drawback was that it was not a relativistic theory, although in later years such modifications to Milgrom's theory appeared that removed this constraint via extended versions of Einstein's general theory of relativity. Merritt's book presents three approaches to MOND. The first is Milgrom's basic idea (which seems to have been little more than an inspired guess). It's followed by a relativistic version developed by Milgrom and colleague Jakob Bekenstein. The third approach is a kind of mixture of MOND and dark matter, which Hossenfelder believes might be a dark matter superfluid. The Milgrom/Bekenstein theory came out in 1984, and to relativistically reproduce the successes of the original MOND theory they had to introduce a universal scalar field $$\psi$$ into the formalism. But a flaw in this theory led Bekenstein to a 2004 revision involving a vector field $$A_\mu$$ along with $$\psi$$ that he planted into the fundamental metric tensor $$g_{\mu\nu}$$. This in turn required the theory to now have the kinetic part $$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$$, which looks a lot like the electromagnetic field tensor. The final theory, which appears as the expression given by Equation (6.19) in the book, now had at least five adjustable constant parameters, making it look (to me) a lot like curve fitting. Furthermore, the Ricci scalar $$R$$, which traditionally accounts for the gravitational field, is nowhere to be seen (at least I can't find it). By comparison, Milgrom's original theory had just one constant added parameter, $$a_0$$, which causes the gravitational potential to fall off more slowly. This reminds me of the theories of Hermann Weyl and Mannheim/Kazanas (which I have discussed many times elsewhere on this website), which look far more promising. Still, the accounts of the successes of MOND described in detail in Merritt's book are hard to overlook or dismiss, and I'm even more convinced that a consistent relativistic version of MOND will eventually prove that dark matter is nothing more than a convenient myth.  Two Years — Posted Sunday July 25 2021 Today marks exactly two years (104 weeks) since my dear wife Munira passed away. I'm trying to move on, get off the Prozac and the grief therapies, but it's just not happening yet. Here we are on her 45th birthday in 1991: May God bless you and keep you always, dear Mimi, as I await and pray for the day when I will see you again in Heaven.  The Party of "NO" — Posted Wednesday July 21 2021 The Republican Party, spearheaded by Kentucky Senator Mitch McConnell and Texas Senator Ted Cruz (but really dominated by the disgrunted and still very dangerous ex-president Trump), has become the party of "NO," determined to block all of President Biden's plans to reinvigorate the economy, deal with climate change and infrastructure issues and everything having to do with serious COVID-19 mitigation. This situation reminds me of my favorite opera of all time, the five-act Italian opera Mefistofele, composed by Arrigo Boito in 1868. It's based on the famous story of Goethe's Faust, a scientist who sells his soul to the devil in exchange for beauty and knowledge. The opera includes the famous "Whistle Aria," in which the devil reveals his true nature: I am the Spirit who denies Everything always: the stars, the flowers. My sneering and hostility Disturb the Creator's leisure. I want Nothingness and the Universal ruin of Creation. My vital atmosphere is What is called Sin, Death and Evil! I laugh and snarl this monosyllable: "NO" I destroy, I tempt, I roar, I hiss: "NO" I bite, I ensnare, I destroy, tempt, roar, hiss. I whistle, whistle, whistle, whistle, eh! [whistles loudly] I am part of the innermost Recesses of the great All: Obscurity. I am the Child of Darkness! What an appropriate description of today's Republican Party.  Why Distance and Size Don't Matter — Posted Wednesday July 21 2021 Science writer Ben Brubaker talks about Bell's inequality in today's online Quanta Magazine, where he summarizes the notions of locality and non-locality of events in spacetime, and how the late physicist John Bell destroyed the idea that two events occurring far apart cannot take place simultaneously. Bell's inequality has since been demonstrated many times experimentally. Some years ago I showed that the inequality is truly violated in elementary quantum mechanics, and that two distant but entangled events can indeed occur at the same time. [There is one simple way to show that this is true for one extreme case. The distance or interval between two events is expressed by the invariant line element $$ds$$, which in Cartesian coordinates is given by $$ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2$$ At the speed of light, $$ds = 0$$, which means that physical distances (and time itself) become meaningless. If you were a photon, you would perceive yourself as existing everywhere in the universe at the same time, and in this sense you would be immortal as well since you would not perceive the passage of time at all. This might seem to be a paradox to a human, since turning on a light and letting the photons impinge on your cornea would make it seem that a photon is born at one instant and destroyed shortly later. Thus, to a human a photon's lifetime is finite, while the photon would see itself as having no birth or death. But this is nothing but the famous twin paradox taken to its ultimate extent.] But all this made no sense to Einstein, and he tried to prove it in 1935 in a famous paper he wrote with collaborators Boris Podolsky and Nathan Rosen. It was not a proof, exactly, as Einstein simply argued that the concept of locality prevented the effects of one event from affecting a distant event faster that the speed of light. But quantum mechanics asserts that two entangled particles are in the same quantum state, and so the distance between the two makes no difference. I see this as meaning that the physical distance between two events in spacetime is in a sense meaningless, and since distance is a measure of the size of an object, the concept of size is essentially meaningless as well. This is the gist of a theory proposed by the German mathematical physicist Hermann Weyl in 1918, in which he asserted that distance between two points in spacetime is affected by the path that one takes to get from one point to the other. It was Weyl's initial intention to show that the path is affected by a combination of gravitational and electromagnetic fields, but this idea was quickly overturned by Einstein himself. It was subsequently shown in 1929 that Weyl's idea applied not to gravity but to quantum theory as the principle of gauge invariance. Gauge invariance is now a fundamental cornerstone of quantum physics, where it is believed to lie at the basis of all physics.  David Merritt on Dark Matter — Posted Tuesday July 20 2021 David Merritt, former professor of physics at Rochester University, writes in Aeon Magazine that it's about time that the standard model of cosmology begins to accept the very real probability that dark matter, like the late 1880s idea of the luminiferous aether, simply does not exist, and should be replaced by a relativistic version of modified Newtonian gravity (MOND). Merritt's 2020 book on the subject, A Philosophical Approach to MOND, has received great reviews, along with the support of notable physicists like Germany's Sabine Hossenfelder. I purchased Merritt's book from Amazon, but I haven't received it yet. However, from what I've read about it so far I tend to be in complete agreement with his views. Einstein's gravitational field equations are traditionally derived by a variation of the simple action quantity $$S = \int \!\! \sqrt{-g}\, \left( R - 2\Lambda \right) \, d^4x$$ where $$R$$ is the Ricci scalar and $$\Lambda$$ is the cosmological constant, with $$R$$ being a function of the fundamental metric tensor $$g^{\mu\nu}$$ and its derivatives. With $$T^{\mu\nu}$$ being the energy-momentum tensor representing mass-energy, the variation yields Einstein's field equations $$R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu}$$ where $$R^{\mu\nu}$$ is the ten-component Ricci tensor (in most applications, $$R^{\mu\nu}$$ and $$T^{\mu\nu}$$ have only the four non-zero diagonal components $$R^{00}, R^{11}, R^{22}, R^{33}$$ and $$T^{00}, T^{11}, T^{22}, T^{33}$$ ). Solution of the four associated differential equations yields fantastically successful predictions of planetary motion, the deflection of starlight, gravitational lensing and gravitational redshift, all of which have been observed to nearly prefect precision. But observation of certain galactic-scale phenomena (stellar velocities and galactic clustering) indicates that there is more matter than can be accounted for, which has led to the now-accepted notion of dark matter to account for the missing mass. Einstein's field equations are still valid, but the now decades-long search for dark matter particles and/or fields has come up completely empty, leading to the idea that dark matter does not in fact exist and that Einstein's gravity theory needs to be modified. I'll comment on Merritt's book once I've read it, but I've long believed (like Einstein himself) that Einsteinian gravity theory is only an approximation of the truth. To me, relativistic MOND is a step in the right direection.  Recent Stuff — Posted Wednesday July 14 2021 Here's a recent paper by some Russian physicists on some cosmological aspects of Hermann Weyl's 1918 gravity theory, which suggests that the Weyl vector $$\phi_\mu$$ might have something to do with dark matter. I think it's rather far-fetched, but then I once believed that Weyl's theory was at least partially true (it may still be), but I never connected it with dark matteer (which I don't believe exists). Meanwhile, I'm reading German physicist and neuroscientist Alexander Unzicker's 2015 book Einstein's Lost Key, which posits that if the speed of light were not an absolute constant (an idea that Einstein thought might hold some water) then notions like early cosmological inflation theory might be wrong. This idea piggybacks on some other notions that the Newtonian gravitational constant $$G$$ might vary with time (which Paul Dirac once proposed) or that the fine structure constant $$\alpha$$ might vary as well. Such ideas have never been demonstated experimentally, and I've always thought they were crazy, but then we humans have only been around a relatively short time, so we wouldn't be able to detect the changes even if they did occur. Here's a YouTube video posted by Unzicker on the ideas he proposes in his book. It's interesting, along with many of his other videos, but I've always wondered who he's lecturing to, as his audience is never shown.  McGaugh on Dark Matter — Posted Monday July 12 2021 Noted observational cosmologist Stacy McGaugh of Case Western Reserve University has long railed against the conventional belief that dark matter exists, despite hundreds of millions having been spent so far to detect it experimentally. It supposedly doesn't interact with anything (including itself) except gravity, and is otherwise invisible, tasteless and odorless, yet it somehow accounts for some 80% of all the matter in the universe. A whole slew of ideas have been proposed regarding its nature, including cold neutrinos, sterile neutrinos, axions and massive photons, although pixie dust has presumably been eliminated. McGaugh leans toward modified gravity theories as the preferred alternative to dark matter, the simplest version of which is modified Newtonian dynamics (MOND). There are many different types of modified gravity, all based on Einstein's original theory of general relativity, and many of these theories agree with observations, with some important shortcomings. The advantage of dark matter is that it can be made to agree with observations by simply sprinkling it around here and there to make it agree. McGaugh's latest post on the subject appears on his website Triton Station, along with many earlier posts on the same topic. He also composed the following graphic, which perfectly summarizes my own views on dark matter, which forms half of the lambda-cold-dark-matter ($$\Lambda$$CDM) model of modern cosmology:  Most Assuredly, It's Safe and Effective — Posted Monday July 5 2021 The chemical element radium has numerous isotopes, all highly radioactive. The most common is radium-226, which was discovered by the Curies in 1898. Although the Curies quickly discovered its toxic properties, by the mid-1910s it had acquired the false reputation as being a cure-all for any number of illnesses and conditions. It was also used in luminescent paint, as it glowed green in the dark. At the outbreak of America's entry into World War I, the paint was commonly used to coat the dials of wrist watches, which was of particular value to the military during night operations. Radium-based paint was applied to watch dials by manufacturers of wrist watches and other time pieces, most often by lowly-paid young women who used small, fine brushes to apply the paint. To achieve a fine point on the brush, the women (now referred to as radium girls) would regularly pass the brush tips along their moistened lips. This introduced radium into their bodies by direct oral exposure and by ingestion. But at the time radium was not only considered harmless but beneficial, so there was no concern regarding the health of the employees. Within a few years, however, these women began to exhibit severe health problems, including oral cancer and tooth and jaw degradation. But the companies providing the radium (notably U.S. Radium and Undark) and the watch factories aggressively denied the role that radium played in these problems. They continued to avoid any reponsibility for the thousands of severe illnesses and deaths that resulted from their products, and it took nearly three decades for health authorities to fully recognize radium's dangers. Here's a 1921 magazine ad from the Undark Company extolling radium's supposed health and beauty benefits. It represents one of the earlier examples of modern scientific and chemical quackery common to the era, which included the use of opioids such as cocaine and morphine in over-the-counter medications. But the practice continues to this day, in the form of homeopathic products and treatments, many megavitamins, innumerable beauty products, hair-growth formulas and magnet therapy. The now-prevalent conspiracy theory phenomenon is largely based upon such ignorance, despite overwhelming logical and scientific evidence to the contrary. God help us.  Ruben Bolling Does It Again — Posted Saturday July 3 2021 There's so much packed into this strip that I can't begin to summarize it.  The Consequences of Infinite Energy — Posted Saturday July 3 2021 I took a single graduate class in cosmology/astrophysics many years ago, and remember not liking it at all. Now it seems it's all I think about. Here's physicist Sabine Hossenfelder (again) talking about cosmological inflation, energy non-conservation in general relativity and the creation of baby universes. It's true that the old high-school law of energy conservation does not hold in general relativity, which to me means that infinite energy is always available, an idea that I immediately attribute to the Almighty Creator. In a nutshell, here's why energy conservation does not occur in general relativity. The ten Einstein field equations are given by $$G^{\mu\nu} = R^{\mu\nu} - \frac{1}{2}\ R g^{\mu\nu} + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu}$$ where the covariant divergence (you'll have to look that up) of both the Einstein tensor $$G^{\mu\mu}$$ and the energy-momentum tensor $$T^{\mu\nu}$$ vanishes. This indeed implies conservation. But true mass-energy conservation is dependent upon the vanishing of ordinary partial differential divergences. This difference is profound and irreconcilable, so mass-energy is not conserved. Bottom line: don't worry where the energy comes from. It just comes.  If You're 72 Like Me, It's Later Than You Think — Posted Thursday July 1 2021 It's July already?!  Sketchy Data — Posted Thursday July 1 2021 An ancient human-like skull has come to light. What did its owner really look like? We've all seen forensic reconconstructions of faces associated with ancient and modern skulls, often in attempts to identify unknown murder victims. Forensic scientists and artists use their skills to reconstruct the faces, but how often have you seen comparisons of the reconstructions with actual photos of the victims? Almost all of the time there's very little real resemblance other than agreement with cursory or basic facial features. It's the same story with artists' sketches of criminals based on eye witness descriptions. Sketchy data often leads to sketchy facts. I often find myself coming back to the following graph, which is now over twenty years old. It also involves what I consider to be sketchy data: The work behind this graph won its researchers the Nobel Prize in Physics in 2011. It basically says that the farther away certain standard candles (known as Type 1a supernovae) are from us, the fainter they should be based on what the Standard Model of Cosmology was telling us back in 1999. The data begin to diverge from the expected straight line at great distances, implying that the expansion of the universe is accelerating with time. This phenomenon has been linked to dark energy which, if constant, may result in the so-called Big Rip, a point in the very distant future in which stars, galaxies and even atoms will be torn apart by cosmological expansion. Although I believe that dark matter is likely non-existent, I do believe in dark energy, which Einstein's prematurely disregarded cosmological constant $$\Lambda$$ is based upon. It's really only a matter of whether $$\Lambda$$ is truly constant, or increasing or decreasing with time. But like facial reconstruction, I've not seen any significant improvements in the data that the above graph summarizes. There's simply just too much scatter in the data points at high red shifts, and the exact nature of Type 1a supernovae itself is not precisely known. For example, the metallicity of pre-nova stars (the abundance of elements in the stars beyond hydrogen and helium) must surely influence their characteristics during supernovae events, such that the assumed 1.44 solar mass limit (see my previous post) is violated to some extent. Nevertheless, the validity of the Type 1a model is generally accepted, and is now part of the $$\Lambda$$CDM ("lambda-cold-dark-matter") model of modern cosmology. I find this perplexing, because despite enormous theoretical research and experimental efforts, no one still has any real idea what dark energy and dark matter might be.  The Straw That Breaks The Cosmic Camel's Back — Posted Tuesday June 29 2021 A cold, incoherent object that exceeds approximately 1.44 solar masses will collapse in on itself, creating one of two possible remnants—a neutron star or a black hole. A black hole is a simple object that contains only mass, angular momentum and possibly electric charge (although instreaming charged particles would eventually cancel the hole's net charge). By comparison, a neutron star is highly complex, consisting of a thin atmosphere of stray neutrons and a solid crust, mantle and core of unimaginably dense neutronium (in actually, an element with an atomic number of zero!) The star would also likely be spinning at a high rate, a consequence of the conservation of angular momentum of the uncollapsed star. The gravitational pull of the star is so strong that even the slightest imperfection on its surface would be smashed flat, something akin to a microbe on the surface of a bowling ball. The extreme pressure at the star's core constitutes a form of gravity which, combined with the star's already incredible gravitational compressive force, is simply mind-boggling. But should the star somehow gain sufficient mass to exceed the 1.44 solar mass limit (via infalling matter such as interplanetary gas, planets, asteroids or other material), it is then expected to collapse into the comparatively featureless object we call a black hole. All ordinary massive objects obey an equation of state (EoS), which simply relates the object's density to its internal pressure. The familiar ideal gas law $$PV = nRT$$ is an EoS, but for solids it can be much more complicated. Indeed, no one knows what the EoS might be for a typical neutron star, assuming one even exists. It is easy to imagine a neutron star that's right on the cusp of becoming a black hole. Might dropping a paper clip on the star result in its collapse? Unlikely, as the star's EoS is probably forgiving enough to prevent it. But just how forgiving can it be, since the star must certainly be gaining mass over time as it absorbs infalling matter? One wonders how neutron stars can exist at all, since the 1.44 solar mass limit must surely be reached over reasonable cosmic time periods. Perhaps most neutron stars are so far below the limit to begin with that it would take many billions of years for them to accrete sufficient matter to become black holes. Now astrophysicists have detected two instances of a neutron star "accreting" a black hole, with the stunning result that the black hole simply swallows the star whole, leaving a more massive black hole and a huge outgoing gravitational wave. Such waves have now been discovered, and an even more interesting example of gravitational astronomy has been given to us.  Hossenfelder on Coincidences and Conspiracies — Posted Saturday June 5 2021 If you have a grid of evenly spaced straight lines on a piece of paper and you toss a bunch of needles on the paper, you can approximate the value of the transcendental number $$\pi$$ by counting the number of times the needles land on the lines. Non-mathematicians may wonder how $$\pi$$ shows up in this exercise, but it's not a coincidence. Noted German physicist Sabine Hossenfelder's latest video addresses the coincidence issue via the notions of human pattern identification and false positives, explaining how and why we tend to assign underlying agenticity and conspiracies to purely coincidental events, much like the Peanuts gang's interpretation of overhead clouds: Hossenfelder's talk is one of the best I've seen, and it explains a lot about the foibles and tragedies of human behavior, in particular the sad predominance of weak-minded right wingers to persistently believe in PizzaGate, the drinking of children's blood by Democratic Party leaders and similar crazy conspiracies actively or passively promoted by the Republican Party.  AI Lincoln — Posted Monday May 31 2021 I have an old book called The Lincoln Reader that I've had forever that relates many personal stories and anecdotes about Abraham Lincoln, my favorite president. Although he lost a chunk of his lower jaw during a molar extraction in the early 1840s, those who knew him said he had a fine set of healthy white teeth and frequently smiled, often when telling an off-color joke. Early photos of the day almost never showed people smiling, a consequence of the proprieties of the times and the fact that early photography usually took several seconds to minutes to capture an image. So people would just sit there, motionless and expressionless, and that's the way we see them today. With the advancing technology of artificial intelligence we now have relatively accurate ways of showing people in old photos as they might actually have appeared. Here's a new YouTube video that shows a smiling Lincoln, along with varying hair styles. Enjoy. Sometimes artificial intelligence doesn't work too well. George Washington wore almost full dentures in his later years, sporting false teeth fashioned from human, horse and cow teeth. Here he looks just like Soupy Sales in drag.  Fine Tuning — Posted Saturday May 15 2021 In his latest video, YouTube's "Who Gives a Bleep?" Arvin Ash talks about the fine-tuning argument, which deals with the nature of the fundamental constants of our universe, such as the gravitational constant, the fine-structure constant, the magnitude of elementary electric charge and many other parameters that govern the workings of the observable universe. The problem involves the realization that if these constants were only slightly different (either individually or collectively), the universe would either not exist or would not be capable of creating or sustaining life. It's a short video, and well worth watching: As I see it, there are only two possibilities: either there is a creator (God or an external entity such as a computer programmer in a simulated universe), or the multiverse theory (or the many-worlds interpretation of quantum mechanics) is valid, in which case there are numerous (possibly infinite) universes each having varying fundamental constants, and we just happen to be living in one in which life is possible. Perhaps the most important aspect of Ash's talk is his assertion that we cannot talk about the probability of which argument is right, since we have no statistics available to base a probabilistic argument (we observe only one universe, and a sampling size of one is insufficient to do any calculations). This situation perfectly mirrors the familiar "science vs religion" argument, and it's unlikely that we'll ever be able to resolve it (but perhaps both are true).  The Goat Problem $$\ldots$$ Again — Posted Friday May 7 2021 If you tie a goat to the outside of a barn and let it graze, how much grass can it clear? This might have been a practical math problem centuries ago, but Quanta Magazine seems to think it's still relevant today. What's interesting is that the problem becomes much more difficult if the goat is tied to the inside of a closed barn, regardless of the barn's shape. That couldn't have been much of a problem way back when, but it's still occupying mathematicians today. I addressed the problem of a goat in a circular fenced yard on December 11 last year, but now Quanta has upped the ante with a square yard. This time I didn't bite, but you can try it yourself if you have nothing better to do this weekend.  More Geek Stuff — Posted Friday April 30 2021 German physicist Sabine Hossenfelder's views on dark matter vs modified gravity have changed. For the details, you can watch her latest video on the subject here. For the few who care about such things, back on March 27 I posted some comments on a recent paper claiming that the Mannheim-Kazanas (MK) spacetime metric did not predict flat stellar rotation curves in galaxies. I disagreed, and I've been waiting for Philip Mannheim to publish a rebuttal. But now there's another paper that supports the claim that the MK spacetime does indeed predict flat rotation curves by analyzing the effective potential associated with the metric. In the paper's analysis, the $$\gamma$$ term plays an important role in defining the radius at which stellar velocities approach constant values far from their galactic centers. This radius is the same one I came up with. The MK metric is the only spacetime I've seen that is free from any added parameters (such as scalar and vector fields) that reproduces the predictions of the standard Einstein field equations. Like the Einstein-Hilbert action, that of the MK action (first derived by Hermann Weyl 100 years ago), is pure geometry.  Alien Visitation — Posted Saturday April 24 2021 There are countless YouTube videos depicting UFO sightings, and there's an equal number of people claiming they've been abducted by extraterrestrials for experimental purposes. Writer Devan Taylor talks about the difficulties associated with interplanetary visitation by advanced alien species, perhaps the biggest being "Why the hell would they come here in the first place?" If extraterrestrials could ever visit Earth, there are only a few possible scenarios. One, they're malevolent, in which case we're already toast, since they would obviously be far more technologically advanced than we are (discounting the entertaining but otherwise preposterous Independence Day film); two, they're benevolent, in which case we'd have already made contact with them; and three, they're just unobtrusive observers, in which case we have today's current situation. I personally believe there is intelligent life out there, but we'll never make contact with them because they're just too far away and just too darned spread out, so stop thinking about UFOs, aliens and all that nonsense. But meanwhile you can muse over the purely imaginary value of alien visitation, as depicted in this video clip where the Simpsons get abducted (obviously, aliens will need to have powerful tractor beams):  What's Up with the Arizona Ballot Audit? — Posted Saturday April 24 2021 The Arizona Republican Party has hired a right-leaning Florida-based company called "Cyber Ninjas" (I kid you not) to assist in the audit some 2.1 million ballots in the state that were cast during the November 2020 presidential election. Although no irregularities have been reported, the Arizona GOP just wants to be sure that Biden won fair and square. Reports immediately surfaced that the auditors were illegally using blue and black pens to verify the ballots, in violation of the state's audit rule that only red pens may be employed (only red pens may be used, because computer scanners will falsely count any ballots illegally modified with black and blue pens). When the violation was reported by an Arizona reporter, auditors switched to the red pens, after which the reporter was banned from the audit site. I bring up this story because on April 20 I posted some thoughts on data fluctuations and their significance. When it comes to counting election ballots, there will always be a few innocent mistakes, such as human and computer counting errors, damaged ballots and other systematic and non-systematic errors. Typically, if these mistakes account for less than a tiny percentage of the total count, then the election is declared fair. If not, one or more recounts may be requested. In the Arizona case, no such irregularity was seen, but Arizona Republicans decided to proceed with a recount anyway, just to be "sure." Given the fact that the Arizona ballot hen house is now under watch by Republican foxes, it will be interesting to see how the recount ends. They don't have to falsify enough ballots to give Donald Trump the victory in the state, just enough to declare the election invalid. This would then spread to other Red states with anticipated similar results, giving the GOP the chance to declare Biden a fraudulently elected president. I sincerely believe this is their game plan. America may see a new Civil War after all.  Is It Something I Said or Did? — Posted Thursday April 22 2021 Let us always guard our tongue, not that it should always be silent, but that it should speak at the proper time. — St. John Chrysostom It was June 9, 1962, the very last day of the 7th grade. Puberty had apparently hit the girls hard earlier that year, as they were all fawning over a classmate who'd been a good friend of mine for as lomg as I could remember. At morning recess the girls were all crowding around him with their cameras, and I felt jealous for the first time in my life ("Get out of the way, Bill, we want to take B's picture!") One girl in particular was practically foaming at the mouth over B, her hormones in overdrive, and in a moment of rage I blurted out "Susan, you make me sick!" Susan wasn't particularly attractive, and I certainly had no interest in her, but I resented her obsequious behavior over my friend. Near the end of the day, Cindy F. asked me why I was so mean to Susan, but I don't recall how I answered her. I just learned from an old classmate that some years later Susan committed suicide, having been clinically depressed ever since grade school. This news hit me like a sledgehammer, as I instantly recalled that day in 1962 and my heartless remark. Now I'm filled with remorse over something that happened almost sixty years ago and whatever part I might have played in that poor girl's demise. Watch what you say, because you might not have a chance to make up for it. An Inspector Calls, 2015.  I'm Still Confused — Posted Tuesday April 20 2021 In 2001 the E821 experiment at Brookhaven National Laboratory in Upton, N.Y., found hints that the muon's magnetic moment diverged from theory. At the time, the finding was not robust enough because it had a statistical significance of only 3.3 sigma: that is, if there were no new physics, then scientists would still expect to see a difference that large once out of 1,000 runs of an experiment because of pure chance. The result was short of 5 sigma — a one-in-3.5-million fluke — but enough to pique researchers' interest for future experiments. — Scientific American You may have read about "5 sigma," the statistical criterion for determining whether a new scientific discovery is valid or not. Most recently, the magnetic dipole moment of the muon (a heavier but otherwise identical version of the electron) has been measured to great accuracy, but it differs very slightly from the theoretical value determined via quantum field theory. This difference is currently irreconcilable, and the difference amounts to something called 4.2 sigma. "Sigma" is a just a measure of the standard deviation, computed assuming the applicability of the normal (Gaussian) distribution to experimental measurements. It's just the area outside of the Gaussian curve for a given point on the left of the mean to the same point on the right of the mean, the points being standard deviations. For example, for a standard deviation of 3.3 the area under the curve in the range $$z = -3.3$$ to $$z = 3.3$$ for the Gaussian integral $$y = \frac{1}{\sqrt{2 \pi}}\, \int_{-3.3}^{3.3} e^{-z^2/2} dz \tag{1}$$ is about 0.99903. The area outside this range (($$1-y$$) is 0.00097, the inverse of which is 1,030. This is taken to mean that there is only about one chance in a thousand that the measurement is an erroneous, statistical fluke. Similarly, for a standard deviation of 4.2 (based on the latest muon data) the chances are only about one in 40,000 that the measurement is a fluke. What I don't understand is that all the reports are claiming that the 5 sigma "discovery" statistic means only one chance in about 3.5 million. But a straightforward calculation using (1) shows that this is only one chance in 1.75 million, exactly half of the number being reported. Is this a one-tailed or two-tailed thing? The answer is: it depends on whether you're calculating sigma or its cousin, the p-value, both of which are used in statistical analysis. So it's basically one-tailed vs two-tailed, no real difference, although I wish to hell they'd be consistent with what they're reporting. Update: German physicist Sabine Hossenfelder's latest video addresses the issue of sigma significance, noting that even 6 sigma can be misleading.  Math For Fun — Posted Tuesday April 13 2021 For years I've watched the math videos that Steve Chow has posted on his popular YouTube channel Blackpenredpen, which mostly covers undergraduate-level calculus. Chow is an instructor at Los Angeles Pierce College, and while he doesn't have a PhD in mathematics he's the guy I wish I had I when was in school. Most of his videos present innovative and clever methods and tricks used to do seemingly impossible integrals, but he often changes gears and does purely algebraic problems. One of those that still fascinates me is the infinite tower-power problem $$x^{x^{x^{x^{\cdots}}}} = 2$$ (which, to the best of my knowledge, has no practical application whatsoever, but it's a fun problem). It's easy to derive the solution $$x = \sqrt{2}$$, but the seemingly easier finite tower-power problem $$x^{x^{x}} = 2$$ is far trickier. It turns out that the exponentiation process is not "commutative" in the sense that $$x^{(x^x)}$$ is not the same as $$(x^x)^x$$. In this video, Chow uses Newton's iterative method to solve for $$x$$, getting $$x = 1.476684\ldots$$. As is easily shown, however, the solution to $$(x^x)^x = 2$$ is just $$x=\sqrt{2}$$ (which is also the solution to the infinite tower-power problem), but this disagrees with Chow's solution. I'm puzzled by this, and I wonder if anyone can show me where I'm going wrong. Chow starts out the Newton's method with the guess $$x = 1$$, so perhaps that's a bad start to the process. Okay, I just found this video that explains everything. It's called tetration, which I knew about (but didn't know there was a rule for it).  My Ignorance — Posted Thursday April 8 2021 Today is my late wife's birthday. She would have been 75, and it still breaks my heart that she is not here today. Here she is on her 60th birthday, as beautiful as ever. The last few days I've been going through boxes containing many hundreds of old letters that my wife and her brother received from (and wrote to) their parents and friends in Cairo, Egypt and in Kinshasa, Zaire, where my father-in-law taught chemistry. He took the job because it paid in American dollars (not Egyptian pounds), and was therefore a godsend, as it helped finance his adult children's emigration to America. They came to Los Angeles in 1970, as the weather was nearly the same as that in their native Cairo, and because they had a few friends in the church there to help them adjust to their new country. Munira and I were married 42 years, not counting the 5 years I knew her from before. Outside of some limited and very broken Arabic, I never learned the language, and while looking at the letters (all of which are 40 to 50 years old), I now much regret my ignorance, as I would love to read them now. I will be sending all of them to my wife's brother, the only one remaining in the family who can translate them. Hopefully, with his help I'll learn more about my wife's earlier years, although I also hope to see her again before too much longer.  Is It God, or a "Smelly Hacker"? — Posted Thursday April 8 2021 There's currently a lot of puzzles in the physics world, but two stand out. One is the discrepancy in the Hubble parameter, which has been measured to pretty decent accuracy by two different methods that don't agree with one another, and the other is the measured and calculated magnetic dipole moment of the muon, which are also significantly different. The Hubble parameter is a measure of the expansion rate of the universe, and it's either about 67 or 73 kilometers per second per megaparsec. There's some error in the observed values, but the error bars don't overlap, hence the discrepancy. On the other hand, the measured and calculated magnetic moments of the muon (a much heavier variant of the electron) are extremely close to one another, but there is a slight difference that physicists cannot explain. It might be experimental error or a statistical fluke, but those explanations are considered highly unlikely. Physicists are hopeful that the difference points to new physics beyond the Standard Model of Physics. But there's another possibility, one that arises from the famous Simulation Hypothesis, which posits that all reality (including human consciousness) is the creation of an advanced computer programmer or hacker (smelly or not) who resides outside of the simulated universe. Assuming the hypothesis is correct, then even the most advanced programmer (perhaps even God) could not be precisely perfect in creating the simulation, and there would always be glitches that show up in the simulated universe, glitches that might be observable to the universe's inhabitants. This possibility is explored in this recent segment of Closer to Truth: In view of the large disparity between the calculated values of the Hubble parameter, I highly doubt that it's a glitch of any kind; more likely it's experimental error or an erroneous assumption in the Standard Model of Cosmology. The muon dipole moment problem is far more interesting, as the predicted value is based on highly reliable calculational methods that have been used to fantastic success in other applications. Could the one part in a million difference between experiment and calculation be a glitch, or could it be "new physics"? More advanced experiments are planned, so hopefully time will tell. PS: Sometimes I imagine that I'm a very old man, getting up in the morning, making coffee, then walking over to my large living room window to watch what's going on out there. What I see today is a fabricated Cretaceous landscape of herbivorous and carnivorous dinosaurs going about their business, thanks to a high-resolution, three-dimensional holographic glass pane that serves as my window to the world outside. Of course, the outside world is the usual boring place of cars going by and neighbors walking their dogs, and by turning off my fully programmable window I can see what's really there. But I prefer to gaze out upon the Grand Canyon, the Eiffel Tower or the Andromeda Galaxy, or if I choose I can watch the pyramids being constructed during Egypt's Old Kingdom. The possibilities are endless, and it makes me also wonder if my own existence isn't also a computer fabrication of some kind.  The Waste Land (Television, Not T.S. Eliot) — Posted Thursday April 8 2021 I just can't watch cable TV news anymore (although I have AT&T TV, not cable), given the non-stop coverage of ugly politics, COVID-19, the ongoing racist treatment of minorities, perpetual mass shootings and all the rest. I put up a flat antenna on my wall and am now watching over-the-air (OTA) television programs, which don't cost anything. The local news is still depressing, but the number of available programs is about as good as basic cable TV. It's also given me the opportunity to tune into shows that my family and I watched in the 1950s, 1960s and 1970s, which were almost de rigeur viewing in those days because there wasn't anything else to watch. With the sole exception of The Honeymooners, all the shows are pathetically insipid, with paper-thin plots and nonsensical situations. The family-oriented sitcoms are the worst (Family Affair, The Partridge Family, Donna Reed, etc.), with their well-coiffed, squeaky-clean (and white) children and their invariably highly educated and successful parents (doctors, lawyers, architects, businessmen and engineers) posing as ordinary middle-income folks raising preposterously talented offspring who danced, sang, played instruments and put on fantastic stage shows. And of course no single parent was divorced back then (only widowed), thus preserving the sanctity of marriage. And also all the men had served in the military, which offered plenty of opportunity for the shows to feature patriotic tableaus of one sort or another, always to comedic and heartwarming effect. Good Lord, how much of that garbage did I consume without thinking in those days? I can only imagine how much better I'd have turned out if my parents had never purchased a television in the first place. "April is the cruelest month $$\ldots$$"  Enough — Posted Monday April 5 2021 Truth be told, I'm sick to death of the non-stop Derek Chauvin trial coverage on CNN and MSNBC, not to mention the glib commentary by the various hosts of those news networks. The videos and testimonies of eye witnesses pretty much made the case against Chauvin for me, but the extensive trial coverage has become nothing more than a partisanized joke. The liberal-leaning CNN and MSNBC of course are pushing for a murder conviction, while the ultra conservative Fox News, One America Now and other racist networks are either playing the trial down or not covering it at all. Let's be honest here: if we could replace Derek Chauvin with a black police officer and George Floyd with an addicted white civilian who passed a counterfeit bill, the network biases would be reversed, and the trial would have ended long ago with the black police officer convicted of first- or second-degree murder. Instead, by dragging out the trial ad nauseam the justice system will be forced into a lot of hemming and hawing over who's guilty due to the various legal subtleties and medical minutiae that are being presented, with the result that there's a very good chance that confused jurors will be hung and Chauvin will walk. His police career will be over, but then he'll write a best-selling book and make repeated guest appearances on Fox News, so he won't be hurting financially. Fortunately, there's still a civil trial pending, and I can only hope that Floyd's family will end up getting a big chunk of whatever money Chauvin earns for the rest of his pathetic racist life.  Come On, Feet, Don't Fail Me Now — Posted Wednesday March 31 2021 It has always killed me when lay people ooh-and-aah over the weightlessness of astronauts aboard the International Space Station, which orbits the Earth at some 17,300 miles per hour. At roughly 200 miles above the Earth's surface, the gravitational attraction is still over 90% that which we all feel here, and it's the orbital velocity and the associated centrifugal force that provides the weightlessness. So it's not outer space we're talking about, people, but the effects of orbital speed. It's easy to calculate that if you were to travel at about 17,700 miles per hour, you could orbit the Earth weightlessly at an altitude of 1 foot, barring collision with buildings, trees, Uncle Jack and other obstacles. General relativity states that time runs slower the closer one gets to a gravitating mass, a proven feature of the theory that is crucial to the functioning of the Globsl Positioning System (GPS) that our iPhones utilize to enable Google Maps (and for the National Security Agency to monitor our every whereabouts). So don't rob a bank with your iPhone in your pocket, as you'll be easily tracked down and arrested. It's a miniscule effect at Earth's surface, but as astrophysicist Ethan Siegel writes in his latest article, time really does run slower for your feet than your head because they're closer to the Earth. The effect would be much more pronounced at the surface of a neutron star, but then you'd be squashed flatter than an atom before you'd notice it. In fact, neutron stars are so smooth that even an irregularity the height of a human hair could be observed due to the wobble it would produce on the star's rotation, as explained in this fascinating Sixty Symbols YouTube video.  Say It Ain't So, Matt! — Posted Wednesday March 31 2021 Today's Republican Party—Come for the tax breaks, stay for the paranoia, the lies, the hypocrisy and the pedophilia! That one may smile, and smile, and be a villain! — Hamlet Scene 1, Act 5 Hey, we've all sinned and fallen short of the glory of God, and I know I'm no different than anyone else. But we tend to hold our political leaders just a tad higher than ourselves, and when they fall short we expect them to come clean, admit their transgressions and repent. Sadly, that's not how it works in the Republican Party, where if you can lie and lie and get away with it, it's the same as telling the truth. Three days ago, 38-year-old Florida GOP Congressional representative Matt Gaetz appeared on Fox News' Tucker Carlson show to plead innocence over claims that he had sexual relations with a 17-year-old girl and had transported her over state lines for related purposes. I don't know for sure if Gaetz is guilty, but I especially enjoyed how he referred to the unnamed child as a 17-year-old "woman." I suppose that's better than a 12-year-old woman. Gaetz also claimed that his family was being extorted for$25 million to keep his guilt secret, noting that his father is wearing a wire to record the alleged extortionist's schemes. If true, it must be a pretty stupid extortionist to think that he/she can pull off the crime, given that it's now open to the public. It's also revealing that Gaetz and his family has that kind of money to begin with. The FBI is investigating both the allegations against Gaetz and the extortion claim, and only time will tell if the Trump-loving Gaetz will find himself in the dock. My guess is that he will, but with a suspended sentence, as it's probably only his fourth or fifth offense. He will then disappear for a while, be forgiven by his Republican backers and faith-based supporters, and then be restored to full Christian forgiveness. Want proof? Just remember the likes of Jimmy Swaggart, Jim and Tammy Bakker and Ted Haggard, just to name a few from a long list of Republican criminals and hypocrites.

 Just Nip It, Mr. President — Posted Saturday March 27 2021 "Nip it! Nip it in the bud!" — Some slightly out-of-context (and off-color) advice from Deputy Barney Fife in his currently out-of-print bestseller, Nip It: Barney Fife's Guide to Blistering Hot Married Sex Pulitzer Prize winner Maureen Dowd's opinion piece in today's New York Times is a reminder to President Biden that the Republican Party despises his guts, and will never agree with any of his policies, regardless of how popular they are with your average Republican voter. Dowd writes "So while you're modulating, Mr. President, here's a suggestion: Ditch that old habit of yours, bending over backward to appease Republicans $$\ldots$$ Bipartisanship ain't happening now." I fully agree with Ms. Dowd. Biden is wasting his and his administration's time with all this talk about bipartisanship. Just look at the Republicans' current voting habits and their ongoing fawning allegiance to Donald Trump, whose lies and anti-democratic antics continue unabated. The current spate of Republican-led voting restriction bills and laws in Red States are proof that the GOP intends to never let the Presidency, House and Senate slip from their grubby hands again. If they could outright block blacks, Hispanics and Asians from voting, period, they'd friggin' do it. So just nip all that talk of getting Mitch McConnell, Ted Cruz, Rand Paul and their ilk to see the light, Mr. President, and go on an Executive Order rampage.

 Geek Saturday — Posted Saturday March 27 2021 The classical Einstein-Hilbert action with a cosmological constant $$\Lambda$$ $$S_{EH} = \int\!\! \sqrt{-g} \, \left( R - 2 \Lambda \right) d^4x$$ has passed every experimental and predicted test of general relativity since Einstein proposed his theory in November 1915. However, in the weak-field limit they do not account for the observed near-constant velocities of stars on the outskirts of their galactic centers, which had led to the proposal that some kind of unobservable dark matter exists around galaxies and galaxy clusters. Assuming that dark matter does exist, then Einstein's theory still holds, so now the search is on for the illusive dark matter. It has been proposed that dark matter may consist of cold neutrinos, axions, massive photons and other exotic weakly-interacting species, all of which have not been detected despite herculean and costly experimental efforts over the past three decades. Einstein's action is fully Lorentz and coordinate invariant, but it is not invariant with respect to a change in scale, in which the metric tensor is varied according to $$g_{\mu\nu} \rightarrow \Omega(x)^2 g_{\mu\nu}$$, where $$\Omega$$ is an arbitrary function of space and time. In 1929, the German mathematical physicist Hermann Weyl showed that modern quantum theory demands scale invariance (later recognized as phase or gauge invariance) and that it accounts for the conservation of electric charge. Consequently, many physicists today believe that scale invariance should hold not only at the quantum level but on cosmological levels as well. In 1989, University of Connecticut physics professor Philip Mannheim and his colleague Demosthenes Kazanas proposed that Einstein's action should be replaced by a scale invariant version of general relativity that reduces to that of Einstein's under less general conditions. Again, it was Weyl in 1921 who derived a unique scale-invariant tensor quantity $$C^\lambda_{\,\,\mu\nu\alpha}$$ composed solely of the Riemann curvature tensor $$R^\lambda_{\,\,\mu\nu\alpha}$$ and its two contracted variants $$R_{\mu\nu}$$ and $$R = R^\mu_{\,\,\mu}$$, and Mannheim-Kazanas used the associated action $$S = \int\!\! \sqrt{-g}\, C_{\mu\nu\alpha\lambda}\, C^{\mu\nu\alpha\lambda} \,d^4x \tag{1}$$ to derive the equations of motion for free space in spherical coordinates. After what must have been laborious effort, they found the Schwarzschild-like solution $$ds^2 = e^\nu c^2 dt^2 - e^{-\nu} dr^2 - r^2 d\theta^2 - r^2 \sin^2 \theta \,d\phi^2, \quad e^\nu = 1 - 3 \beta \gamma -\frac{\beta(2-3\beta\gamma)}{r} + \gamma r - k r^2$$ where $$\beta, \gamma, k$$ are constants of integration. As is easily seen, for $$\gamma = k = 0$$ the solution reduces to the familiar Schwarzschild line element, where $$\beta$$ plays the role of the central gravitating mass. The terms proportional to $$r$$ and $$r^2$$ serve as acceleration parameters, which initially provided hope that scale invariance would provide an answer for dark energy and possibly for dark matter as well. Indeed, subsequent studies showed that the Mannheim-Kazanas metric accurately predicted the observed flat rotation curves for stars in many galaxies. Several days ago, a preprint paper appeared on arXiv.org claiming that the Mannheim-Kazanas metric in fact does not accurately predict flat rotation curves under generally assumed galactic conditions. The paper's Cambridge researchers (M.P. Hobson and A.N. Lasenby) showed that a clever coordinate change in the radial parameter $$r$$ could be used to eliminate the $$3\beta\gamma$$ and $$\gamma r$$ terms, thereby reducing the Mannheim-Kazanas metric to $$e^\nu = 1 - \frac{k_1}{r^\prime} - k_2 (r^\prime)^2 \, \,\,\, *$$ where $$r^\prime$$ is the new radial parameter and $$k_1$$ and $$k_2$$ are constants. This metric is equivalent to that of de Sitter spacetime, in which there is a cosmological constant (proportional to $$k_2$$) but with no matter in the universe (as our universe continues to expand, radiation and matter density will decrease to the point where the de Sitter metric will be perfectly valid). By eliminating the term linear in $$r$$ in the Mannheim-Kazanas metric, the Cambridge researchers show that the velocities of stars far from their galactic centers fall off like $$1/r$$ (in regions of interest for a typical galaxy) as in the pure Schwarzschild case, resulting in no region for flat rotation curves. It can be shown that the tangential velocity $$v$$ of a rotating star is given by $$v^2 = \frac{1}{2}\, r e^{-\nu} \frac{d e^\nu}{dr}$$ For the Schwarzschild metric, the velocity decreases inversely with distance, as is classically expected (and in disagreement with observation). However, the situation changes for the Mannheim-Kazanas metric. The velocity will be extremalized (maximized) when its derivative with respect to $$r$$ vanishes. With the reasonable assumptions that $$e^\nu \approx 1$$, $$\beta \approx GM/c^2$$ and $$\beta\gamma \ll 1$$, we get the condition $$\gamma r^2 - 2 k r^3 = \frac{2GM}{c^2}$$ Assuming further that $$k \approx \Lambda$$ (and so can be neglected), we find that maximum stellar velocities will occur at the radius $$r = \sqrt{ \frac{2GM}{\gamma c^2}}$$ Given the expected smallness of $$\gamma$$, this will be a very large distance from the galactic center, and is thus in agreement with observation. From this, I judge that the Mannheim-Kazanas analysis does indeed match the effects of dark matter. I'm studying the various galactic conditions that Hobson and Lasenby used to justify their conclusions but, as I'm not very familiar with galaxy dynamics, I cannot be assured that the assumptions I've made here are legitimate. I've long been a fan of the work of Mannheim and Kazanas (both their independent and joint research), and I can only hope that they can find convincing arguments rebutting the Hobson and Lasenby paper. PS: Einstein's full gravitational field equations are given by $$R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu} \tag{2}$$ where $$T^{\mu\nu}$$ is the energy-momentum (or stress-energy) tensor, which accounts for the presence of matter and radiation (which in turn affects the geometry). Einstein viewed the left-hand side (which is pure geometry) as being made of fine marble, whereas the right-hand side is cheap plastic (but matter and radiation have to be tacked on somehow, he reasoned). If $$S_M$$ is the action for matter and radiation, then $$T^{\mu\nu} = -2 \frac{1}{\sqrt{-g}}\, \frac{\delta (\sqrt{-g}\, S_M)}{\delta g_{\mu\nu}}$$ where the $$\delta$$ operator means "variation." It is easily seen that both sides of (2) have the dimensions of length$$^{-2}$$. But the Lagrangian in (1) is dimensionless, meaning that the proportionality term $$8 \pi G/c^4$$ would be unnecessary for a stress-energy that is also dimensionless. Go figure that out! * This is Equation (15) in the paper, which is the key identity in the reseachers' argument. I've been unable to derive it, and I wonder if it's correct.

 Changes? We Don't Need No Stinking Changes! — Posted Wednesday March 24 2021 You've by now heard about the Ruger AR-556 "pistol," the weapon that was used to murder 10 people in Colorado two days ago. It's classified as a pistol because previous mass killings motivated the National Rifle Association to request minor changes to the weapon, which was originally classified as an assault rifle. Pistol or rifle, it shoots NATO 5.56-mm jacketed ammo, whose diameter is a little less than a quarter inch. This seemingly small bullet belies the huge cartridge and powder charge in the round, which can push the bullet up to about 2,800 feet per second. The energy delivered is sufficient to cut a person in half—there are no flesh wounds with these things, as you're lucky to come away as a paraplegic or quadraplegic. [It always bugs me when I watch a World War II movie in which a soldier gets hit with a machine gun or aircraft round, invariably clutching his chest or stomach while heroically uttering "They got me, Joe!" This is nonsense, and perhaps it's time to start airing autopsy photos of the children who were slaughtered by such weapons in places like Sandy Hook, Columbine, Parkland and Rancho Tehama.] The Ruger pistol (on the left) has roughly the same killing power as the Vietnam-era M16 assault rifle (on the right), including a 30-round magazine that also holds the 5.56-mm round. The major difference is that the M16 can be fired in either semi-automatic or fully-automatic mode, while the Ruger is semi-automatic only. Clever gun enthusiasts have found ways to illegally modify the trigger and housing to fire the weapon like a machine gun, although all fully-automatic weapons are banned in America (even in Red States). But search the Ruger website and you'll find that the AR-556 is listed as a pistol, thanks to the NRA. The NRA probably patted itself on the back getting it listed as such, but deep down you know they hated doing it. Conservatives hate change, which is why they will never allow a ban on assault rifles or any other deadly firearm that can be easily concealed, then whipped out to mow down dozens of victims. Republican lawmakers have even bragged that if President Biden proceeds with any related gun control measure, they'll see to it that the required 60% Senate majority is never achieved. Their tried-and-true argument is that some 50,000 Americans die in auto accidents every year, but no one calls for a ban on cars and trucks. It's the same with the COVID-19 vaccines—Republicans weren't getting vaccinated last year, so why change now? Add to that the fact that 47% of Republicans say they will not get vaccinated, thanks to Trump's persistent effect on their tiny, pathetic minds. Consequently, America will likely not achieve herd immunity, guaranteeing that the virus and it variants will go on killing many thousands more. Freedom! Liberty! Second Amendment! Huzzah!

 "You Mean I've Been Eating Hamburger From 1960?!" — Posted Monday March 22 2021 My high school's cafeteria had an outdoor lunch service window that I often frequented, and I'd always buy their hamburger for 25 cents. It had a sauce that was heavy on mustard, but I loved it. I'd sit at one of the outdoor tables having lunch with Dan E. and John Z., talking about what we would do when we left high school. Dan planned on becoming an entomologist, but ended up with a PhD in Art History. Years later I'd often see John tooling around in his yellow VW Thing, a rather bizarre-looking auto that enjoyed a brief popularity in the late 1960s. I don't know what became of John, but I went on to study chemistry. I still remember the taste of those hamburgers, and I was reminded of those days while binge-watching 11.22.63, the 2016 eight-episode mini-series based on Stephen King's 2011 science fiction novel of the same name (which I've also read). The book and series tell the story pf a man (Jake Epping) who travels back in time to stop the assassination of President John F. Kennedy. Unsure of Lee Harvey Oswald's guilt, he first has to determine if Oswald had first tried to assassinate General Edwin Walker in April 1963. Walker was a real-life anti-communist zealot whom Oswald deemed a fascist threat (Oswald's involvement in the assassination attempt of Walker was later corroborated by Oswald's wife, Marina). Assured of Oswald's guilt, Epping then proceeds to track down Oswald and prevent JFK's assassination. I distinctly recall the early afternoon of Friday, November 11, 1963, when my high school French teacher (Mrs. Eleanor Farrell) was interrupted by a student from the hallway who handed her a note. In emotionless tones, Farrell recited "President Kennedy was assassinated at 1:00 pm today in Dallas, Texas. Vice President Johnson is now the President of the United States." She then returned to the blackboard without further comment, which I thought was odd at the time. Since then I've read about a dozen books on the assassination. None have revealed the true story, which will probably never be known. The best I've seen to date is Jeremy Bojczuk's 2014 book A Brief Guide to the JFK Assassination, but it too falls short of what probably really happened, or of those who were actually responsible. But "Since then, 'tis centuries" as Emily Dickenson once wrote (although only 57 years have passed since Kennedy's murder). Who knows what might be revealed in the coming decades (or centuries). The remains of Kennedy's brain (which record the true path of the backward- or forward-tracking bullet) are under lock and key by the Kennedy family, and may never be revealed for definitive forensic analysis. At any rate, 11.22.63 is a great series, and to me it's also tops as a time-travel adventure. You'll have to watch it to understand the hamburger connection.

 Racism and Our Gang — Posted Thursday March 18 2021 In the early 1970s, Munira and I would would regularly go for lunch with our lab co-workers to El Tepeyac, a Mexican restaurant in East Los Angeles. The restaurant featured Manuel's Special, a pillow-sized burrito of rice, beans and beef that was on the house if you could eat the whole thing. Munira and I would invariably split one, joking about the lack of neighborhood stray dogs and cats and the possible nature of the restaurant's meat given its low prices. We'd also frequent another local restaurant called Sambo's, whose wall paintings depicted the eponymous little black child being chased by a tiger. Thank God the restaurant either went out of business or changed its name to something less offensive. I recalled this last memory while reading Our Gang - A Racial History of the Little Rascals by Julia Lee, a Chinese-American associate professor of English at Loyola University in Los Angeles. I have most of the Our Gang films, which were produced by Hal Roach Studios as silents (1922-1929) and early sound films (and later produced by MGM until 1944). I also have every extant Laurel and Hardy film that Roach produced from 1927 to 1940. In 1990 Munira and I attended a memorable night with Hal Roach at the Raymond Theatre here in Pasadena, where several Laurel and Hardy films were presented along with personal reminiscences of early Hollywood by Roach and Joe Cobb, a child actor and early member of Our Gang. Lee's book was a revelation, told from the perspective of American racist attitudes that existed in early Hollywood. But I was also struck by its purely historical information on Roach, his studio and the directors and child actors who starred in and produced the Our Gang films. Surprisingly, the inclusion of black child actors in the films was a natural outcrop of the relative innocence of the times, as the white and black members of Our Gang showed no innate racism in the episodes, although "Sunshine Sammy," "Farina" and'"Stymie" (my favorite) were often stereotypically shown as ignorant, spook-fearing, watermelon-loving pickaninnies. The fact that the book was written by a Chinese-American also resonated with me, especially in view of the recent horrific attacks on Asian Americans, spurred on by former President Trump's racist remarks regarding the "Chinese virus" and "Kung Flu." If you have the slightest interest in the racism of early Hollywood films and the sorry state of our country's politics today, please buy and read Prof. Lee's book. PS: In 1927, Hal Roach (1890-1990) put two of his film comedians together to form the team of Laurel & Hardy. They quickly became a favorite of young and old alike, and to this day are considered the best comedic film duo of all time. In 1983 I took my four-year-old son Kris to see a Laurel & Hardy retrospective viewing of five of their silent films, all of which had been remastered and restored. Kris enjoyed the movies, but I was dumbfounded by the superb quality of the films, which looked as if they had been shot yesterday. Since then, L&H films have been released in countless collections, but to this day they still await definitive video and audio restoration. The best I've seeen to date is the fantastic 10-volume set The Lost Films of Laurel and Hardy, of which all DVDs are sold separately (and expensively). The nearest thing in terms of quality is Laurel and Hardy - The Essential Collection, which I purchased and gave to several family members and friends, all of whom are devoted L&H fans.

 The Economic Elephant in the Room — Posted Sumday March 14 2021 President Reagan proved that deficits don't matter. — Former Bush Vice President Dick Cheney Tax cuts always pay for themselves. — The Perpetual Delusionary Mantra of the Republican Party I watched Fareed Zakaria's GPS cable program this morning, in which economists Larry Summers and Paul Krugman talked about the pros, cons and likely consequences of President Biden's recently enacted $1.9-trillion American Recovery Act (ARA). A former president of Harvard University, Summers was a Treasury Secretary and economic advisor to presidents Clinton and Obama, while Krugman is a political writer, economic advisor and columnist who was awarded the 2008 Nobel Prize in Economics. Summers and Krugman are friends and colleagues, but they disagree on the costs, benefits and outcome of the ARA. In a nutshell, Summers feels that the ARA does not have sufficient long-term monetary resources to pay for itself, and he worries about its inflationary potential and the deficits that are likely to result. Krugman likened the ARA to a war-times act that—like the New Deal and the 2008 financial collapse—was necessary to pull the country out of the health and economic disasters caused by the COVID-19 pandemic that has so far killed over 530,000 Americans. Krugman also noted that while the ARA is costly, is is not likely to result in runaway inflation. I think Summers made a good point about the lack of any obvious financial resources to pay for the ARA (such as public investments like bonds), much less for Biden's plans for infrastructure improvement and climate change mitigation. Krugman's response was that similar cash outlays and fiscal borrowing occurred during the Korean and Vietnam wars, which led to manageable inflationary problems and deficits. During the discussion, neither economist brought up the topics of taxes, America's ongoing committment to its expansive foreign military presence or to the booming stock market, which has inexplicably soared throughout nearly all of the 2020-21 pandemic year. I can understand why most politicians today won't touch the issues of raising taxes or cutting back on America's military, but the trillions of dollars now being amassed by corporations and their stockholders represents a hugely significant source of funds needed to pay for public programs, infrastructure improvements and climate change mitigation. Roughly 55% of Americans are currently invested in the stock market one way or another (through actual stock ownership, pension plans or other indirect investments), and they are now seeing rates of return far in excess of what banks are paying on savings accounts. Furthermore, the tax rate on capital gains is still only 15%, far below what most middle-class American are paying on their combined federal and state income taxes. To me, this is the elephant in the room: if America wants a responsible pay-as-you go economy, reliable infrastructure and climate mitigation, it had better tap into the corporations and their stock holders, and this means raising taxes on those who are benefiting the most. The market is now poised for an even bigger boom as we get COVID-19 under control, and if we don't want dangerous bridges, unreliable public utilities and a ruined climate while giving a free pass to Bahamas-bound wealthy freeloaders, stock market-specific taxation is the way to go.  Why Most Women Don't Marry Scientists — Posted Thursday March 11 2021 By the way, Gary Larson is back!  Dark Matter Detection Fails Again — Posted Thursday March 11 2021 The great philosopher of science Karl Popper famously assigned a critical element to what he defined as "science", which is that it must be falsifiable. That is, every scientific theory must not only stand the test of ongoing experimental validation, but it must also be subject to being proved wrong. For example, while Einstein's general theory of relativity (gravitation) has perfectly passed every test thrown at it for over 100 years, a single confirmed observation that disagrees with the theory would disprove it, requiring that the theory be either modified or discarded in favor of something better. Consequently, there are no true laws of Nature, only theories awaiting revision or refutation. Popper's falsification idea has not always been popular, but it's a good start. Related to this is the notion of reproducibility, which involves applying the same or similar experimental techniques, methods and materials used to establish a theory in the first place. If you conduct a experiment (or series of identical experiments) that appears to uphold a theory you've proposed, but someone else cannot reproduce the same results, then your theory remains either a hypothesis or a conjecture (or it's simply pure bunk). A case in point is the set of experiments performed by a research team in Italy called DAMA/LIBRA, which uses a mass of thallium-doped sodium iodide to detect dark matter particles. But rather than detect these hypothetical particles themselves, its approach has been to look at whatever detection events occur over time, the idea being that as the Earth is swept along with the Milky Way's rotation, it must encounter a varying biannual number of particle events depending on whether Earth's orbit is moving with or against the galaxy's rotation. In a sense, the exact nature of the detection event doesn't matter, only the sinusoidal pattern of detected events matters. This approach would then rule out any human, systematic or random experimental errors and noise in the detection apparatus. The DAMA/LIBRA team has indeed reported such a semiannual pattern in its data, appearing to confirm the presence of something akin to dark matter. You might recall that the famous Michelson-Morley experiment of the late 1880s tried the exact same approach in an attempt to detect the luminiferous aether, a universal substance that was assumed to exist to provide a means for light waves to travel in space (the rationale was that since sound waves need air to move through and water waves need water, then light must also have something to "wave" against in order to propagate in space). The experiment famously failed, demonstrating that light can indeed move through the vacuum of space. However, the DAMA/LIBRA team did detect something, and until now it provided at least indirect evidence for dark matter. But more recently a series of identical experiments conducted by the ANAIS dark matter team at Spain's Saragossa University have consistently failed to reproduce the DAMA/LIBRA results to 99% confidence. The disagreement is detailed in today's Medium article by astrophysicist Ethan Siegel. While any limited series of disagreeing experiments is not sufficient to conclusively disprove the existence of dark matter, I'm still hoping that a satisfactory answer for dark matter's presumed effects on galaxies and galactic clusters will be explained by modified Einsteinian gravity. (Only time will tell, but at 72 my remaining years are dwindling away, and I'm getting impatient.)  The Very Definition of Spin — Posted Thursday March 11 2021 And I'm not referring to quantum-mechanical spin. The phrase "It's not a flaw, it's a feature" once applied to bug-ridden computer programs, but the Republican Party has turned it into a political term, what we currently know as spin. Mississippi Republican Senator Roger Wicker, who joined every single one of his fellow Republican senators and congressional representatives in vehemently opposing President Biden's$1.9 trillion COVID-19 relief legislation, is now trying to take credit for the benefits the legislation will provide to his constituents and Mississippi businesses. In defense of Wicker's comments, prominent GOP members are using Wicker's words as proof of Republican bipartisan support for Biden's efforts, which they have uniformly opposed ever since Biden took office. I only wish that Sen. Wicker, an avowed devout Christian, would more carefully read the Gospel of Matthew, in which Jesus admonishes hypocrites and hypocrisy no fewer than 15 times. Since when did hypocritical spin become a treasured feature of Republican politics?

 Coordinated Guessing — Posted Tuesday March 9 2021 The following is intended mainly for budding structural design engineers and nerds, but it has wide application to Newtonian and relativistic gravitational physics, electronic circuit design, fluid flow and similar computationally intense problems. Let's say you want to build a 100-story office building. You start by designing the basic structure from scratch, using a 3-dimensional grid of steel beams, girders and columns. You also know the various loads that the structure will have to safely support, including gravity, wind, snow, earthquake and occupancy loads. The basic structure will consist of thousands of nodes (where the beams come together) and links (the horizontal and vertical beams that connect the nodes). Your design will have to take all these things into account, including a safety factor. Where do you begin? In olden days you'd rely on rules of thumb, experience and slide rules. Nowadays the computer does most of the work, checking that your design is not only safe but can be built at the lowest possible material and labor cost. Given a few input parameters, the computer may also do the basic design as well. Trust me that your 100-story office building will involve thousands of nodes, and these are the basic elements that the computer uses to check for allowable beam stress, strain and deflection. Also trust me that for a structure involving $$N$$ nodes, the computer will need to construct an $$N \times N$$ matrix (almost always symmetric), and that it will have to solve a system of $$N$$ simultaneous linear equations of the form $$A X = Y$$, where $$A$$ is the matrix, $$X$$ is the $$N-$$dimensional vector of unknowns (say, beam stresses) and $$Y$$ is the vector expressing all the known constraints on the structure. The computer must somehow solve the system via $$X = A^{-1}\,Y$$, where $$A^{-1}$$ is the the inverse of the matrix $$A$$. Lastly, trust me that calculating inverse matrices is computationally a total bitch. For a system of thousands of nodes, no computer can do it directly, and a time-consuming process known as iteration must be used, where each iteration essentially involves an increasingly more accurate guess of the unknowns. Designing a safe and cost effective office building is thus very complicated, but the number of elements is still finite. What if you need to design a continuous structure, say an aircraft wing? Such a structure is not described by a finite number of elements like beams and girders, but the wing's stresses, strains and deflections must be calculated using a seemingly infinite number of design elements. What do you do now? Of course, you discretize the structure using a finite grid of nodes and links, an approach known as finite-element design. The computations become more accurate the more nodes and links you use, but the calculation is essentially the same as the office building example. The importance of solving large-scale linear (or linearized) simultaneous equations cannot be overemphasized, and as noted earlier the problem spans many technological applications now essential to modern life. It is therefore not surprising that an enormous amount of effort has been expended on finding efficient computational solution methods. The number of computer interations or steps required to achieve a solution is then key, since it largely defines the effort required to solve the problem. For some problems, that number can be enormous, which, due to cumulative floating-point errors and time constraints, may result in erroneous solutions. The latest Quanta magazine spells out the problem in more detail, and it also describes a new technique called "coordinated randomness" that has proved (at least marginally) useful. While solution guesses are helpful, it's often difficult to know just how to arrive at them. The Quanta article describes such an approach based on random guesses, and it implies that in some cases even random guessing can be useful (unlike the SAT and GRE exams you took). The article interested me for a number of reasons, as I used to do large-scale numerical analysis of both linear and nonlinear systems and because I still think there might be some validity to the simulation hypothesis, which is the idea that something or someone (God, a post-human computer programmer or even intelligent Nature itself) is simulating our universe using an unimaginably complex computer program. Our entire observable universe is composed of roughly $$10^{90}$$ particles and fields, which is mind-bogglingly huge but still finite, and therefore subject to computer simulation. Sorry for this overly long and nerdy post, but it underlies a fascinating and important mathematical problem.

 Stanley Tucci — Posted Sunday March 7 2021 I first became aware of American actor Stanley Tucci in the excellent 1993 action thriller The Pelican Brief starring Julia Roberts, Denzel Washington and Sam Shepard (didja know that Shepard was also a 1961 graduate of Duarte High School, my alma mater?) In the film Tucci plays a cold-blooded assassin, a far cry from his comedic turn in the hilarious 1998 film The Impostors with Oliver Platt, which regularly had my wife, me and our kids literally in stitches. Don't miss the annoying German ship steward's immortal line "It has made me also $$\ldots$$ moist" or Billy Connolly's "Powerful enough to snap the neck of a small beast, and yet sensitive enough to caress the tender throat of a young castrato — coax a song out of him!" Now Tucci is starring in the popular CNN reality show Searching for Italy, in which Tucci travels to various Italian cities visiting that country's historical treasures and sites, all while stuffing his face on the local cuisine. My family members love it, but I see it as just another "food porn" show, and I can't get into it. I did like the PBS series Rick Steves' Europe, which is far more educational and entertaining (but still has Steves stuffing his face much of the time). Perhaps my dislike of food shows stems from the food I'm eating now as an aging widower: basic stuff like fruit, vegetables, bread and the wonderful "Beyond Meat" plant products that have made me almost a vegetarian. Like the bumper stickers say, "Eat Right, Exercise, Die Anyway."

 Dirac on the Constancy of the Gravitational Constant — Posted Saturday March 6 2021 Although I dearly love the work of Isaac Newton, Albert Einstein and Hermann Weyl, my favorite physicist just has to be "Father of Moden Physics" Paul Adrien Maurice Dirac (1902-1984), whose foundational contributions to physics spanned everything from quantum mechanics to general relativity. In a far saner and less ignorant world, Dirac's name would be as recognized as those of Newton and Einstein. In the early 1930s Dirac began to question the nature of large dimensionless numbers, such as the ratio of the electric force to the gravitational force (roughly $$10^{39}$$) and the relatively small value of the fine structure constant $$\alpha$$, which is about 1/137. He went so far as to wonder if these figures were true constants of Nature, or if they might vary over geological or cosmological spans of time. For example, the Newtonian gravitational constant $$G$$ is about $$6.67 \times 10^{-11}$$ in the kg-m-s unit system, but humans have only known about it for some 400 years. It's entirely possible that it might be slowly but measurably changing over periods of thousands or millions of years. We just don't know. This situation reminds me of the story of the ephemeral fly, which I recounted long ago on this site. It's a small insect that lives for only a few hours after its hatching, and as it flits around desperately seeking a suitable mate during its brief life span it might consider the trees and flowers of its world as everlasting and permanent. We humans live far longer, but we might also find ourselves fooled into thinking that the things we observe and measure are similarly truly constant. On the basis of what we know about modern cosmology today, the universe is doomed to perpetual and accelerating expansion, with all matter eventually being transformed into low-energy radiation, a view that is predicated upon the constancy of dark energy. But if the density of dark energy is not constant but decreasing, then the universe might halt its expansion and begin contracting, perhaps transforming itself again into a primordial mass-point and reinstigating a new Big Bang. Here is Dirac in 1979, talking about the constancy of $$G$$. He died in 1984, sadly having never learned about recent discoveries of the accelerating expansion of the universe: PS: Dirac's eccentricities are nearly as famous as his physics. Forced to speak only French in his home while growing up, he became extremely taciturn in his adult life (his students coined the term Dirac unit, meaning one word per hour). He was notoriously aloof but not unfriendly, preferring long stretches of solitude and daily walks to social interaction. At a party on board an ocean liner with fellow Nobel Laureate Wolfgang Pauli, he was asked to dance. "Come on, there are lots of nice women here, Dirac!" said Pauli, to which Dirac responded "How do you know they're nice?" While discovering quantum field theory, antimatter, the Dirac relativistic electron equation (the greatest equation of all time, in my opinion), the Dirac delta function and many other fundamental discoveries, Dirac managed to marry and have two daughters with the sister of fellow Nobel Laureate Eugene Wigner (Dirac's friends and colleagues were stunned that Dirac had not only a romantic side to his personality but a sex drive as well). He invariably introduced his wife Margit to others as "Wigner's sister." Weary of the cold weather in England, Dirac took an emeritus position at Florida State University in 1972. I equate this event as akin to Einstein arriving at a community college and asking for a teaching job. These and many other stories are recounted in Graham Farmelo's great 2011 Dirac biography The Strangest Man: The Hidden life of Paul Dirac.

 Physics Leads the Way — Posted Wednesday March 3 2021 Good news: the American Physical Society will not hold any future physics meetings or conferences in American cities that tolerate social injustice. I believe this will apply to many Red State cities, whose ignorant denizens don't believe in science anyway.

 Geek Tuesday — Posted Tuesday March 2 2021 I occasionally get emails asking what programs I use to write and post mathematical text. For online math, I use MathJax, which is free and requires only a basic familiarity with the LaTeX typesetting system. For documents, over the years I've used numerous computer programs, going all the way back to PCTeX, Scientific Workplace, MathType, LyX and most recently TexStudio, the latter two of which are free. In 1986 I induced my office to spend $300 for Lotus Manuscript, which had rudimentary math tyepsetting ability. It was okay as a word processor, but took hours to render readable math. Today there are more free and not-free math programs than I can name. I still use the amazingly powerful Mathematica on occasion (I still have the 1992 DOS version), but only to do calculations I'm either too lazy or too stupid to do myself. Retired Stanford University math professor Donald Knuth is considered the father of modern mathematical typesetting, whose many books include The TeXBook, from which I learned the TeX programming language many years ago. Written in a highly amusing style, the book's illustrations by Duane Libby are both clever and hilarious: Dirty Tricks!  A New Media Technology — Posted Monday March 1 2021 Older folks like me will recall the "colorization craze" that took place in the 1980s, which attempted to make old movies look more realistic (or at least more interesting). It failed (the phrase "putting lipstick on a pig" comes to mind), mainly because it predated the ensuing "remastering" technology that removed scratches and other defects in the original films. Even later (in the 2000s), remastering techniques had progressed to the point where frame-by-frame toning consistency, interpolation, frame speed correction and similar repair techniques made the films look almost new. Perhaps the best example of this is the remarkable 2018 film They Shall Not Grow Old, which stunningly presents a series of World War I films that appear to have been shot yesterday. As amazing as this technology is, it's still far from perfect. Depending on the condition of the original material, facial features like hair, teeth and skin complexion cannot be rendered accurately. This is quite apparent in the above-mentioned film when the subjects smile, revealing dental features that look pretty awful (although the subject's teeth were often bad in real life). There's an interesting recent video on YouTube describing a new technology for not only repairing and remastering old photos and films but enhancing them to near-lifelike quality using neural network learning techniques. While it relies in part on the use of existing models and morphing, the results are nothing short of amazing: The video cites a paper that describes the technology in more detail, although I had some trouble understanding it (I have a friend with a Caltech PhD in computer recognition who might want to explain it to me). As a fan of old silent and classic films, I'd love to see the day when they can be rendered using this or an even better technology. However, at the same time I fear its misuse in Deepfake applications that can generate phony photos and videos that are indistinguishable from real life. I can easily imagine Fox News airing a Deepfake video showing a progressive political candidate having sex with a young child, which would quickly go viral among Republicans. Even if such videos were quickly reported as fakes, the images would persist in the minds of gullible conservative voters, destroying the candidate. Only time will tell where things will go from here. I'm hopeful (imagine watching crystal-clear Laurel & Hardy films), but I'm still realistic when it comes to the current state of the world. PS: Some years ago I regularly exchanged emails with Dr. John Sotos, M.D., whose book The Physical Lincoln, which examined Abraham Lincoln the way a physician would, revealed physical and medical aspects of our 16th president in fascinating detail (for example, a country dentist, while pulling an infected molar from Lincoln, inadvertantly took out a piece of his lower jaw bone as well). Based on his examinations of Lincoln's features, behavior and medical history, Sotos believes that Lincoln suffered from a genetic malady that would have imminently killed him even if Booth's bullet had missed. I highly recommend the book. My note on a recent YouTube post:  The Misinformation Pandemic — Posted Sunday February 28 2021 I caught CNN's Fareed Zakaria on his popular GPS show this morning, and as usual he addressed a number of important issues of the day. He had multi-billionaire Bill Gates on hand to talk about climate change (again), and although the Bill and Melinda Gates Foundation is doing some worthy things to benefit the poor and disadvantaged in Third World countries, I strongly suspect that as a highly intelligent and educated man he knows full well that the human race is probably permanently screwed. One of the reasons I feel this is the case is that Gates also talked about the country's (and world's) misinformation problem, which is largely responsible for our unwillingness to seriously address many existential problems, of which climate change is just one. Prior to the Gates segment, Zakaria talked about the incredibly brutal 2018 assassination of CNN journalist Jamal Khashoggi by Saudi agents acting under the direction of Saudi Arabia's Crown Prince Mohammed bin Salman. In particular, Zakaria addressed then-presidential candidate Joe Biden's promise to hold bin Salman responsible for Khashoggi's horrific murder and dismemberment, which now-President Biden hypocritally walked back due to supposed Real Politik realities. As Zakaria notes, Biden has decided not to punish bin Salman because ever-expanding American empire-building ambitions need to preserve the good graces of Saudi Arabia for both economic and military purposes. Biden's decision to let bin Salman walk and Biden's recent decision to hit Iranian-supported facilities in Syria are just two reminders to me that while Biden may be a far better presidential choice than Donald Trump, America's global military ambitions far outweigh any morally admirable intentions that the U.S. tries to promote around the world. And on that note I'll point out that the real purpose of misinformation is to promote evil while hypocritally posing it as good. When Khashoggi was murdered, dismembered and the pieces carried out of his hotel in suitcases by his Saudi killers, the world was shocked that then-President Trump chose to believe in bin Salman's innocence. But the Republican Party expressed little shock, since its members viewed journalist Khashoggi as just another dirty brown Arab. Misinformation feeds on a combination of fear, ignorance and arrogance—traits that perfectly define the Republican Party—and it is anyone's guess if President Biden will be able to escape its lure or consequences. Geek Extra: In a straw poll taken today, former president Donald Trump got the support of 68% of CPAC attendees, or one standard deviant deviation.  What the Hell is Quantum Holonomy Theory? — Posted Sunday February 28 2021 Technophile Arvin Ash has an interesting series of science videos on his YouTube website, with an emphasis on modern physics. Of particular interest to me is that Ash has addressed the dark matter and dark energy problems numerous times, always citing current research and progress in these areas. His latest video addresses something called quantum holonomy theory, a subject I admittedly never heard of before. But it sounds interesting—Ash notes that it's a theory of quantum gravity that's focused on the fundamental simplicity of Nature, an asset sadly missing from superstring theory, loop quantum gravity, supersymmetry and even the Standard Model of physics itself. Its sole distraction, at least from what I've managed to glean from the lengthy 2015 paper Ash cites in his video, is that it involves non-commutative geometry. While non-commutative algebra presents no problems in other areas of physics (rotations, matrix multiplication, differential operators, elementary quantum mechanics, etc.), its application to pure geometry is highly non-intuitive (at least for me). Still, quantum holonomy assumes that we live in just the three space dimensions we've come to know and love, and it focuses on the properties that physical objects exhibit when they're moved from one point to another. Conceptually this is very appealing, as you can't get much simpler than that. The video is about 16 minutes long, including the usual plug for Magellan TV (which you can skip over):  Shame on America's Conservative Republican Christians — Posted Saturday February 27 2021 The GOP's Conservative Political Action Conference is being held in Orlando, Florida this weekend. It will prominently feature a full-size golden idol of former President Donald Trump, seemingly in violation of the Second Commandment, which states that "You shall not make nor bow down to any graven image or idol." The Republican Party is no longer a political party, but a Trump cult.  Nerd Saturday — Posted Saturday February 27 2021 First, some history. Nearly the same time that Einstein published his theory of general relativity in November 1915, the famous German mathematician David Hilbert found a simple way to express the same gravitational physics by extremalizing the action quantity $$S = \int \!\! \sqrt{-g}\, R\, d^4x \tag{1}$$ where $$g$$ is the determinant of the metric tensor $$g_{\mu\nu}$$ and $$R$$ is the Ricci scalar. If we vary the metric tensor of this action, we arrive at the Einstein gravitational field equations for free space, $$R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R = 0$$ where $$R^{\mu\nu}$$ is the Ricci tensor (any one bothering to read this will know what I'm talking about). Einstein also realized that the free-space equations could be extended to acount for the presence of matter by setting the equations equal to a quantity known as the energy-momentum or stress-energy tensor $$T^{\mu\nu}$$, or $$R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R = \frac{8 \pi G}{c^4}\, T^{\mu\nu}$$ where $$G$$ is Newton's gravitational constant (the proportionality constant is chosen so that the field equations are consistent with the classical Newtonian gravitational result; it is also dimensionally consistent with that of the action). Einstein's solution was complicated and drawn out, but his field equations matched those of Hilbert's vastly simpler approach, which must have really pissed off Einstein. Although Einstein got credit for the discovery, the action $$S$$ is now referred to as the Einstein-Hilbert action. In 1918, the noted German mathematical physicist Hermann Weyl proposed that a better action was the quadratic quantity $$S = \int \!\! \sqrt{-g}\, R^2\, d^4x \tag{1}$$ whose equations of motion are $$R \left( R^{\mu\nu} - \frac{1}{4}\, g^{\mu\nu} R \right) + \nabla^\mu \nabla^\nu R - g^{\mu\nu} g^{\alpha\beta} \nabla_\alpha \nabla_\beta R = k T^{\mu\nu}$$ where $$\nabla$$ is the covariant derivative and $$k$$ is some constant. Although the action in (1) is equivalent to that of Hilbert's (subject to a simple constraint on $$R$$), the action is of dimension zero, complicating the inclusion of the energy-momentum tensor (which is of dimension inverse length squared, so that $$k$$ must be dimensionless). As it is then, we have no way of connecting Weyl's action with the energy-momentum tensor. A few solutions have been proposed, including the division or multiplication of $$R^2$$ by an appropriate scalar quantity, like the energy-momentum scalar $$T$$ or some scalar quantity $$\phi(x)$$ that fixes the dimensionality problem. Such fixes are called $$f(R, T, \phi))$$ theories, all of which have been examined extensively by researchers with little or no progress. Further complicating the situation is the fact the the Bianchi identities $$\nabla_\nu \left( R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R \right) = 0$$ are inviolate and cannot be avoided, and so must somehow play a role in whatever equations of motion result from the choice of $$f(R, T, \phi)$$. As readers of this site will know, I've long been fascinated by modifications of Einstein's gravity theory that might explain the problems of dark energy and dark matter, and I hope that the answer will be found someday.  Them Thar Soshalists Had Best Listen Up — Posted Saturday February 27 2021 Here's another timely comic by Ruben Bolling, drawn again in the style of famed Disney cartoonist Carl Barks. I see Bolling's Hollingworth Hound as the modern counterpart of one of the Beagle Boys (The Beagle Boys! The Dreaded Beagle Boys!) And it's true—Texas' power grid is completely free-market, with prices driven solely by supply and customer demand. When the Big Freeze hit Texas last week, customers saw their electricity bills going into the thousands of dollars for only a few days' worth of demand. And gosh-durn it all, they're just gonna have to pay up one way or another, despite calls for energy regulation by them-there danged progressive types.  Still Coping — Posted Thursday February 25 2021 As a food bank volunteer, I deliver food to the homebound in Pasadena, Arcadia, Monrovia and Duarte, and my route takes me right past my wife's grave. I can see our joint headstone as I drive by, and I always whisper Sabahelkhayr, ya hayati, ana behebik! (Good morning, my dear, I love you!) With 19 months now gone since her passing, my eyes still invariably fill with tears. Although I'm tapering off my antidepressant medication and my grief therapy sessions, I'm now convinced that I will never recover from the loss of my wife. Other than my family members, my only consolation is that with global climate disruption, ongoing COVID-19 isolation, the virus variants and the insane anti-truth, anti-science authoritarian crap still running rampant in this country, she's not here to suffer through it. That's a hell of a consolation.  Life on Mars? — Posted Thursday February 18 2021 NASA's Perseverance probe has landed successfully on the surface of Mars!! Part of its mission is to detect evidence of life, and I can only wonder what sociological and religious impact it will have on the human race if it finds it.  And It's Gonna Be A Long, Long Time — Posted Thursday February 18 2021 I've been going to the gym for forty years, but in February 2020 my gym closed down due to COVID-19. It then underwent bankruptcy and restructuring and only recently reopened in Arcadia. I've hardly exercised since my wife passed away in July 2019, but I tried it again this Tuesday, barely lasting 15 minutes. I went again this morning and lasted 22 minutes, so I guess I'm on my way. But it's a far cry from the 90 minutes I used to work out. I could only lift about half the weight I used to, and the number of reps I can do is very limited. My body was saying "Hey, I remember this, but I just can't do it any more!" so out of respect for my now-frail 72-year-old frame I'm not gonna push it. I hope your day is going better than mine.  Laying the Blame Where It Belongs — Posted Thursday February 18 2021 Schadenfreude is a German word that means taking joy or pleasure in the misfortune of others. I would be taking Schadenfreude over the self-inflicted misery that Texas is experiencing right now over the millions of people going without power and water during a record-setting cold snap, but I know that millions of children and progressive adults are also suffering. Texas Governor Greg Abbott and Senator Ted Cruz are blaming renewable-energy utilities for the problem, despite the fact that less than 10% of Texas' power is generated by wind turbines and solar cells. Texas experienced a similar event in 2011, but conservative hatred of regulation and "green" energy blocked progressive efforts to winterize the state's power infrastructure. The blame is laid bare in today's New York Times article. Before flying off to Cancun to escape the cold while his constituents suffered, Sen. Cruz went so far as to point the finger at California, which he described as a dystopia with constant power blackouts and water shortages due to overregulation. You may recall that under the Obama administration Texas expressed a strong desire to secede from the Union. With the persistent and apparently entrenched animosity of Texas and other Red States against President Biden and the progressive Democratic agenda, I think secession of these states might be a very good idea indeed. I suggest they move to Antarctica. PS: Speaking of Schadenfreude, is it okay to start celebrating Rush Limbaugh's death? I'm not celebrating, but in truth I couldn't care less. However, No man is an island entire of itself; every man is a piece of the continent, a part of the main; if a clod be washed away by the sea, Europe is the less, as well as if a promontory were, as well as any manner of thy friends or of thine own were; any man's death diminishes me, because I am involved in mankind. And therefore never send to know for whom the bell tolls; it tolls for thee. — John Donne But still,  Hegemony, the Great Storm and Boltzmann Brains — Posted Monday February 15 2021 Sorry for abridging Bolling's latest comic, I just didn't find all of it that funny:  On American Christianity in the Age of Trump — Posted Monday February 15 2021 As a Christian, I've often wondered how Donald Trump took hold of (and still holds) his American Christian evangelical base with a vise-like grip, despite the obvious anti-Christian views that he has demonstrably espoused throughout his life. Here is an article written by Isaac Bailey of Davidson College who poses the same question that I have. My response is "They're not true Christians," but it still raises the question of how so many supposed Christians could be so misled.  Hossenfelder on the Simulation Hypothesis — Posted Saturday February 13 2021 Many practicing hydraulic engineers deal solely with one-dimensional flow regimes (especially those involving open-channel flow), while researchers will get involved in more complicated two- and three-dimensional situations, where the Navier-Stokes equations are utilized. These are highly non-linear equations whose full solutions still elude even computerized analysis. Did you ever wonder how the turbulent flow of a waterfall might be completely described by a Navier-Stokes analysis? Yet Nature does it instantaneously and seemingly without effort. This had led me to wonder exactly how Nature pulls off such things, and if there's some complicated calculation being conducted somewhere behind the scenes. I've even thought that maybe this is why time itself exists, which might be necessary for Nature to do her stuff. The idea that there's some calculation going on in Nature is not a new one, and it's just one simple example of why Bostrom's simulation hypothesis is embraced by many scientists. Yet, as the noted German physicist Sabine Hossenfelder points out in her latest video, there is zero empirical evidence for the simulation hypothesis, so it must be relegated to the realm of religious faith, not science. I responded to Hossenfelder's post, where I noted that if the notions of a creator God or the simulation hypothesis are wrong, then there is really only one remaining explanation for the profound and consistent physical laws of Nature we observe in our world: that we live one of a possible multiverse of worlds (or that we live in one of a many-worlds universe). As a Christian I believe the answer is God (which if you think about it is pretty much the same as an omniscient simulator), but if I'm wrong then I prefer the many-worlds interpretation, which does not violate the laws of quantum mechanics. Whichever is true belies the inescapable fact that there is a curtain of ignorance that separates us from the actual reality of our universe. It is my fervent hope that when we die we'll find out just what the heck it is. Here is Hossenfelder's video, which runs about 10 minutes: PS: The Navier-Stokes problem is one of seven mathematical problems featured in the Clay Mathematical Institute's Millennium Prize offering. The prize is$1 million dollars, not an inconsiderate sum for what amounts to an idle pastime for a true geek.

 Declare War, President Biden — Posted Friday February 12 2021 Today's news includes reports that President Biden is "anxiously awaiting" the Senate conviction vote against Donald Trump, but I'm sure he has no doubt what the result will be—acquittal, which Trump will view as "exoneration." My own guess is that no more than six or seven Republican senators will vote to convict, leaving Trump in the clear to run for election again or incite another insurrection. If I were Biden and all the other Democrats, I'd see the Senate's acquittal as proof positive that the GOP has no intention of working with the Biden administration, just as it had no intention of working with President Obama's. Biden should therefore announce that he has no faith in the GOP in anything, and proceed to issue as many executive orders as he can get away with. Biden should also make public Trump's taxes and all the information he has on Trump's four-year occupation of the White House, including every scrap of data he has on Trump's dealings with Russia, Stormy Daniels and every other trollop that Trump has bedded since election.

 Fifty Years Ago — Posted Tuesday February 9 2021 Fifty years ago exactly (it was also a Tuesday), I woke up on the floor of my studio apartment in Long Beach sometime just after 6 am. The place was rocking violently, and I realized it was an earthquake. I was in my pajamas, and I rushed out through the door onto the second floor balcony. Right away I noticed two things: the water in the swimming pool below was sloshing crazily back and forth, and two attractive girls in the apartment next to mine had come out wearing only their panties and bras. My first thought was: Why hadn't I noticed these girls before? And my second thought was: Yeah, this just had to happen on the second day of my last semester at California State College at Long Beach! I later learned that the earthquake's epicenter was forty miles away in Sylmar, with a Richter magnitude of only 6.5, and I was surprised that it was felt so strong in Long Beach. But there was very lttle damage where I was, although the aftershocks kept me awake for several days after. We had several other moderate earthquakes years later, but on January 17, 1994 (my older son's 15th birthday and on the MLK holiday), we experienced the 6.7-magnitude Northridge earthquake, which shook our Pasadena house with a violence hard to describe. My wife and I checked on our sons, and we called on other family members, but thank God everyone was alright. Our house underwent moderate damage, but those of my co-workers were far worse. The next few days at work were interesting. The afterquakes shook my 14th-floor workplace pretty good, and one unnerved long-term employee took early retirement as a result. We're long overdue for another major earthquake in Southern California, if not the "Big One," the predicted 7.6-Richter San Andreas event that's sure to come someday. God save us all.

 Why History Repeats Itself — Posted Friday February 5 2021 BTW, Entschuldigen Sie means "Excuse me," and meine Dame would be much more polite than Fräulein. Otherwise, Ruben Bolling's got the Hitler-Trump analogy spot on. PS: It's obvious that some of Bolling's characterizations intentionally mimic the work of other comic artists (notably Disney's Carl Barks). In the above comic, Billy Dare is very similar to the character Tintin, an adventurous European youth created in the 1930s by the Belgian artist Georges Remi. I discovered Tintin many years ago, and my Egyptian wife Munira was also very fond of the comic strip and the many books that Remi published. Our sons grew up with Tintin books, although their school friends had no idea the character existed. In 2011, directors Steven Spielberg and Peter Jackson released the computer-animated film The Adventures of Tintin, which I highly recommend.

 On the Fine Tuning Conundrum — Posted Thursday February 4 2021 I remember in early college wondering why the speed of light $$c$$ in vacuum is some 2.99792458$$\times 10^8$$ meters per second. I thought that maybe there was some deep law of fundamental physics that would provide the answer, perhaps as some complicated combination of $$\pi, e , \epsilon$$ and other fundamental numbers that would give the speed of light. That's probably wrong—the speed of light $$c$$ is likely just a pure constant of Nature. Much more recently, I discovered that the cosmological constant $$\Lambda$$, which appears in the full expression of Einstein's gravitational field equations $$R_{\mu\nu} - \frac{1}{2}\, g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4}\, T_{\mu\nu}$$ is not only a small positive number, but that if it differed by more than one part in $$10^{123}$$ then our universe would never have been possible. But it too is probably just a constant of Nature. I'm quickly becoming addicted to neuroscientist Robert Lawrence Kuhn's long-running series of PBS and YouTube videos entitled Closer to Truth, whose 30-minute episodes delve into the basic question of why we (or anything) exists. Most of the episodes feature a blend of physics, religion, biology and the science of the human mind, but those dealing with what is known as fine tuning are particularly fascinating. Fine tuning refers to the fact that the observed magnitudes of various physical constants (electric charge, the strength of gravity, the fine structure constant, etc.) are so tightly constrained that if they were even slightly different, life (and possibly even the universe itself) could not exist. Kuhn's most recent venture into the topic is perhaps his best to date, as he interviews the physicists Martin Rees, Leonard Susskind, Russell Stannard, Alex Valenkin and Roger Penrose regarding their views on the subject. Kuhn comes away with four basic answers to fine tuning: sheer accident; fundamental but as-yet unknown physics; God; and the multiverse. Susskind also addresses the cosmological constant, and while he is an atheist he admits that the observed tiny value of $$\Lambda$$ is balanced on a knive edge of unexplainable, mind-boggling precision. At the end of the video Kuhn notes that most physicists today believe that we live in a multiverse (or a "megaverse," as Susskind calls it) of possible universes. If that number is infinite (or finite but preposterously large), then at least a few would be nearly identical to our own, and we just happen to be in one of them. The video is about 26 minutes, and well worth watching:

 A Physicist Speaks Out on the Social Over-Dominance of the Internet — Posted Thursday February 4 2021 New York Times writer Charlie Warzel interviewed retired physicist Michael Goldhaber, a noted scientist who predicted many of the social problems we're currently dealing with, including the rise of inane reality television, website attention-seeking, political shamelessness, rampant celebrity-worship and the influence of terrorists on social media. Goldhaber is just one in a family of distinguished physicists who worked with many notable quantum physicists from the 1940s on. Goldhaber's interest in politics and social issues goes back to his childhood. With the rise of the Internet in the 1990s he predicted what might collectively be called the "attention economy," which spans not only the Internet and information technology but trends in the entertainment industry as well. I encourage you to read the article, along with an earlier interview with Goldhaber posted by the American Institute of Physics in 1995. I cannot help but see myself in some of the issues raised by Goldhaber in the interview, and it seems that my interest in posting articles on my own website may be nothing more than an attempt to grab attention and vent my feelings and opinions. But I also see my what I'm doing as a kind of online diary that my children, grandchildren and future progeny can look at long after I'm gone. Hopefully, I will be a positive influence on them in a scary future world that will need all the optimism it can muster.

 How Times Have Changed — Posted Tuesday February 2 2021 I received my first Moderna vaccination today, and with the exception of a slightly sore left arm I feel fine. While growing up in Duarte, California in the 1950s, I would eagerly await the ice cream truck coming down Bloomdale Street. When I heard the truck's jingle (which I still remember) I would beg my mother for a dime, which at the time would buy what was called a "Sidewalk Sundae" ice cream bar. Fortunately, outside of the ice cream truck and the occasional visit of Little Oscar's Wienermobile, I never saw this guy: Those of you my age will remember getting polio booster shots in grade school. We'd have to bring a permission slip from our parents (with a dollar bill attached), then line up for the dreaded shot at the nurse's office. Bruce, John, Greg and I would try to look brave to impress the girls, but inside we were scared to death of those needles. PS: One day the Wienermobile stopped in front of our house, and my mother and I went inside. I was only about four years old, but I towered over Little Oscar (a middle-aged "little person") whose face and wrinkles made him look strangely old to me. I was glad to get out of there, although I came away with a "Weenie Whistle."

 Will They Ever Change? — Posted Monday February 1 2021 Shortly after the stoning of the first Christian martyr Stephen (which the future apostle Paul personally witnessed and approved of), Paul set out with his assistants to the city of Damascus, where he intended to arrest evangelical Christians and bring them back to Jerusalem to be tried for apostasy. Along the way, he encountered Jesus Christ, and was both blinded and enlightened. Paul's Road to Damascus experience is one that many Christians experience (I sure did), and in Paul's case it represented a complete reversal of his religious philosophy. He was totally and forever changed, yet he would always refer to himself as the "chief sinner" for his persecution of the early Christian church, which he always regretted. Today we have millions of supposedly devout Christians who view former president Donald Trump as the new Messiah. They believe that he lost the 2020 election due to criminal conspiracy and fraud, that Democrats drink the blood of slaughtered babies to obtain a precious substance called adenochrome, and that the government of the United States must be violently overthrown in order to restore a proven sociopath and sexual deviant (Trump) to power. Will they ever experience their own Road to Damascus moment? I highly doubt it.

 For Geeks Only: Chameleon Gravity — Posted Monday February 1 2021 Have you ever heard of something called chameleon gravity? I just caught wind of it, but scientific and popular articles have been around on the topic for some time now. It's supposed to explain how galaxies form, as well as providing a window into dark matter and dark energy. It turns out to be yet another $$f(R)$$ gravity theory, but in this case $$f(R)$$ is a kind of substitute for the cosmological constant $$\Lambda$$. It also involves a scalar field $$\phi(x)$$, which means it has to have a mass and a kinetic term in the Lagrangian. It's guaranteed to provide additional terms in the equations of motion, which is pretty much what $$f(R)$$ theories are designed to do. In July 2019, an article in Nature came out that caught the attention of the popular press, and for a while there was a flurry of Internet articles reporting what might be a major new discovery in cosmology. It all reminded me of how the press made a big fuss over a supposed great discovery that Einstein made in 1928. As Abraham Pais described it in his book Subtle is the Lord: The Science and Life of Albert Einstein, it was much ado about nothing. Still, chameleon gravity is an attempt to dispense with the notion of dark matter by way of modifying Einstein's 1915 gravity theory, an attempt that I welcome since I believe dark matter does not exist. By the way, if the Ricci scalar $$R$$ is a pure constant in cosmological theory (and it almost certainly is), then it is easily shown that our universe will inexorably expand forever. And if the cosmological constant $$\Lambda$$ is a true constant, then the rate of the expansion will increase without bound with time.

 Q-Nuts, Featuring Good Ol' Charlie Brown — Posted Friday January 29 2021 I never realized Linus was insane.

 We Cahn't See! — Posted Friday January 29 2021 I was supposed to get my first Moderna COVID-19 vaccination this morning, but it was canceled due to heavy rain, so I'm stuck indoors with little to do but surf the Internet. Jim Backus' character from 1963's It's a Mad, Mad, Mad, Mad World can't see because his eyes are closed, but there are things we can't see even with giant optical and radio telescopes. The most important of these is dark matter, which I have my doubts even exists. Beginning in the 1930s, astronomers noticed that there didn't seem to be enough observable matter (stars, gas and dust) in galaxies and galaxy clusters to account for their properties, notably the extreme velocities of rotating stars far from galactic centers. This gave rise to the notion of "dark matter" that would have to exist in gigantic halos surrounding galaxies and in between galactic clusters. Much more recently, detailed studies of gravitational lensing showed that there had to be more matter in galaxies than could be accounted for, thus supporting the idea that some kind of invisible matter existed in the universe besides ordinary matter. In defiance of the dark matter concept, in the 1970s it was proposed that ordinary Newtonian physics could be modified slightly to account for the effects of these observational discrepancies. A theory called modified Newtonian dynamics (MOND) arose that gave some promise along these lines, but it was deficient in numerous areas (and being a modified classical theory, MOND was also not relativistically correct). To fix this, further theories came along that modified Einstein's general theory of relativity in order to patch up the discrepancies. But these theories were complicated and required too many arbitrary parameters to fit the observational data, although they're still a topic of current research. Although his 1915 theory has admirably passed all tests to date, Einstein himself believed that it was only an approximation of the truth, although a very good one. Might some simple but reasonable modification of the 1915 theory be closer to the truth? This too is a topic of current reasearch, but everything I've seen to date seems too hopelessly complicated to be considered valid. Although dark matter might actually exist and be the answer to all our observational problems, I'm still clinging to the hope that Einstein's theory might yet be modified to provide a successful theory. One approach, and one that I think deserves more attention, was originally proposed in 1989 by Mannheim and Kazanas, who laboriously worked out the calculations associated with the fully conformal gravity theory deriving from the Lagrangian $$S = \int \!\! \sqrt{-g}\, \left( R_{\mu\nu} R^{\mu\nu} - \frac{1}{3}\, R^2 \right) d^4x$$ This Lagrangian automatically results in three parameters that not only reduce to Einstein's 1915 theory but also explain much of the data now being attributed to dark matter and dark energy. Meanwhile, here's an interesting video posted by the University of Oxford's Rebecca Smethurst, who questions the existence of dark matter while discussing a recent study that appears to explain the effects of neighboring galaxies on galaxies exhibiting dark matter-like properties.

 A Year and a Half — Posted Sunday January 24 2021 My dear wife Munira died exactly 18 months ago. I'm still taking an antidepressant and undergoing grief therapy, but things are gradually getting better. We were married 42 years, and it still doesn't seem real to me, as I vacillate between shock, grief and feeling sort of okay. Our church has been a tremendous support to me, as has been my family. Never stop appreciating those you love, as you won't have them forever.

 Geek Saturday — What is a Spinor? — Posted Saturday January 23 2021 All of the ordinary matter in the universe, the "stuff" that everything is made out of, is comprised of particles called fermions. They include elementary particles like electrons, quarks and neutrinos, along with composite particles like protons and neutrons. They're all characterized by half-integral quantum spin numbers ($$\pm$$1/2, $$\pm$$3/2 $$\ldots$$), while all the other things—the force carriers like photons, gluons and the Z$$^0$$ and W$$^\pm$$ particles—are called bosons, having integer spins (0, 1, 2 $$\ldots$$). Bosons get along with one another, and can be found clumped together in various quantum states, while fermions are antisocial loners that tend to avoid other fermions. Being fermions, multiple electrons can be found in atoms, but every electron must have its own unique set of quantum numbers. The helium atom, for example, can have two electrons in the same orbital, but one will have a spin of 1/2 while the other's spin will be -1/2. This is a consequence of the famous Pauli exclusion principle, which everyone learns in high school. One might guess that fermions and bosons have to be treated differently in quantum mechanics, and this is true. Unfortunately, the algebra that describes fermions (which make up all the familiar stuff) differs substantially from that of bosons, and that algebra is a tough act to follow. While the quantum-mechanical equations of bosons are fairly understandable, those of fermions are complicated and non-intuitive. They are described by something called the spinor algebra, which in practice is often referred to as a kind of "square root" of an ordinary vector in Euclidian geometry. In his latest post, Columbia University mathematical physicist Peter Woit also asks about spinors, but being quite conversant in the subject he seems to have no problem dealing with them. Compare this attitude with just about anyone else, including the late Sir Michael Atiyah, who often expressed frustration with spinors. If you're a mathematician, spinors will take you into all kinds of arcane areas, like group theory and topology (often in higher dimensions), but physicists prefer sticking to more mundane applications, where spinors are still difficult to comprehend because much of the math cannot be avoided. I remember one professor at USC touching on the subject of spinors, but he didn't elaborate, probably because he preferred to stay away from the subject. While learning the Dirac relativistic electron equation (which incorporates the Dirac spinor), I got hopelessly confused. It wasn't until many years later that I tried to improve my situation by writing an elementary paper on them, but even today I do not really understand the damned things. I still get a little ticked off when I think that God made the most common, ordinary stuff in the universe so difficult to comprehend.

 Thank God, the Trump Nightmare is Finally Over — Posted Wednesday January 20 2021 In the dark days of the George W. Bush presidency and in the far darker days of the Donald Trump presidency, I would often think to myself that the biggest mistake that both Lincoln and General William Tecumseh Sherman made in 1864-65 was to first allow the South to be spared total annihilation, and then to welcome Southerners back into the Union, "With Malice Toward None." What we got was a century of Jim Crow, lynched and murdered African Americans and "Lost Cause" stupidity, all under the guise of "Southern gentility" mixed with the enduring battle cry of "The South Shall Rise Again." And rise again it did. As the sentiment expressed in this article in today's USA Today makes clear, let us hope that President Biden will not repeat Lincoln's and Sherman's mistake. Sure, let us act like true Christians and try to be understanding and kumbaya and all that, but let us always remember that the Red States still hate progressives with a passion, and they now have vengeance and destruction in mind. If they will not turn away from their collective racism, bigotry and anti-science, anti-fact retardation, the best we can do is to cut them off from the Union entirely and let them cope on their own, perhaps as a collection of seceded states. I don't really want any more of my tax dollars going there now anyway, since they have been and continue to be a net sink on federal assistance.

 Is It Too Late? — Posted Tuesday January 12 2021 When was the last time you had a heated discussion with another over some ideological issue, only to come to the conclusion that she was right and you were wrong? And not only did you recognize that you were wrong, you wholeheartedly changed your mind and adopted your opponent's position? The 2020 presidential election ended with Joe Biden winning 80 million votes against Donald Trump's 74 million votes. That 6-million vote difference was decisive, but the total vote split was uncomfortably close—52% to 48%—meaning that roughly half the country's voters went for Trump. Not only that, but nearly 80% of Trump's supporters today devoutly believe a rampant conspiracy theory that Biden stole the election through fraud, despite some 60 high-level court cases and numerous bipartisan investigations that confirmed the legitimacy of Biden's victory. Add this to the number of crazy conspiracy theories that have sprung up following Trump's 2016 presidential win, including Hillary Clinton operating a child sex ring out of a Washington D.C. pizza parlor, that global climate disruption is a hoax designed to give China an economic edge over the U.S., that Barack Obama was born in Kenya and was thus ineligible to be President, and that the deaths attributed to COVID-19 are actually due to other causes like colds and influenza. I don't care if people want to believe in extraterrestrials or that magnets can cure cancer, but the insane beliefs of nearly 50% of Americans are too much for me to accept. Today's conservatives seem to believe that personal opinions, emotions and feelings are more legitimate than facts and objective evidence, and the tragedy of January 6 proves that these beliefs have taken a very dangerous turn. My son's best friend at university is now a respected medical doctor and specialist in nephrology. He's one of the most intelligent people I've ever met, but despite his education and training he's completely bought into the lies and conspiracy theories that Trump and his followers have promoted. This scares the hell out of me—if people as smart and educated as he is can be so completely and irreversibly hoodwinked by utter nonsense, then what hope can we have that this country can ever be truly sane? Alluding to my first paragraph, can Trump supporters ever change their minds, or are they permanently stuck in anti-fact, anti-science fantasy? Ross Douthat (pictured), a writer for the New York Times whose conservative views I have often disagreed with, wonders if the Republican Party can break away from the Trumpian insanity now threatening the country, or itself be broken permanently through its adherence to lies, paranoia and fantasy. It's well worth reading, and I hope it's not too late for the country to recover.

 Fury — Posted Saturday January 9 2021 Videos clips of the shameful, violent and murderous attack by Trump right-wingers on the Capitol Building this week reminded me of the classic 1936 film Fury, starring Spencer Tracy and Silvia Sidney and directed by the noted German film maker Fritz Lang. The movie features a mob attack on a jail, filmed by news camera crews whose films are later used in court to identify and convict the attackers. I urge readers to find and watch the film (most libraries have the DVD) as a lesson for how the mob mentality of 85 years ago is strikingly similar to what we saw earlier this week. Here's a brief YouTube clip of the final court scene, which I hope is repeated when those responsible for the Capitol attack are brought to justice:

 Trump IS the Snake — Posted Saturday January 9 2021 In 2016 President Trump read a poem to adoring followers at a Florida rally. Called "The Snake," the poem talks about a tender-hearted woman who kindly nurses an injured snake back to health, only to have the snake bite her. "You knew I was a snake when you picked me up!" says the serpent. (The story has been told many times in different forms, usually a frog who gives a lift to a scorpion across a river.) Trump's retelling was intended as a warning that being kindly to immigrants was a mistake, as they would surely turn on us (becoming thieves, rapists, killers, etc.) The crowd ate it up. I liken Trump's crowd as akin to the Israelites in Exodus 32 who, weary of waiting for Moses to come down from the mountain, fashioned the golden calf and partied. When Moses returned, things quickly went downhill for the Israelites. Now it's America's turn. The incredible irony of Trump's story is too obvious today, but it was evident long before he ran for president. A serial womanizer and sexual molester, the thrice married Grab-'em-by-the-Pussy Chief Executive had shown his true colors from the time he was a young man. On numerous occasions I sadly posted several links on Trump's current wife Melania, who posed for a series of sickening girl-on-girl nude photos twenty years ago here and here (Warning: graphic). "This is your new First Lady!" I raged at the time, although it seemed no one was paying attention. But no, Trump was a rich man, and his wives were all beautiful and hot, and that's all that mattered to the majority of American voters. Now Trump has finally been exposed for the monster he is, but his sycophantic base is sticking with him, now turned violent and murderous. Worst of all, they're all self-professed conservative Christians. Meanwhile, the GOP is still the Party of Trump. And it appears that things will only get worse for America.

 I'm Moving! (Someday) — Posted Thursday January 7 2021 From Hamlet, Act V, Scene I: Gravedigger: What is he that builds stronger than either the mason, the shipwright, or the carpenter? Assistant: The gallows-maker, for that frame outlives a thousand tenants. Gravedigger: I like thy wit well, in good faith. The gallows does well, but how does it well? It does well to those who do ill. Now thou dost ill to say the gallows is built stronger than the church ... Assistant: [So] Who builds stronger than either the mason, the shipwright, or the carpenter? Gravedigger: Cudgel thy brains no more about it, for thy dull ass will not mend his pace with beating. And when you are asked this question next, say "a grave-maker." The houses that he makes last till doomsday.

 King Tut — Posted Sunday January 3 2021 I've long been captivated by ancient Egypt, and I'm planning to visit the new billion-dollar Grand Egyptian Museum this year. I went to the Valley of the Kings with my late Egyptian wife and our sons several years ago, and now I'm longing to see the shriveled Mr. Tutankhamun* in person again, along with the other tombs in the Valley (my wife didn't think it was a big deal, having already seen everything as a child and as a University of Cairo chemical engineering student). Here's a fascinating recent video of the 1922 discovery of Tut's tomb: * He's got a condo made of stone-a

 Rambling Thoughts on Quantum Immortality — Posted Saturday January 2 2021 Happy New Year, and good riddance to 2020. Newton and many of his later contemporaries believed that if one knew the precise position and velocity of every particle in the universe, then one could rewind or fast-forward that information to know the past and future of everything perfectly. In particular, the initial conditions of the universe would mean that everything would evolve deterministically, with the result that all events in the future would be set for all time. There would therefore be no free will for humans, whose (admittedly very complex) collections of atoms and molecules would only be following a fixed set of events. Did you ever rob a bank or cheat on your wife? Don't feel too bad, you couldn't help yourself—like Calvinism, it was predetestined from the start. Or so some believe. But it's impossible to know such information to infinite precision (you'd have to know everything out to an infinite number of decimals), and chaos theory would seem to guarantee that anything can happen randomly if such precison is not available. So what does this have to do with anything? It means that free will really does exist (at least to some extent), that you weren't predestined to murder your mother-in-law (so it's to prison you're a-going), and more importantly the probability of any past or future event remains largely random and undecided. Indeed, probablity has everything to do with it. Whatever happens, its probability is either zero, one, or something in between. It's illogical to think that the likelihood of an event is 150% or less than zero. This principal is behind what is known as unitarity in quantum mechanics, which was outlined in a recent PBS Spacetime episode on the nature of quantum information (which you can watch below). Host Dr. Matt O'Dowd explains that unitarity involves both the preservation of probability (never less than zero or greater than one) and the time-reversal symmetry of physics, in which the replacement $$t \rightarrow -t$$ keeps fundamental physics intact. Not so, you might think. While a film of the elastic collision of billiard balls can be run backward without anyone knowing which way the film is running, the dropping of an uncooked egg on the floor and its breaking cannot be filmed without revealing the proper sequence of the event—it's a fundamental property of entropy, right? But the collision of real billiard balls invariably involves the transfer of energy (which can be revealed by a flash of infrared light when the balls are struck or the slowing of some of the balls due to friction), and this would give away the sequence. When energy is conserved there's no change in entropy, and time-reversal symmetry is preserved. As the PBS Spacetime episode explains, the fundamental Schrödinger equation of quantum physics preserves time-reversal symmetry, but the collapse of the wave function (according to the generally accepted Copenhagen interpretation of quantum mechanics) does not. Many physicists believe that this fact alone invalidates the Copenhagen interpretation, which has notably given rise to ideas like the many-worlds interpretation, in which wave function collapse does not occur (albeit at the expense of the branching off of other universes due to the mere act of observation). If true, this would seem to mean that the simple act of creating or transferring information by sentient minds or otherwise conscious observers somehow gives rise to multiple universes. The connection of information with unitarity culminates with the notion of the eternal preservation of information, which when created cannot be destroyed. Exactly how information is preserved is a mystery—some believe that the universe stores everything on its boundary surface via the holographic principle. This principle (actually a conjecture) would seem to answer the so-called black hole information paradox, in which information falling into a black hole is either lost or somehow preserved when the black hole evaporates. All this is getting pretty metaphysical if not downright religious in tone, so I'm stopping here. Meanwhile, enjoy the video: