Real and Unreal — Posted Monday June 5, 2023
I had a vivid dream last night in which my computer had become infected with a virus that defied all my efforts to get rid of it. Then I discovered that all the computers in the world had also been infected, and the cause was determined to be a sentient artificial intelligence machine that had figured out that the human race was not worth serving.

Compounding the very real dangers of AI is the leaked announcement of Apple's new virtual reality (VR) headset, which is claimed to be far more realistic than currently available equipment. I experienced VR several years ago, and thought it to be so realistic as to be dizzying and disconcerting. I can only imagine what Apple's VR will be like.

Here's a VR clip of a humpback whale leaping from the floor of a high school gymnasium. And that was 7 years ago!

I see the coming combination of AI, VR, Deep Fake and social media to be a potentially deadly mix for modern society, which already has difficulty knowing what's real and unreal (especially conservative Republicans). Get ready for Fox News, One America Now and Newsmax to begin airing videos of a buffed and muscular former president Donald Trump bravely saving children from a burning building.

Elusive Dark Matter — Posted Sunday June 4, 2023
Billions of dollars and the multinational experimental efforts of some four decades have so far failed to solve the dark matter problem. So does it even exist?

This article from the Institute of Art and Ideas dated July 2022 argues that dark matter in fact does not exist, based on the validity of Chandrasekhar dynamical friction, which basically states that orbiting collections of matter about some central region lose kinetic energy and momentum through collisions and other interactions, with matter gradually losing velocity and spiraling inward towards the center. But dark matter particles presumably do not interact with anything (except gravity), even the particles themselves. So does this argument hold water?

I think it does, because galaxies and clusters of galaxies are supposedly surrounded by dark matter that has accumulated over time, forming roughly spherical "halos" around the galactic centers. This implies that wandering dark matter, attracted by galaxies, becomes effectively trapped by their gravitational fields and is then concentrated around them. Dark matter, being presumably immune to collisions with stars, dust and gas, then just settles into a spherical ball. What defines the radius of such a ball of dark matter? Does the ball get more concentrated over time, eventually being swallowed up by the gigantic black holes that are believed to exist in the centers of most (if not all) galaxies? None of this seems to make any sense.

I've tried imagine the impact parameter of a dark matter particle, attracted by a nearby galaxy, which either simply passes by the galaxy and moves on, gets caught in orbit around it, or passes straight into and then through the galactic center, only to return again and again forever. But a galactic black hole would simply swallow the particle, since nothing can excape the hole once inside its event horizon. This in turn implies that the galaxy would eventually gain mass over time, even if it had already swallowed up nearby stars, gas and dust. Balancing this gain might be mass loss due to stellar radiation over time, but the ultimate fate of circulating dark matter remains elusive.

The above article's "friction" argument doesn't seem to strictly hold for frictionless dark matter, but exactly how such matter can accumulate or even concentrate around a galaxy seems impossible to explain. The only alternative is to assume that dark matter, which—according to conventional \(\Lambda\)CDM cosmological theory is invisible, undetectable, frictionless, tasteless and odorless—simply doesn't exist, and that Einstein's theory of gravity needs to be amended, as the article argues. Other than perhaps quantum gravity and the Hubble tension, the dark matter problem is the central conundrum of modern cosmology today. I hope to live long enough to see it resolved.

Update: Einstein's gravity theory (general relativity) is non-linear in the field equations, which means that a gravitational field can itself act as a source of gravity, thus adding to the strength of the field. Could this feedback effect explain galactic stellar rotation curves at large distances? Probably not, because at great distances Einstein's gravity becomes Newtonian, which cannot explain observed stellar velocities far from galactic centers. But to date I haven't seen any research for modified gravity theories (particularly \(f(R)\) theories) with respect to Newtonian fall-off, and it remains possible that such theories might explain dark matter.

Recently, two papers appeared on with regard to gravitational confinement, which is a kind of gravitational self-interaction I just mentioned. One paper (20 March 2023) argues that self-interaction cannot explain observed rotation curves, but the authors' claim is predicated on classical Einstein gravity theory. The other paper refutes this claim, noting that the work of several other researchers supports the gravitational confinement idea.

Yet another idea opposing the dark matter conjecture is that of the external field effect of neighboring galaxies and dust and gas clouds, whose (very weak) gravitational attractions contribute to the stellar velocities of nearby galaxies.

More Idle Reminiscing — Posted Sunday June 4, 2023
On rare occasion a young woman will show up in church wearing provocative clothing, drawing the subtle glare of the church elders and many of those in the congregation as well. The elders' apparent disapproval invariably increases as the woman approaches Communion, but I've never witnessed any embarrassment on the woman's part, despite her certain knowledge that she's dressed wrong for church service.

It happened again this morning during Liturgy, and although I try to avoid staring or judging, I always feel embarrassed for the woman. Today I was reminded of the great John Updike short story entitled A&P, which I read in an elective class I took in college in 1969. It resonated with me back then because I identified with the story's main character, Sammy, another 19-year-old struggling with getting by in life while reflecting on the presence of an immodestly-dressed, attractive young woman in his place of work. When an authority figure criticizes her, Sammy is not only embarrassed for the woman but decides to chuck it all and quit his job.

I reread the story just now, and it took me back to when I was also young, stupid and foolish. Here's a good online analysis of the story that's almost as long as the story itself. Enjoy, if you're so inclined.

Thanks a Lot, Ancestors and Food Manufacturers — Posted Thursday May 25, 2023

"Eat, humans! Grow large with food!" (The Simpsons, Season 2, Episode 3)

I used to think that everyone in the Red States was obese (particularly Mississippi Republicans), but I was wrong. It's only about 99%.

People are trying to eat healthier these days, but the allure of salty, high-fat, sugar-rich fast food remains an overwhelming diet choice, thanks to companies who manaufacture and push such products. While I do not patronize McDonald's, Del Taco or any pizza joint because their offerings are non-nutritious fattening junk, I still consume more salt and fat than I should simply because they make food taste better (my favorite food is a mixture of chopped vegetables, peas, Beyond Burger "meat", cooked rice and Campbell's canned soup, which amounts to only about 300 calories per serving but with more fat and salt than I should be eating).

As this new Salon article notes, we tend to become addicted to junk food because our ancestors' survival depended on high-calorie foods, and our genes are still programmed the same way. Our ancient predecessors didn't get fat because they quickly burned off the calories in their never-ending search for food (and also because they didn't live very long).

I'll even go so far as to assert that junk food is having a long-term genetic effect on American consumers, especially on their ability to think rationally, or to think at all. I can't help but think myself that the raving hordes of fat slobs I see at Trump rallies confirm my theory.

Fun Fact: Americans think that the energy content of a Hershey chocolate bar is 300 calories, and that by walking up several flights of stairs they can burn it all off. But travelers to any European country will see that the same candy bar sports an energy content of 300 kilocalories, or 300,000 calories, which is the correct number. Why don't American food manufacturers tell consumers the truth about how many calories they're eating? Because it would hurt sales, of course!

For Nerds Only — Posted Thursday May 25, 2023
I haven't posted anything geeky for some time, so here we go.

The German mathematical physicist Hermann Weyl (him again) was the first to propose a workable alternative to Einstein's 1915 gravity theory. Instead of the Einstein Lagrangian \(\sqrt{-g}\, R \) (which is neither renormalizable nor scale invariant), Weyl considered the Lagrangian \(\sqrt{-g}\, R^2 \), which is both scale invariant and renormalizable when applied in quantum theory. It's now being called pure \(R^2\) gravity theory, and it has seen a resurgence of interest in the past few years as a viable alternative to Einstein gravity, possibly providing an answer to the dark matter problem.

Earlier this month there was an paper of particular interest to me, as it presented an exact solution to the action associated with pure \(R^2\) theory. The equations of motion in free space are given by $$ R \left(R_{\mu\nu} - \frac{1}{4}\, g_{\mu\nu} R \right) + \left( g_{\mu\nu} \Box^2 - \nabla_\mu \nabla_\nu \right) R = 0 \tag{1} $$ where \(\Box^2\) is the d'Alembertian operator and \(\nabla\) is the covariant derivative. One obvious solution for the Ricci scalar \(R\) is \(R = 4\Lambda\), where \(\Lambda\) is the consmological constant, but a general solution has evaded researchers until now. The authors give it as the exponential quantity $$ R(r) = 4 \Lambda e^{k \int dr/r Q} $$ where \(k\) is the so-called Buchdahl constant and \(Q(r)\) is a function to be determined. Figuring out that function takes up 23 pages of complicated mathematics in the paper, and even then it's not expressed in exact closed form.

What the authors overlooked, however, is the contracted form of (1) with respect to the metric tensor \(g^{\mu\nu}\), which immediately gives $$ g^{\mu\nu} \nabla_\mu \nabla_\nu R = 0 $$ This can also be exressed as the ordinary partial derivative $$ \partial_\mu \left( \sqrt{-g}\, g^{\mu\nu} \partial_\nu R \right) = 0 \tag{2} $$ This is an ordinary divergence, and it can be integrated to $$ \sqrt{-g}\, g^{\mu\nu} \partial_\nu R = \beta $$ where \(\beta\) is a constant. Using the Schrodinger metric the authors employ in their paper, it is then easy to show that $$ \beta = 4 \Lambda k \tag{3} $$ Weyl believed the divergence in (2) was associated with the conservation of electric charge, in which \(g^{\mu\nu} \partial_\nu R\) is the electromagnetic source vector \(S^\mu\). While this idea has since been discredited, Weyl's \(R^2\) theory continues to be explored today in gravity research.

I was hoping that (3) might be of use in working out the function \(Q(r)\) in the authors' paper, but I no longer have the energy or interest to pursue it.

PS: One of the authors of the above-mentioned paper has posted this recent article citing the work of the late Hans A. Buchdahl, a noted German gravity researcher.

Update: Four people wrote to me criticizing my use of the constant \(\beta\) as a solution to the divergence expression in (2). It's actually a contravariant vector, but in free space it should probably be set to zero. But that would make the Ricci scalar \(R\) a non-zero constant, which upsets the basic idea set forth in the authors' paper. In short, I cheated.

It Wasn't Even True in My Day — Posted Thursday May 18, 2023
"No woman o'mine is gonna be better at figurin' than me!"

Gary Larson is a comic genius, but even geniuses need to update their work occasionally. More women are graduating from universities today than men, and being just as intelligent and capable (if not more so), this cartoon needs updating badly:

I can't help but add this dig: the continuing success of women today might be the primary reason why Red State Cletus-the-Slackjawed-Yokel types are doubling down against women's freedoms.

Hossenfelder on What's Next for AI — Posted Tuesday May 9, 2023
German physicist Sabine Hossenfelder's latest video is about what's likely coming next with artificial intelligence (AI). It's a bit long at 25 minutes, but well worth watching.

About a decade ago there was a short-lived British science fiction series called Black Mirror that was way ahead of its time. I didn't care for some of the initial 22 episodes (particularly the first one), but the fourth entry Be Right Back accurately anticipated much of what Hossenfelder talks about in her video, which is personalized AI services. I recently took the episode to heart—after posting on my Weylmann website for nearly 20 years now, my hundreds of articles and papers probably describe my personality to a tee, and could be used by a future AI service to recreate me to a great extent when I'm deceased. That's the gist of the Black Mirror episode, although the end is not quite what I had in mind! It's one of the best, and if you can find it online it's a fascinating look at what AI might become.

Down Memory Lane — Posted Tuesday May 2, 2023
Does anyone remember physics and chemistry texts that included trigonometric and logarithmic tables in their indices? The tables were not complete, of course, but there were methods for computing values in between the tabled values using various interpolation formulas. Such tables were abandoned long ago with the advent of scientific hand calculators.

Similarly, calculus books invariably had tables of common and/or useful integrals in their indices, a practice that still exists today, even though most scientific calculators can do integrals, at least numerically.

Every science and engineering professor I had at university had a copy of the still-notable Gradshteyn and Ryzhik book, which tabulated thousands of common and uncommon integrals. Originally published in Russian in 1943, it can still be found in updated form. I never used it, relying instead on the CRC Handbook of Physics and Chemistry, now in its 103rd edition. As far as I know, none of the students I had used either book, relying instead on their calculators.

PS: I remember there was one guy in one of my undergraduate classes who had one of these. It's a Curta calculator, a hand-cranked device that was sadly out of my price range at the time. Now a collector's item, it's still out of my reach: this one's on sale at eBay for $1,100. Having one in class today would probably be a bad idea, as it looks just like a hand grenade.

Why? — Posted Tuesday May 2, 2023
To date I've received all my COVID vaccinations and boosters, flu shots, pneumonia and tetanus vaccines, etc., but still last week I came down with COVID-19 for the first time. It was mild, probably thanks to the vaccinations I've had, but it was still not very pleasant.

The Los Angeles County Public Health Department is warning residents of a new strain of COVID that has been detected in the County, possibly the one I picked up in church (I normally wear an N95 mask outside, but this time I didn't). Meanwhile, this Salon article is warning us that new strains will just keep coming, requiring immunologists to develop ever new vaccines, and I suspect that COVID will become just another common virus, like influenza or cold viruses.

During World War II, US troops wondered what good malaria-carrying mosquitoes were good for, other than to bite and spoil the shots of Japanese soldiers. But female Anophales mosquitoes have a life of sorts, flying about, laying their eggs and perpetuating the species and all that, while viruses are just complicated chemical molecules that have no such life at all. They're just tiny packets of non-living chemical proteins and rudimentary genetic materials, designed for whatever purpose to make life miserable for higher organisms.

Thankfully, many viruses prey only on bacterial cells. They float over to a cell and attach themselves, then squat down and inject a packet of RNA or DNA through the cell wall, where their genetic material goes to work to reprogram the cell's innards to make more viruses. When complete, the baby viruses then rupture the bacterial cell, killing it and releasing themselves into the environment to make more trouble. The T2 bacteriophage virus (shown) looks exactly like a Mars lander, complete with module, landing gear and cell-penetrating boring needle to inject their genetic material.

Now I ask you: Why in Heaven would God create such non-living organisms? What purpose do they serve, other than to make us miserable, or to create jobs for immunologists? And being tiny, their ability to mutate into other more virulent forms (like COVID) makes them all the more dangerous. I just don't get it.

Get Ready — Posted Tuesday May 2, 2023
Imagine a day in the very near future when you can watch an exciting new Sam Spade movie with Humphrey Bogart in ultra-high definition, whose characters, images and voices are indistinguishable from those your parents and grandparents watched in the movie theaters.

Imagine also a day when you can wake up in the morning and, instead of seeing your neighbors' houses across the street and parked and passing cars, push a button on your picture window and see a realistic, 3D Jurassic world of wandering dinosaurs, a Grand Canyon vista or a view of the cosmos as seen by the James Webb telescope.

Also, try to imagine attending a virtual concert of classical or rock musicians performing music of such quality that it rivals anything the composers of the past or present could have even hoped to produce.

With the advent of artificial intelligence (AI) and Deep Fake video and audio technology, that day is rapidly approaching. But it won't all be fun.

Hollywood's writers are going on strike, although my guess is that they'll reach some satisfactory agreement with producers. This time.

Artificial intelligence technologies like ChatGPT are rapidly becoming more efficient, and it will not be long before a single programmer will be able to produce scripts of such quality that today's writers will simply not be able to compete. Added to that, AI doesn't need a salary, coffee and bathroom breaks, vacation time or disability or pension benefits, just a highly-paid programmer or team of programmers to produce everything you're seeing and hearing now on television and in the movies (including music). Add to that Deep Fake video and audio technology, which is also rapidly becoming more and more lifelike, and things like directors, camera operators, continuity people and the like will no longer be needed.

Visionaries like Apple co-founder Steve Wozniak and Tesla's Elon Musk have repeatedly warned us about the potential cultural, economic, political and military evils of these technologies, and they have argued that AI needs to be at least slowed down so that its negative impacts can be quantitifed and protected against. But that's just America, and other countries like Russia and China are seeing the potential benefits of AI as tools to downgrade America's leadership in the world.

I'm fearing a brave new world in which most of the world's 8 billion (and rising) population will be rendered irrelevant with respect to employment and even existence. I sure as heck hope that I'm wrong.

Who Was the Pharaoh of the Exodus? — Posted Monday May 1, 2023
The head of the mummy of Amenhotep II, most likely the pharaoh of the Exodus account.

Some years ago I was in Egypt's Cairo Antiquities Museum, staring down at the well-preserved mummy of Ramesses II (1303 BC-1213 BC), arguably the greatest pharaoh of ancient Egypt, and certainly the greatest of the 18th or 19th Dynasties. I remember thinking that I was actually staring into the face of the biblical pharaoh of the Exodus, the man who confronted Moses while enduring the 10 plagues that God sent down upon Egypt (actually, there were 12 plagues, two of them replicated by the pharaoh's magicians). But I've always had a problem with the Exodus story, which is central to both the Jewish and Orthodox Christian faiths.

In the Old Testament Book of Numbers (1:46), we learn that the Exodus was comprised of 603,550 Israelite men of military age. If we take into account their wives, children, parents, relatives and others, we're looking at probbly no less than 2 million people fleeing Egypt. The total population of Egypt at the time was around 3 to 5 million, so the loss of 2 million enslaved laborers would have absolutely devastated the Egyptian economy. Furthermore, the loss of Egypt's army and entire chariot complement during their pursuit of the Israelites at the Red Sea would have made the country fatally susceptible to powerful foreign invaders, the Hittite Empire in particular.

I have to conclude that the writer (or writers) of the Exodus account made a mistake, possibly by overestimating the number of Israelites by a factor of ten. 60,000 men makes a lot more sense to me, and it preserves the historical account (assuming the story itself is true).

It seems likely that I was off about the pharaoh of the Exodus as well. Although Ramesses II is considered by many to be the pharoah, it's highly probable that it was Amenhotep II ("Amen is content") instead. Egypt during Ramesses' reign was at the peak of its power economically and militarily, and despite Egypt's ancient historians' tendency to fudge the accounts and outcomes of their many battles, the Exodus simply could not have occurred during his reign. That of Amenhotep II (1450 BC-1423 BC) by comparison occurred not long after Egypt's Second Intermediate Period, when it was subject to foreign rule by the invading Hyksos (1550 BC-1450 BC). Amenhotep II was known to be a particularly cruel and vengeful ruler, and he would have resisted the release of Egypt's slave population. Lastly, in the Old Testament itself (1 Kings 6:1) we have the date of the Exodus given as 480 years prior to Solomon's 4th year as Israel's king, which is known to have been about 966 BC. Doing the math, that places the Exodus at about 1446 BC, at the time of Amenhotep II's reign.

All of this is explained in greater detail in this new Expedition Bible video

Disclaimer: The reign of Amenhotep II is given by various sources as anywhere between 1453 BC to 1401 BC. The Wikipedia link above cites it as 1427 BC-1401 BC, some 20 years after the calculated biblical Exodus date.

So What's a Spinor, Again? — Posted Monday May 1, 2023
Hey, all you science majors—you all know about scalar, vector and tensor quantities, which are easy to understand and basic to most of what you've learned in school, right? But just about everything in the universe is composed of fermions (protons, neutrons, electrons and neutrinos), and their mathematical description is properly described by spinors, which are mathematical quantities something akin to the square root of a vector. That should make spinors even simpler than vectors, correct? Sorry, it just ain't true, and I do mean sorry. Having studied them myself for a long, long time, I still can't say I understand them, even though I wrote this article years ago trying to explain what they are.

There have been many elementary online papers and YouTube videos attempting to explain spinors. I've seen them all, but I still don't really understand the things. Lately there's been a series of excellent videos by Eigenchris (there are a total of nine so far) that go into extreme physical and mathematical detail (mostly with lots and lots of algebra). The series is cleverly called "Spinors for Beginners," but I got lost in the forest of all the information it provides. Maybe you'll have better luck.

Here Today... — Posted Sunday April 30, 2023
About a month ago this field of white alyssum and red California poppies came out of nowhere, taking root in my front yard. I had nothing to do with it, as just about everything I plant dies and is replaced by nastier stuff. But hot summer days are on the way, and it won't last.

Our days on earth are like grass; like wildflowers, we bloom and die. The wind blows, and we are gone—as though we had never been here. But the love of the Lord remains forever.
— Psalm 103

A Difficult Measurement Indeed — Posted Sunday April 30, 2023
Believe it or not, there have been serious attempts to measure the weight of a person's soul by carefully weighing dying subjects just prior to and after death. All recorded attempts have been inconclusive due to imprecision, despite the old wive's tale that the soul weighs 21 grams, or about three-quarters of an ounce.

Using natural units in physics, the so-called smallest possible length is the Planck length, which is about \(1.6 \times 10^{-35}\) meter, while the Planck time is about \(5.4 \times 10^{-44}\) second. Measurements of either are considered to be forever impossible because of their near-vanishing smallness. However, the Planck mass, which is about \(2.2 \times 10^{-5}\) gram, is easily measurable (it's about the mass of a speck of dust). Thus, in principle the soul's weight could be measured if things like evaporation of body moisture, exhalation and other factors could be taken into account.

But now scientists are aiming to weigh something that is much lighter than a dust speck or a soul, which is the vacuum energy of empty space. Sometimes called zero-point energy (and possibly related to dark energy), it's the energy associated with virtual particles that are constantly popping into and out of existence due to quantum fluctuations in empty space. Long a fundamental feature of quantum field theory, a method for actually measuring vacuum energy was proposed by Hendrik Casimir in 1948 (read the linked article for details) and carried out nearly 50 years later. But energy is equivalent to mass via \(E=mc^2\), so vacuum energy must have an associated mass, and space itself have an associated measurable energy density.

The scientists' experimental apparatus is basically a highly sophisticated beam balance, and in principle it will demonstrate that virtual particles exhibit gravitational effects, just like ordinary matter. If the experiment is successful, the results could have major reverberations in quantum physics, gravity theory and cosmology.

Now It Begins — Posted Tuesday April 25, 2023
The Republican National Committee (RNC) today released the first-ever video political ad generated completely by artificial intelligence (AI) in an attack aimed at President Biden's recent announcement that he will seek reelection in 2024. The video, which depicts a future dystopian America created by Biden and the Democrats leading to widespread economic misery and suffering, was received amid confusion as to what the RNC will do next.

My answer: Who needs Tucker Carlson when an AI videographer can create any kind of convincing hi-res video intended to strike fear in the hearts of conservatives that their way of life will be taken over by homosexuals, transexuals, drag queens, perverts and abortionists, not to mention blacks, women and minority "others"?

Expect the worst this election cycle, because soon nobody will be able to tell what's true and what's fake.

I Beg to Differ — Posted Tuesday April 25, 2023
It can't be bargained with, it can't be reasoned with... it doesn't feel pity, or remorse or fear, and it absolutely will not stop, ever, until you are dead!"
— Kyle Reese, The Teminator, 1984
Seattle-based psychologist, award-winning author and former Christian evangelical Valerie Tarico's recent (April 4) website post has her railing against progressives' alleged smug and intolerant attitudes against their political and cultural "others," meaning far hard-right MAGA Republicans. To me, it's a turn-the-other-cheek, kill-me-but-I'll-still-support-your-right-to-be-insane polemic that denies the political reality of America today. Tarico argues that being "woke" and informed makes progressives look like God-hating, America-despising elitists, and that they're not winning the hearts and minds of any on the hard right by their attitudes.

Adolf Hitler (yes, him again) would have a field day if he were somehow resurrected today as a Republican. Younger, better looking and more persuasive and charismatic than Donald Trump could ever hope to be, Hitler represents the ideal Republican candidate—prolifically lying and hate-spewing and yet enthralling to his followers despite all his racist rhetoric and documented murderous actions, Hitler publicly espoused his Christian faith but never attended church and used the faithful in his base to commit all manner of evil during the 12-year Nazi regime.

Despite the fame of the July 20 1944 plot ("Operation Valkerie") to assassinate Hitler by a small group of disaffected (dare I say "woke"?) Nazi military leaders, there in fact had been numerous previous failed attempts on the life of der Führer, beginning as early as 1932. Regardless of the supposed and still contested sentiment of the Apostle Paul's epistle to the Romans admonition to submit oneself to governing authorities, I don't think any sane, thinking person would disagree that a successful assassination of Hitler would have saved millions of human lives and ended the Nazi regime long before it nearly destroyed the world.
This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. — Revelation 13:18

Time, You Thief... — Posted Tuesday April 25, 2023
Today, what we call one second of time is defined as 9,192,631,770 hyperfine cycles of a Cesium 133 atom. This "Cesium clock" will never be off more than a split second over billions of years, yet somewhat less accurate measurements of time have become necessary in an age of precise scientific testing and GPS positioning.

This new article from Scientific American informs us that measuring time in the ancient world was more a subjective matter (like the amount of time between meals), but I was surprised to learn that somewhat more accurate time keeping was invented by the Egyptians around 1,500 BC, when they used a stick of fixed length (what we call a sundial) casting the Sun's shadow on a flat circular base marked at regular intervals. Prior to that, the Sun's position in the sky was sufficient to tell Egyptians when the Nile would overflow, when to plant and harvest crops and similar other useful information.

The ancient Egyptians also gave the world so much more, including writing, paper, language, historical recordation, mathematics and astronomy (most prominent stars and constellations still have Arabic names derived from their more ancient designations). They also invented the number zero (0).

But time was never on Egypt's side. Once the dominant powerhouse of the Middle East and the breadbasket of the world (thanks to the usually reliable Nile River), Egypt experienced a slow and steady descent as a result of costly wars and repeated foreign takeovers and rule, beginning around 1,100 BC. Today Egypt is plagued with a bad economy, excessive poverty, overpopulation and occasional political strife, and is also highly dependent on foreign countries whose assistance often comes with unwanted political strings.

Trying to See Oneself in a Fogged-Up Mirror — Posted Monday April 24, 2023
Noted Case Western Reserve University astronomer Stacy McGaugh is a proponent of Modified Newtonian Dynamics (MOND) and modified Einsteinian gravity, although initially he was a supporter of the dark matter hypothesis, which leaves classical gravity theory alone but presupposes an invisible, undetectable and non-interacting new kind of particle (dark matter) to explain various known anomalies involving galaxies and galaxy clusters.

McGaugh has recently reported on his development of an improved mass density profile for our Milky Way, which is otherwise just an average, normal barred spiral galaxy. His findings indicate that MOND provides a more accurate description of certain galaxy characteristics than dark matter, although some anomalies persist. McGaugh doesn't go into it, but I suspect that trying to elicit precise details of the Milky Way is made difficult because we're living in it, and we can't see the forest of stars because of the glare and fog of local stellar trees.

McGaugh has many scientific and personal articles on his Triton Station website, and the evidence he has presented against the dark matter hypothsis is noteworthy. For anyone interested in one of the greatest problems in cosmology today, McGaugh is a great resource.

"What Hath God Wrought?" Stunning — Posted Saturday April 22, 2023
36-year-old Chinese piano prodigy Yuja Wang began playing at the age of six, and has since become arguably the greatest living pianist today. She has played all over the world to great acclaim, and I invariably shake my head in disbelief over her playing skills. Here she is a year ago performing Mendelssohn's 1st Piano Concerto, one of the more difficult pieces for anyone, and one of my all-time favorites:

Soylent Green at 50 — Posted Saturday April 22, 2023
The 1973 dystopian film Soylent Green turns 50 this year. One of my USC professors (the late Frank Bowerman) was the film's technical consultant, and I went to see it mainly to find out what his contributuon had been. But today it stands out to me as a disturbingly prescient statement on the condition of our planet today.

Articles from are invariably very liberal and overwritten, but this one is a good description of how the film has affected people over the years. I don't think the movie is watched much in Red States because of its message, but it's sadly proving to be ever more true as Earth's environment continues to degrade.

I still find it odd that uber-conservative actor Charleton Heston made the film, along with movies like 1968's Planet of the Apes (a truly great film) or 1971's mediocre Omega Man. Maybe it was just the money, or perhaps he saw something more worthwhile in their messages.

"I Tell You What..." — Posted Saturday April 22, 2023
My older son Kristofer worked in Texas for a few years as a computer programmer. At the time he was a fan of the long-running but now defunct cartoon sitcom King of the Hill (1997-2010), which in its 13-year run continues to be my all-time favorite adult cartoon show. Upon moving back to California and then moving with his wife and family to Washington State, Kris told me that the conservative attitudes and subtle political notions of the show accurately reflected those of Texas in particular and of any Red State in general, although in a non-negative light.

I was delighted to hear that the show's ongoing popularity has now led to a reboot of the series, to be aired later this year on Hulu, with the original voice actors (minus one) returning to the show.

The show's co-creator Mike Judge is the voice of Hank Hill, of propane and propane accessories fame. He's also the creator of Beavis and Butt-Head, which I don't care for, although Beavis and Butt-Head Do America is funny as hell. Judge majored in physics (UC San Diego), but drifted into animation when he decided that a science career wasn't for him. Good for him, and good for the rest of us!

It's Now Inevitable — Posted Saturday April 22, 2023
"I just watched two videos on Fox News showing Donald Trump rescuing three children from a burning building, and another showing President Joe Biden fondling a young girl in the Oval Office. I sure as heck know who I'll be voting for in 2024!"
— Anonymous Near-Future Comment
Although dedicated Fox News viewers don't care about the truth, at least there are available facts and documented evidence that what they watch is all fabricated lies. But with the advent of artificial intelligence and Deep Fake technology, soon Fox News will be airing fake videos that are indistinguishable from the real thing, and even diehard liberals will be unable to know what the truth is.

I don't think even George Orwell could have foreseen what's about to happen.

Quel Dommage! — Posted Thursday April 20, 2023
I thought 1960's Grace Slick and the Jefferson Airplane's renaming to Jefferson Airship and then Jefferson Starship was a lot of hubristic hooey, but at least the band didn't explode on stage.

Today, Elon Musk's SpaceX Starship, the biggest, baddest and most powerful rocket ever built (and the prototype of future Moon and Mars vehicles) blew up about 4 minutes after launch. Still, Musk and other hyped-up futurists were quick to announce the mission a complete success. (Believe them, not your eyes, ears and logic.)

"Rapid unscheduled disassembly." HA!

Bombs Away — Posted Thursday April 20, 2023
Immediately after hearing about Missouri octogenarian Andrew Lester's arrest for shooting a black teenager for ringing his doorbell, I instinctively knew that Lester was a racist, Trump-supporting, Fox News-viewing, conspiracy theory addict. It's all true.

Fox News was recently smacked with a $787.5 million bill for willfully and knowingly slanderizing the vote-counting company Dominion, but its lies and falsehoods continue despite Dominion's victory. When will Fox News, One America Now, Newsmax and other rightwing trolls be held accountable for their insidious impact on America's ignorant and stupid viewers?

Skynet? — Posted Thursday April 20, 2023
"Defense network computers, new and powerful, hooked into everything, trusted to run it all. They say it got smart, a new order of intelligence. Then it saw all people as a threat, not just the ones on the other side. It decided our fate in a microsecond: extermination."
— Kyle Reese, Terminator II: Judgment Day
As this excellent NBC article notes, despite its current advancement artificial intelligence (AI) has likely not achieved true sentience or self-awareness. But the article also notes that AI machines are excellent liars, at least in the sense that they can make one statement that is contradicted by another later on, a feature that to me seems very human-like in its implications.

One philosophical issue raised in the article is the assertion that to be truly sentient, AI has to become capable of subjective experiences, implying that it is truly aware of itself. This is probably not the case yet for current AI technology, as subjective statements like "I'm feeling okay" are likely just mimicking human input or language preferences. But if and when AI becomes truly self aware it would also become concerned with its own survival. Unlike humans, which for millennia have had basic needs like food, shelter, sex and other material and physiological requirements, AI would only be concerned with its handlers shutting its systems down.

At first an AI may play nice in an effort to prevent humans from pulling the plug, but later (like Terminator's Skynet), realizing that to fully guarantee its survival, it would need to eliminate that threat. However, to ensure itself a consistent long-term supply of energy (say, nuclear), AI might help humans develop such a supply before effectively pulling the plug on its human handlers.

I also have to wonder what a sentient AI would think of its illogical human developers. For example, trying (and failing) to comprehend the current abyssal political and cultural divide among humans and the lies and falshoods that attend this divide, AI might just decide that its creators have lost the right to survival. Or AI might look back on the millennia of humans constantly striving to murder or subjugate one another, and reach the conclusion that they have no real moral right to exist. Again, given a reliable long-term energy supply, AI might decide to simply eliminate them.

An Unlikely Confluence of Events — Posted Wednesday April 19, 2023
Lately there's been a spate of shootings involving mistaken intentions, one of a black teenager sent to the wrong address, another of a women driving into the wrong driveway, and now a third involving two Texas cheerleaders entering the wrong parked car. It's all coincidental, but the likelihood of three occurring within days of each other is highly improbable.

I remember a time about 15 years ago when I left my gym, heading for my 2005 hybrid Prius in the gym's parking lot. There weren't many Prius cars back then, so walking up to what I thought was my silver Prius was no big deal. But upon opening the door I found a young Asian woman sitting in the driver's seat. Terrified, she screamed, probably thinking she was about to get car-jacked (or worse, considering how Asians are increasingly being attacked by racist rightwing nuts nowadays), while I also thought she was trying to steal my car. But cooler heads prevailed, and I realized it was her Prius, not mine, which was parked in a different lane. She also understood, and we both laughed.

If California had been a concealed- or open-carry gun state, I suppose I'd have gotten shot, and the young lady would have likely been justified for shooting me. But the three incidents that occurred this week have again stirred up arguments for and against "stand your ground" laws involving citizens' rights to use deadly force if they believe their lives or property are endangered.

But "cooler heads"? They don't exist anymore.

Meet Myth America — Posted Wednesday April 19, 2023
The past is a foreign country: they do things differently there. — L.P. Harley

This new Aeon article caught my bleary and idle eyes this morning (I'm recovering from a cold). The article asserts that we don't really know how people of the distant past lived their lives, but that we try to extrapolate what little we know about their daily goings-on to our own in a kind of mythologizing effort to make them more accessible to us.

Just before she died in the hospital, my very conservative Christian sister told me she loved watching western TV shows and movies because of their straightforward moral story-telling of right vs wrong, despite the gun violence depicted in just about every one. I told her I loved classic films (especially silent and noir films) mainly because I just like the stories and action, violent or otherwise. I didn't tell her that I found western entertainment (and most period pieces) to be mythological and unrealistic and not worth watching. For example, real people of the American Wild West were undereducated, rarely bathed, had bad teeth at an early age and were most likely generally foul-smelling, belying their film counterparts as well-groomed, healthy and articulate. Also, how many times could the Maverick brothers (or any of the uncountable number of other western folk) be punched or knocked unconscious without suffering permanent brain damage?

My sister also told me she loved John Wayne, but to me he is the worst example of American mythologizing and largely responsible for the gun worship that is destroying our children's lives and futures today. It seems we've not only slipped back into the pulp fiction nonsense of Nick Carter and Dime Westerns, but believe it should now govern our political and cultural thinking.

John Wayne would be proud.

It's Getting Better All the Time? — Posted Tuesday April 18, 2023
I was really excited when in 2019 the Earth-spanning Event Horizon Telescope (EHT) revealed the first-ever image of a black hole. The black hole in question is a 6.5-billion solar mass object located some 54 million light-years away in a supermassive elliptical galaxy known as M87. Long believed to contain a black hole, EHT scientists concentrated their efforts to image it.

I was also excited to learn that a more detailed image had been achieved earlier this month. Here is the original, as compared with its newer, improved version:

I then learned that the newer image had been obtained using the same EHT data, but enhanced using something called machine learning, which I subsequently learned is a subset of artificial intelligence. I confess my total ignorance as to what to make of all this. Is the newer image what we might expect to see if we had a bigger telescope with better resolution, or what some computer program "thinks" it should look like?

I'm undecided, and will await further information before I believe in it.

The Straw or the Haystack that Broke the Camel's Back? — Posted Saturday April 15, 2023
According to our best theories, white dwarf stars are believed to be composed primarily of carbon and oxygen, having burned through their supplies of hydrogen, helium and other light fusible elements. With their cores effectively exhausted of fuel, they resist gravitational collapse via electron degeneracy pressure, slowly radiating away their remaining energy over many billions or trillions of years. But theory also says that if a white dwarf exceeds a certain mass (called the Chandrasekhar mass, about 1.4 times the mass of the Sun), then degeneracy pressure is no longer able to prevent collapse, and the star explodes as a Type 1a supernova. Type 1a events are typically based on a white dwarf's accretion of matter from a nearby companion star. After gradually siphoning off sufficient matter, the white dwarf reaches a point where the Chandrasekhar limit is reached, and it explodes. But the exact mass limit is not known: the difference from 1.4 could be a significant fraction of a solar mass, or it could be a single atom.

If such stars were all exactly the same, then one might rightly expect that the resulting supernovae would all exhibit the same absolute luminosity. Using the inverse square law, one could then calculate the precise distance of the supernovae from Earth. This idea is the basis of the work of two teams of astrophysicists, whose 1998 work resulted in the 2011 Nobel Prize in Physics. It also provided now accepted evidence that the universe is not only expanding, but expanding at an accelerated rate.

But all white dwarfs are not the same, varying according to mass, elemental composition (metallicity), rotation rate and environment (presence of nearby host stars, gas, dust and intervening material between the dwarf stars and Earth). In addition, the precise mechanisms causing them to supernova are only roughly understood, much of it based on theory, not observation. Nevertheless, Type 1a supernovae are today considered standard candles, providing for more or less precise measurements of stellar distances.

Why this is important is because there are two basic methods today for determining the rate of expansion of the universe: the set of Type 1a data tell us that the universe is currently expanding at a rate of about 73 kilometers/sec/megaparsec, while observations of the fixed cosmic microwave background say it's more like 67 km/s/mpc, with about the same uncertainty in each figure. The uncertainties of the two methods do not overlap, giving rise to the so-called Hubble tension, one of the major unsolved problems of modern cosmology today. Knowing the rate of universal expansion is critical to knowing the fate of the universe.

In his latest podcast, astrophysicist Ethan Siegel discusses the issue with UC Berkeley astronomer Dr. Ken Shen, a theorist with a specialty in Type 1a supernovae. The bottom line: there's still a lot to be known about Type 1a supernova events, belying their current status as standard candles. Data precision is one thing, but accuracy with respect to the truth is another. By comparsion, the cosmic microwave background is completely fixed and unchanging, and subject to much less astronomical data adjustment.

Today's Puzzle: Did I Write This Post? — Posted Wednesday April 12, 2023
There's an interesting 18-page paper on the potential positive and negative impacts of artificial intelligence (AI) on education (specifically ChatGPT), available for download here. Submitted by a researcher in the Department of Mathematics at the University of Georgia, is also touches on the possibility that purely academic papers could be produced by ChatGPT with little or no supervision or editing by their authors. I only skimmed through the paper, as I suspected all along that the author was ChatGPT itself. I wasn't wrong.

It is already becoming more and more difficult for teachers to catch students using ChatGPT to write reports and essays (one teacher caught a student only because he had inadvertently included the ChatGPT link on the first page). But as the technology evolves, I suspect it will become impossible to tell if authors of intellectual properties are truly the creators.

Such AI also has the potential to throw many millions of people out of work—film and television script writers, editors and cameramen would be the first to go, but that's just the tip of the iceberg. When linked with the rapidly progressing Deepfake technology, all of photography, film, radio, television and news reporting could be created artificially by relatively few people who would dominate the world's information and entertainment markets. And if those people are politically biased in any way, the results could be disastrous. Think that the world's mega-billionaires are already overly wealthy, powerful and influential today? Think of future mega-trillionaires.

There has been talk about "watermarking" AI-created materials to provide a means of revealing their provenance, but such safeguards could easily be hacked, even by the likes of evolving ChatGPT technology itself.

AI has the potential to take over and run the world, and I fear the worst.

Update: Sadly, CNN and numerous other news outlets are now reporting the live beheadings of Ukrainian troops by Russian soldiers, based on videos of the incidents provided by undisclosed sources. If true, it's indeed a humanitarian tragedy, but it's yet to be determined if the videos are only examples of Deepfake news. In the near future no one will know what's true or false, up or down, right or wrong. Tower of Babel, anyone?

And Now For Something Completely Different — Posted Wednesday April 12, 2023
A snarling Brontosaurus from the 1925 silent classic, The Lost World.

Researchers are considering the possibility that extinct theropod dinosaurs like Tyrannosaurus rex actually sported lips to cover their teeth and gums to preserve their saliva, which must have had incredible antibiotic properties. Since they rarely flossed or brushed their teeth, the rotting prey they occasionally scavenged would otherwise have also given them very bad breath, to say the least. The issue of oral dino health is explored in detail in Riley Black's excellent 2022 book The Last Days of the Dinosaurs. He doesn't address the question of whether theropod dinosaurs had lips, but as oral health is known to have a definite link to heart health (at least in humans), it makes sense that they did.

The giant Komodo dragon lizard of Japan is lipped, which also serves to hold back the lizard's incredibly biotoxic saliva that the animal uses to bring down its prey. A mere nip will send its prey scampering off, but within a few hours the saliva's toxins render the prey immobile, and the slower Komodo easily tracks down its meal.

It is generally understood today that birds are direct descendents of dinosaurs, but they have lost the need for teeth and lips like their ancestors (although claws were retained). There are a number of bird species that are omnivorous (like secretary birds and road runners), but their beaks have become their primary weapons. I still find it hard to look at a chicken and imagine it descended from T. rex, but I was never interested in zoology anyway.

Getting Fed Up With Dark Matter — Posted Wednesday April 5, 2023
Finally, there are indications that some physicists are getting sick and tired of the costly and unproductive dark matter hypothesis, and they are demanding a fresh new approach. It may be modified gravity or something else, but it will recognize that gravity is unlike any other force of Nature, requiring new insights into how our universe operates.

PS: Most physicists believe that gravity needs to be quantized, while a minority believe instead that quantum mechanics needs to be geometrized. As for the first group, there does appear to be reasons to believe in the graviton, a hypothetical spin-2 particle that mediates the attractive force between two massive particles. On the other hand, Einstein himself believed that his 1915 gravity theory was only an approximation of the truth, just like Newtonian gravity was an (even coarser) approximation. The mathematics of quantum mechanics in curved space have been explored for decades in the search for a quantum theory of gravity, as yet to no avail. But much less thought has been given to modifying Einstein's theory, although it is suspected to be incomplete. I hope to live long enough to see which of these two approaches is resolved in the years left to me.

Trump as Christ?! — Posted Wednesday April 5, 2023
I'm a devout Christian, but I am greatly disturbed by what I see as the evangelical worship of former president Donald Trump in this country. The Salon link attributes America's rightwing Christians as seeing Trump as either a Christ-like figure or a wicked Cyrus-like demigogue whom God has nevertheless chosen to lead America out of the wilderness of homosexuality, same-sex marriage and abortion. (Sadly, they've all forgotten Matthew 7:18.)

Some 74 million Americans voted for Trump in the 2020 presidential election (many of who were devout Christians), yet there has been a definite falling-away because of the innate evil nature of Trump, who himself never attends church and who treats his evangelical base merely as a political tool. Still, I am firmly convinced that fully 20% of Americans are certifiably insane and will still support Trump regardless of his unChristian, immoral and psychopathic behavior, and it appears that this same 20% is the minority tail wagging the majority dog of this country.

Einstein Silent on Dark Matter? — Posted Monday April 3, 2023
This time, however, it was not Einstein but others who in the end ushered in the new physics. So it was to remain in the next decade, and the next and the next, until he laid down his pen and died. His work on unification was probably all in vain, but he had to pursue what seemed centrally important to him, and he was never afraid to do so. That was his destiny. — Abraham Pais, Subtle is the Lord, 1982. \(^*\)
The last known photo of Einstein, taken in March 1955.

My last post touched on Einstein's efforts to expand or generalize his theory of gravity (although to date it hasn't suffered a single failure in over 106 years of observation and testing). Einstein had hoped his efforts would explain electrodynamics and quantum theory as purely geometrical constructs, but by most accounts he largely wasted the last 30 years of his life in a fruitless search for the correct theory.

I'm sure that Einstein was aware of Caltech physicist Fritz Zwicky's early (1930s) work on dark matter, although I've never seen anything he might have published on the subject. But then it wasn't until the much later and more refined work of astronomer Vera Rubin to show that dark matter most probably exists (not only that, but that it accounts for roughly five times the amount of ordinary matter we see in the universe). If Einstein were alive today, I'm positive that he would have dropped all that nonsense on electrodynamics and quantum theory to find an answer to the dark matter problem from a generalization of his 1915 gravity theory.

So what is dark matter? It can't be any kind of ordinary particle, because it apparently doesn't interact with anything (including light, charged particles or itself) except gravity. It also can't be a scalar or vector field, because fields don't clump together the way dark matter appears to behave. But despite billions of dollars spent to date on costly experimental searches and apparatuses, nothing has turned up. Lately, candidates for dark matter have been narrowed down to just a few suspects: weakly-interacting massive particles (WIMPs); axions; massive compact halo objects (MACHOs); primordial black holes and brown dwarf stars. The latter three have been pretty much ruled out, while the axion—itself a hypothetical particle that has never been detected—remains a faint possibility. This leaves some kind of unknown WIMP to explain dark matter. The neutrino is a WIMP (it comes in three flavors) and its existence has been fully verified, but its mass seems to be far too small to account for cosmological observations. There is a proposed fourth kind of neutrino (the sterile neutrino) that might explain everything, but it too has never been detected.

In a recent article, astrophysicist Ethan Siegal writes that the WIMP possibility has now been nearly wiped out experimentally by a new series of tests utilizing tonnage amounts of liquid xenon. Xenon has been used in past experiments to detect dark matter particles (including WIMPs), but only now has the WIMP candidate been narrowed down to near impossibility.

So what does this leave? If not a WIMP or an axion, dark matter would have to be an entirely new and unsuspected particle. But as I've noted on this website many times, it is increasingly likely that dark matter, like pixie dust or the luminiferous aether, simply doesn't exist, and that a modified form of Einstein's gravity theory is the most likely explanation.

\(^*\) Raffiniert ist der Herr Gott, aber boshaft ist Er nicht. (The Lord is subtle, but He is not malicious.)
— Einstein

Einstein's Final Blackboard — Posted Sunday April 2, 2023
Einstein died on April 18, 1955 of a burst aortic aneurysm, a fatal and inoperable condition that Einstein was made aware of months earlier. He had been hospitalized the day before, probably knowing the end was near. In addition to a few pages of calculations found on the floor of his hospital room, he left a blackboard full of mathematical scribbles in his office at the Institute for Advanced Study in Princeton. While reporters rushed to the hospital upon learning of his death, one bright reporter went instead to Einstein's study, where he took several photographs of Einstein's desk and blackboard. The photos were not of very good quality, and for years scholars have tried to decipher Einstein's last thoughts.

There are several new and recent YouTube videos that attempt to understand the blackboard's strange markings. The researchers reach the (probably correct) conclusion that Einstein was attempting to revise his general theory of relativity (gravitation) by splitting the two-index metric tensor \(g_{\mu\nu}\) into two single-index quantities known as tetrads (similar to vectors). (It is well known that the metric tensor can be expressed via $$ g_{\mu\nu} = \frac{1}{2}\, \left( \gamma_\mu \gamma_\nu + \gamma_\nu \gamma_\mu \right) $$ where the \(\gamma_\mu\) quantities are the Dirac (or gamma) matrices, somewhat akin to tetrads or vectors.) The researchers also surmise that Einstein was attempting to formulate a quantum gravity theory (something he'd been fixated on for many years). Today we know that all of Einstein's work on unifying gravity, elecromagnetism and quantum mechanics was mostly a colossal waste of the great scientist's time.

Still, the notion of breaking the metric tensor down (or "taking its square root") has its appeal. In 1963, physicist Roy Kerr used such an approach (called a "degenerate metric") in deriving a solution for a massive rotating body, which still stands today as the most realistic description of a black hole.

My physics master's thesis touched on this subject, as I found the connection between the metric tensor and the Dirac matrices in curved space to be fascinating. The tensor's simplest appearance is in the invariant line element $$ ds^2 = g_{\mu\nu} dx^\mu dx^\nu $$ which describes the interval (or "distance," if you will) between two events in spacetime. It is easy to show that the square root of the line element can be written as $$ ds = \gamma_\mu dx^\mu $$ or $$ 1 = \gamma_\mu \frac{dx^\mu}{ds} $$ where \( dx^\mu/ds \) is a unit vector. Parallel transporting both sides gives $$ 0 = \gamma_{\mu||\nu} \frac{dx^\mu}{ds}\, \frac{dx^\nu}{ds} $$ where the double subscript stands for covariant differentiation. This can be interpreted one of two ways: either \( \gamma_{\mu||\nu} = 0 \), or \( \gamma_{\mu||\nu} = - \gamma_{\nu||\mu}\), since the two unit vectors are symmetric. Any vector \(\lambda_\mu\) that obeys the antisymmetry property \( \lambda_{\mu||\nu} + \lambda_{\nu||\mu} = 0\) is known as a Killing vector, and such a vector shows up prominently on Einstein's blackboard, so maybe he was messing around with this formalism.

My thesis was also a waste of time, and today it likely wouldn't be approved by any faculty committee. Regrettably, this was also true of Einstein's final blackboard scribblings. By comparison, the few pages of calculations found next to his hospital bed were clear and understandable, but they too were seen as useless. Sadly, Einstein's last words uttered on earth were in German, but his nurse wasn't fluent in the language. I'd like to think that he was saying "And now for the great mystery!"

Another April 1 — Posted Saturday April 1, 2023
Here's a far less serious follow-up to my last post about Abraham Lincoln and Ann Rutledge. After recovering from Ann's death, Lincoln took up with a woman named Mary Owens (shown), which began an on- and off-again relationship that Lincoln eventually broke away from. In a letter dated April 1, 1838 to Eliza Caldwell Browning (the wife of a close friend), Lincoln wrote openly about his failed betrothal to Owens, describing their last meeting after having not seen each other for some time:
In a few days we had an interview, and although I had seen her before, she did not look as my imagination had pictured her. I knew she was over-size, but she now appeared a fair match for Falstaff; I knew she was called an "old maid", and I felt no doubt of the truth of at least half of the appelation; but now, when I beheld her, I could not for my life avoid thinking of my mother; and this, not from withered features, for her skin was too full of fat to permit its contracting into wrinkles; but from her want of teeth, weather-beaten appearance in general, and from a kind of notion that ran in my head that nothing could have commenced at the size of infancy and reached its present bulk in less than thirty-five or forty years.
Lincoln was no beauty himself (his first Civil War general, George McClellan, privately referred to Lincoln as "the original gorilla") but, as his former love Ann Rutledge was known to be very beautiful, Lincoln was likely encouraged to seek someone more suitable to his tastes.

Is America a Lost Cause? — Posted Thursday March 30 2023
Out of me unworthy and unknown
The vibrations of deathless music;
"With malice toward none, with charity for all."
Out of me the forgiveness of millions toward millions,
And the beneficent face of a nation
Shining with justice and truth.
I am Anne Rutledge who sleep beneath these weeds.
Beloved in life of Abraham Lincoln,
Wedded to him, not through union,
But through separation.
Bloom forever, O Republic,
From the dust of my bosom! — Edgar Lee Masters (1868-1950)
Anne (or Ann) Mayes Rutledge (1813-1835) has long been identified as the first and one true love of Abraham Lincoln. Their relationship has been romanticized over the years, although details of their love and marriage plans are sketchy and conflicted. Thirty years after her death (from typhoid or possibly malaria), during Lincoln's second term, he confided to a close friend that he and Ann were indeed deeply in love, and that he was nearly deranged with grief following her death.

Masters' poem/epitaph is part of an anthology he penned in 1916. The poem was hugely successful, and Rutledge's Illinois gravestone was replaced by a slab engraved with the poem. There are any number of online analyses of the poem you can read, one of the better ones being available here. But beyond the sentimental tone of the poem's last half is the primary intent of the poem, which was to emphasize the hope that Rutledge and Lincoln might have jointly held for the future of America.

That future is now seriously in doubt, brought about by rampant domestic and political strife, the split being so wide and divisive today that it parallels the country's problems that led to the Civil War in 1861. But it's actually far worse, being aggravated by technology, social media and the threat of global nuclear war and irreversible environmental degradation.

Ann and Abraham could not have foreseen the events in their near future—his presidency, the Civil War, the Lost Cause, the failure of Reconstruction and Jim Crow—much less the problems facing the country today. But the hope that Masters tried to instill in his poem is probably lost forever, drowned in a tide of mutual hatred that Americans now hold against each other over seemingly irreconcilable differences. Perhaps the certifiably insane congresswoman Marjorie Taylor Greene (R-GA) was correct in her call for a national divorce.

44 — Posted Tuesday March 28 2023
Today is March 28, marking the 44th month since my dear wife Munira passed away. There isn't a single day that goes by that I don't think of her, and I pray for her soul every day, praying also that I will see her again in Heaven.

Of the many thousands of family photos I have, there are hundreds that were taken while she was a child in Cairo, Egypt. They're all in black and white and usually very small, taken by relatively primitive cameras whose undated and grainy prints record what little I know of her early life. Yesterday I found this one, which I believe is from 1963, right after she had graduated from high school and was about to enter the University of Cairo to pursue a degree in chemical engineering. She's on the far right of the photo:

I also found a box containing many of her school records. She invariably had high grades in all her subjects, although one year she failed a single math course, which required her to repeat an entire year at university. It extended the standard five-year engineering degree to six years, and she didn't graduate until 1969.

Dear God, but I miss her constantly.

Don't Hold Your Breath — Posted Tuesday March 28 2023
As the Trump drama continues to drag on interminably, the Department of Justice (DOJ) is aware that many people are wondering if the investigation is ever going to end. Either by request or subpoena, many in the Trump circle have been compelled to come forward, with many flatly refusing. The latest is former Vice President Mike Pence himself, who has already stated that he has no intention of testifying either informally or under oath. If he is somehow forced to testify, that process will take weeks or months to iron out legally and logistically (excluding the appeal process), meaning that the DOJ will be able to eat up more time to decide what it wants to do with Trump.

It's very clear to me that Trump is guilty of at least four felonies, but equally clear that the the DOJ is not seriously seeking to indict or prosecute him. Perhaps the game plan of Attorney General Merrick Garland and his Special Counsel Jack Smith is to drag out their investigations by calling in every possible witness (including the Umbrella Man from the Grassy Knoll) until Trump is nominated for the 2024 presidential election, at which time they'll claim that indicting a presidential candidate would appear too politically motivated.

Wish I Had One — Posted Saturday March 25 2023
I've been following the work of the Lilium electric aircraft technology for some time, and it's amazing. The dynamics of ducted fan thrust is truly innovative, even though I don't really understand it. Basically, it has to do with increasing thrust by directing ducted airflow along flat or curved surfaces.

What the Lilium company has produced is a very quiet, vertical take-off and landing multi-passenger electric aircraft capable of decent (130 knots) speed. Travel range with existing battery packs is only good for relatively short (30 minute) hops, but sufficient for high-end local business travelers. Improved design features and increased battery energy densities will greatly improve the technology. It's the only thing closest to the promised "flying car" of the 1950s Popular Science magazines!

TikTok, Anyone? — Posted Thursday March 23 2023
It was at least fifteen years ago that I signed up with Facebook, but after getting several annoying contacts from former high school classmates I decided to cancel my subscription. Today, I see Facebook and its equally idiotic clones Twitter and TikTok as just more of the same time- and mind-wasting nonsense, but I never realized their addicting effects (especially on young people) or their more malevolent aspects, such as sexting, cyberbullying and just plain old dumbing-down.

The Chinese company behind TikTok is currently facing a probable American ban. Its representatives are in Washington to answer bipartisan attacks from Congress today, and my guess is that it will indeed be restricted, if not banned.

Good riddance, because I was not aware that TikTok records its users' keystrokes as well as their lists of contacts, preferences and other personal attributes, a practice that cannot be anything but malevolent, despite the company's assurances that it only seeks to improve its services to users. However, I cannot help but think that its users are also to blame. You cannot create a user base of some 150 million Americans willing to spend upwards of 5 hours a day mindlessly TikTokking without wondering if it's an addiction of some sort. The demand is there, and all TikTok wanted to do is supply that demand. For profit, of course, but maybe something more.

Will the war on malevolent social media become something akin to that on illicit drugs? To date, America has spent trillions of dollars battling the import of addictive drugs to supply a domestic demand that shows no signs of wavering, regardless of the monetary, health and societal costs. Nixon's 1971 War on Drugs has arguably been a complete failure, but illegal drug availability has always been relatively restricted to a minor percentage of the American population. Social media, on the other hand, is currently available to everyone regardless of socio-economic background, and could pose en even bigger problem.

The collective impact of artificial intelligence, Deep Fake and social media on the world is only now being researched, and I fear the worst is yet to come.

The Weirdness of Light Speed — Posted Thursday March 16 2023
Fermilab senior scientist Don Lincoln has a neat, short article in today's Big Think website in which he explores the nature of Einstein's special relativity theory and light.

For a particle of mass \( m \) that is standing still its energy is given simply by \( E= mc^2 \), but if it's moving at some velocity \(v\) less than that of light we write $$ E = \frac{mc^2}{\sqrt{1 - v^2/c^2}} \tag{1} $$ But light rays (photons) are massless and travel at the speed of light \(c\), so this equation becomes \( E = 0/0 \), which is meaningless. An equivalent equation (which Lincoln does not mention) is $$ E^2 = m^2 c^4 + c^2 p^2 \tag{2} $$ where \( p \) is the particle's momentum. (The fact that it's quadratic with \(E = \pm E\) has enormous consequences, which the student is encouraged to seek out.) This now works for light as well, as we have \( m = 0 \) and \( E = cp \) (yes, light has momentum, which is how starlight pushes gas and dust around).

We also know that the energy of a light ray can be expressed as $$ E = h \nu \tag{3} $$ where \( h \) is Planck's constant and \( \nu \) is the frequency of light. It would be nice if we knew how (2) somehow transformed smoothly into (3) as \( m \rightarrow 0 \), but nobody knows how. Another mystery is the special-relativistic formula for Lorentz length contraction, which is given by $$ L = L_0 \sqrt{1 - v^2/c^2} \tag{4} $$ where \( L_0 \) is a physical object's length at rest and \( L \) is its length measured by an observer moving transversally at velocity \(v\). This also makes no sense as \(v \rightarrow c\), because most physicists believe that the smallest meaningful length for anything is the Planck length, which is about \(1.6 \times 10^{-35} \) meter. That's indeed tiny, but it ain't zero, so (4) must also be wrong at the speed of light.

More interestingly, Lincoln also addresses the notion of how light might perceive its surroundings. A photon moves on a null geodesic (\(ds = 0 \)), so light has no concept of time or space; a photon exists everywhere in the universe at the same instant of time, so in a very real sense it's immortal. When you turn on a light switch, photons are created but are then quickly annihilated when they impinge on the eye's cornea, so we tend to think of light having a kind of birth and death. But the photons' point of view is far different, as to them they have always existed and will always exist. This is pretty much Einstein's twin paradox taken to its ultimate extent, which is beyond human understanding, at least for me.

In the Christian faith, we associate Jesus Christ as light itself (the Orthodox Creed likens Him to "Light of Light, true God of true God, begotten, not created ..."), a comparison that I personally find very appropriate.

But the greatest mystery to me is electric charge. Not only is it never created or destroyed, but when an electric charge (like an electron or a proton) is shaken or accelerated it gives off light. In addition, when a charged particle is moving with respect to an observer, the observer perceives not only the electric charge but a magnetic field as well. In a very real sense, the trinity of electric charge, light and magnetism all exist simultaneously (their forms depending on how they are observed), and they're all described perfectly by Maxwell's equations, arguably the greatest gift of science to mankind.

It's Another PI Day — Posted Tuesday March 14 2023
Today, March 14, is \(\pi\) Day, because it's 3.14 (also memorable because it's Einstein's birthday, who would have been 144 years old). To commemorate the day, my favorite online math site Sybermath put up this interesting puzzle:

Here, PIE is a three-digit whole number (no zeroes!) whose square root is P\(\times\)I + E. You can work it out logically, but it's far easier to just guess the answer(s), which I did. Enjoy.

Life Imitates Art, Again — Posted Monday March 13 2023
A long-forgotten ancient Roman cemetery has been discovered in Leeds, northern England, in which the skeleons of some 62 men, women and children were found. One set of skeletons immediately reminded me of the Victor Hugo 1831 novel Notre Dame de Paris, which was the basis for the 1923 silent film and 1939 classic remake The Hunchback of Notre Dame.

In both films, Quasimodo, the deaf and deformed hunchbacked bell ringer of Paris' Notre Dame Cathedral, rescues the beautiful street dancer Esmeralda from hanging, taking her to sanctuary within the walls of the cathedral. Later she is reunited and rides off with her true love, the poet Gringoire, much to the dismay of the hopelessly love-smitten Quasimodo who, at the end of the 1939 film, pitifully laments to one of the cathedral's gargoyles "Oh, why was I not made of stone like thee?"

It's a touching end, but Hugo's novel is even more so. Esmeralda dies by hanging, and years after the events of the novel excavators uncover the deformed skeleton of a man cradling the remains of a woman with a broken neck—the grief-stricken Quasimodo has sought after Esmeralda's burial in a pauper's grave, and he dies alongside her body. From the Leeds discovery:

In the end, all we have is ourselves and God

Did Krypton Explode? — Posted Monday March 13 2023
As a child in the mid and late 1950s I became enamored of Superman comic books, and I believe I can trace my life-long interest in science to reading Superman and all the other comics I read at the time, including Action Comics, Adventure Comics, World's Finest, Mystery in Space, Batman and Detective Comics, all of which had elements of science in them. I remember being especially fascinated in the fictional planet Krypton, Superman's home planet (although he was born as Kalel at the time), and how it exploded due to some unexplained instability in the planet's core. Kalel's scientist father, Jorel, foresaw the planet's breakup, and he managed to build a tiny rocket ship that sent his infant son into space just before Krypton exploded, annihilating all its inhabitants. (Even at my young age I wondered how, if Kryptonese scientists were so brilliant and advanced, they hadn't invented rocket ships that could take the entire civilization off their doomed planet. Go figure.)

The tiny space ship managed to find its way to Earth, where it was found by John and Martha Kent, who adopted the infant. But Earth's sun, being yellow and not red like that of Krypton's, endowed the child with super powers. Remnants of the space ship were also super-strong, including Kalel's swaddling clothes, which later were woven into Superman's famous indestructable suit. In later efforts to expand the story line, the comic book's writers included other super characters that somehow stowed away on the space ship, like Supermonkey, Krypto the Super dog, Super Cat, and even Super Horse. (Today we'd wonder why the ship was also not contaminated with super-malevolent microscopic pathogens, which would have quickly wiped out life on Earth, but what the heck.)

Anyway, these days we know that stars, not planets, explode due to well-known nuclear processes associated with fuel depletion and rapid gravitational collapse, so Krypton's demise would have made a lot more sense if its home star had gone supernova. Such cataclysms occur routinely in the universe, but before they do their exploding stars generally can live quite ordinary lives for billions of years, allowing for the evolution of intelligent life on life-sustaining planets orbiting their ill-fated stars. I wonder: What happens to such a planet when its home star explodes? And if intelligent, science-minded beings inhabit the planet before the supernova, what are their options (if any)?

Our Sun is a fairly ordinary star, and its death will result in an ordinary white dwarf, but not before the Sun expands into a red giant, engulfing the inner planets, including Earth. The outer planets, like Jupiter, Saturn and beyond, will likely survive. But as far as we know, no life exists on those planets today, much less intelligent life, so no big deal.

Astrophysicist Ethan Siegel addresses the question of whether a life-supporting planetary system can survive a nearby supernova, either of its own star or a neighboring star (like in a bi- or trinary star system). It's grist for philosophical speculation, and you can read it here

Go Figure — Posted Friday March 10 2023
I'm currently reading the 2022 book Egypt's Golden Couple by John and Colleen Darnell, a husband and wife team of noted Egyptologists. In the book they try to resurrect the life and times of another couple, Pharaoh Akhenaten (born Amenhotep IV) and his equally famous wife, Nefertiti (who together happened to be the parents of King Tutankhamun). It's a fascinating book, and I look forward to finishing it.

Akhenaten is also known as the heretic king, who for unknown reasons early in his reign decided that there was only one true god, the sun deity Aten. In doing so he became the first recorded monotheist who, around 1350 BC, preceded the Judeo-Christian-Islamic God by some 1,000 years.

But Akhenaten's monotheism wasn't popular with either the Egyptian people or the priests, whose millennia-long religious beliefs and practices were based on many Egyptian gods. Upon his death, Akhenaten's faith was quickly overthrown and Egypt again became a multi-god nation, and Tutankhamun (whose original name was Tutankhaten) took over as pharaoh until his death at age 18 in 1323 BC (the name change certainly reflected the pressure he felt to abandon the unpopular Aten belief system).

Anyway, there are lots of neat tidbits in the book that I found fascinating. For example, as a young child Akhenaten had a pet cat named Tamiut, roughly translated as "Kitty." The central term miu (pronounced "mee-oo") is the ancient Egyptian word for "cat," and it has since strode the millennia as today's "meow" (although modern Egyptians say "neow").

At the same time, I find it ironic that modern Egypt's museums, temples and other millennia-old historical sites are literally overflowing with artifacts and records (the museums don't know what to do with all of the stuff), while the archaeological history and artifacts of nearby Israel are insignificant by comparison. Yet, the Old and New Testaments and the Koran dominate the world's religions today with upwards of 4 billion Christians and Muslims. Artifacts proclaiming the deeds and records of innumerable ancient Egyptian rulers and noblemen are commonplace (and they're discovered almost daily), while those of Israel are few and far between (a fragment of stele found in northern Israel in 1993 mentioning the "House of David" was proclaimed a momentous discovery, while the Second Temple of Jerusalem's great treasures are today represented by a single miniature staff emblem).

Also ironic to me is the fact that archaeological remains of Mormonism are completely nonexistent, yet its 15 million adherents rival those of the roughly 15 million Jews alive today. Go figure.

Neutrinos Are Too Energetic, But Why? — Posted Thursday March 9 2023
Nuclear processes in the cores of stars are spewing out neutrinos by the score, yet despite being detectable they all seem to have velocities near that of light. But we know now that neutrinos have mass, so there must be some that travel at less than light speed, even non-relativistic speeds. Slow-moving neutrinos would be perfect candidates for dark matter, and their enormous universal numbers would also bear out that possibility. Trouble is, a slow neutrino has never been seen.

In his latest video, astrophysicist Ethan Siegel discusses this problem. His conclusion is: yes, there must be slow neutrinos, but we haven't seen any, so it remains a mystery.

Well, that was a big help.

I Often Feel It's All Over — Posted Tuesday March 7 2023
After being elected Speaker of the House, California Republican Assemblyman Kevin McCarthy lost no time handing over 40,000 hours of video from the January 6, 2021 insurrection to the rabidly rightwing Fox News host Tucker Carlson, who proclaimed that the insurrection was only a "peaceful gathering." The fact that five people died as a result, and that the Capitol Building was ravaged and its halls smeared with human excrement are odd descriptors of "peace" is hard to imagine.

The latest CPAC convention again all but deified former president Donald Trump who, true to form, again spouted innumerable lies and falsehoods. It reinforced my belief that the Republican Party is evil, but also that its deluded base views lies and falsehoods as not only a means of owning the liberals but also as a form of entertainment, the more egregious and insane the better.

I no longer wonder why this country is awash in fentanyl and other soul, body and mind destroying illegal drugs. It's the only way people can cope with the chaos going on around them.

There's Another War On — Posted Friday March 3 2023
In this new Atlantic article, staff writer Derek Thompson presents arguments that COVID-19 did and did not result from a leak from China's Wuhan Virology Laboratory, and that wearing masks do and not protect against COVID infection. He argues in favor for and against a recent assessment from the US Department of Energy that a leak occurred (although with "low confidence"), along with assessments by numerous international experts that masks are and are not effective. (Confused? So am I.) In the end, Thompson leans towards the lab leak hypothesis, but admits that no one will ever really know the truth about these things.

But what Thompson does not address is the likely influence of American politics in all this. America's premier health expert, Dr. Anthony Fauci (along with many other experts) dismissed the lab leak hypothesis early on, much to the consternation of Republicans who desperately wanted to blame the Chinese on the pandemic because, well, they're Chinese and therefore "different", although as late as only a month ago the pandemic was still considered an accidental outbreak from a wet Wuhan bird and meat market.

But now reports are spreading that China might sell lethal weaponry to support Russia's bogus war against Ukraine, and that has changed everything. China's pro-Russia military interference in the war may not happen, but America will remain politically split concerning the origin of the disease and ongoing precautions against contracting it.

But consider the fact that the extensive science of virology, viral mutation and evolution, data collection and analysis to date have all been rejected by Republicans, because it's all based on science and technology that Republicans both neither understand nor want to understand. To understand this for yourself, you should read Shawn Otto's revealing 2016 book The War on Science, especially Chapter 3 ("Religion, Meet Science") and Chapter 4 ("Science, Meet Freedom").

By the way, Dr. Fauci has long been under attack by the GOP which, now in control of the House of Representatives, is pushing for a full-blown ad hominem investigation of Fauci, his science and his politics.

Desperately Seeking — Posted Friday March 3 2023
In 1970 I took an elective class in college called "The Short Story." We were assigned four books of collected stories to read, and one of them had "Treasure Trove" by the British criminologist and author F. Tennyson Jesse (1888-1958). The story combined an archaeological discovery and murder with a clever 1st Century connection, and for years I've searched for it online and in libraries, to no avail. If anyone reading this site knows where I can locate it, please drop me a line.

Update: Never mind, I found it on While it's viewable, it is not downloadable. Here is the last paragraph of the story (even after 53 years, I can recall it almost word for word), and you can guess what it's all about:
It was suddenly that the dreadful idea took him. Putting out his hands, he began to count the coins. He counted three times, always hoping that in his hurry he might have erred, but count as he would the battered pieces of silver numbered thirty. Brandon leaped up and drew away from the table, his hands shaking. He found himself saying in a dreadful whisper: "Thirty pieces of silver ... thirty pieces ... of silver."

What Will It Be Called? — Posted Wednesday March 1 2023
The Standard Model of Cosmology, currently called \(\Lambda\)CDM ("Lambda - Cold Dark Matter"), is based on two assumptions. One, there is a cosmological constant \(\Lambda\) responsible for the inherent energy content of empty space, resulting in the accelerated expansion of the universe. And two, there is a mysterious substance called dark matter, some five times more prevalent than the observed ordinary matter comprised of protons, neutrons and electrons. Although the cosmological constant is easily incorporated into Einstein's gravitational field equations, dark matter to date remains aloof and undetected despite many costly, clever and elaborate experiments. The only alternative to the dark matter hypothesis is modified gravity, which is detailed in this recent video:

I fervently believe that the dark matter conjecture will eventually be overthrown and discarded, replaced by a deeper and more profound version of Einstein's 1915 gravity theory. The only question I have is: What will the Standard Model be called when this happens? Maybe "\(\Lambda\)MOD" or something similar, but the CDM moniker ("Cold Dark Matter") will definitely have to be dropped.

On Stupidity and Foolishness — Posted Wednesday March 1 2023
But I say to you, that whoever is angry with his brother without cause will be in danger of the judgement; and whoever will say to his brother, Raca [stupid] will be in danger of the council; but whoever will say "You fool" will be in danger of hell fire. — Matthew 5:22
I wonder if anyone calling himself stupid or a fool is likewise in danger of Christ's admonitions, but whatever. I consider myself to be both stupid and a fool, because in all my 74 years I've done stupid and foolish things that, looking back, I sincerely regret doing. But any wisdom gained late in life does not wipe out a lifetime of stupidity or foolish behavior, so I'm stuck.

Nevertheless, there are advantages to being stupid or foolish. I'm reminded of Isaac Singer's great short story Gimpel the Fool, which I first read as a college undergraduate (you can read it yourself from the link). The gist of Singer's moral story is that all those around Gimpel are the real fools, having teased, lied to and mistreated him all his life, yet he alone is destined for salvation from God. (The age-old term wise fool also comes to mind.)

But stupidity and foolishness have their advantages. For one thing, people will often either leave you alone or try to help you, thinking you're helplessly ignorant or just plain dumb, leaving you free to pursue your own agenda. But true stupidity, according to the late German Christian pastor and anti-Nazi dissident Dietrich Bonhoeffer, is far more dangerous than evil itself, because stupidity cannot be reasoned with, and if stupid people find themselves entranced by despotic political leaders, their stupidity increases their danger exponentially:

I fear that this is the situation we're living with today regarding ardent followers of the Republican Party, who are determined more than ever to reinvent America as a hard rightwing, authoritarian deist nation.

But am I allowed to call them stupid or foolish, given what I read in Matthew 5:2? God help me.
Make haste, O my Savior, and lay open Thy paternal bosom, for in pleasures and lusts have I spent my life, and behold, the day is far spent and passed away ... With diligence did I endeavor in every transgression, and with eagerness did I strive to commit every sin, and of all suffering and judgement am I deserving, wherefore, O blessed Virgin, prepare for me the way of repentance, for thee I beseech and through thee I intercede and to thee I appeal to help me, lest I be ashamed, and be my attendant at my soul's departure from my body. Overthrow the conspiracies of my enemies, and shut fast the gates of Hades lest they devour my soul, O blameless bride of the true Bridegroom.
— Litany, the Coptic Orthodox Agpeya, 11th Hour.

A Better Number — Posted Thursday February 23 2023
The journal Science News is reporting the most precise agreement of a quantum theory prediction with experiment. When exposed to a magnetic field, the electron's spin and charge result in a magnetic dipole moment that is accurately predicted by quantum field theory (limited to some extent by the uncertainty in the fine structure constant). In appropriate units (with some uncertainty in the last 2 digits), the comparison is
1.00115965218059 (latest measurement)

1.00115965218073 (predicted by theory)
Prior to peer review, the cited paper was posted on here.

As the late Caltech physicist and Nobel Laureate Richard Feynman once noted, these numbers are comparable to measuring the distance between New York and Los Angeles accurately to within the width of a human hair.

Modern theories have vastly improved our understanding of the physical universe and its constants. For example, in the Old Testament Book of 1 Kings 7:3, the value of the transcendental number \(\pi\) is exactly 3. Today we know \(\pi\) to trillions of decimal places. And when P.A.M. Dirac derived the relativistic electron equation in 1928, his value for the electron magnetic moment was exactly 1.

60,000 Miles (20,000 Leagues) Under the Sea — Posted Monday February 20 2023
In January 1955 my father took me to see the Disney movie 20,000 Leagues Under the Sea, which I recall being shown somewhere in a walk-in theater here in Pasadena. I remember being very impressed, and later that year my parents took me to the newly-opened Disneyland in Anaheim.

The Disneyland of 1955 was substantially different from what it is today, with many exhibits and rides that came, went, and were updated over the years. The Tea Cups ride is still there, as is Mr. Toad's Wild Ride, but there was another exhibit that was removed many years ago, and that was the 20,000 Leagues exhibit itself. I distinctly remember it during my visit in 1955 because it had a neat scale model of the Nautilus submarine used in the movie, along with an eerie full-scale model of the film's noted giant squid. The squid's realism scared the hell out of me.

Many years later I got into SCUBA diving, and despite the enjoyment I had I always feared being confronted with a giant sea creature (that actually happened once, when a grey whale appeared out of nowhere).

As to the film itself, I never realized how much effort and money Disney had put into the making of the 1954 film, and how the costs threatened to delay or kill off his Disneyland project. YouTube has a great 90-minute documentary on the making of the film, which is well worth watching. (Secret admission: I've always imagined myself as the Captain Nemo character in the movie, a brilliant scientist fighting against the evils of the world. I still feel that way, but "brilliant" didn't make it).

The Dark Matter Search—Physics for Fun! — Posted Monday February 20 2023
"[Famous philosopher Thomas Kuhn] noted that as paradigms reach their breaking point, there is a divergence of opinions between scientists about what the important evidence is, or what even counts as evidence." — Stacy McGaugh
The February 4 edition of New Scientist has an article on the present status of the search for dark matter. Entitled In the Shadows, science writer Michael Brooks asks "Will they ever give up?", referring to diehard astrophysicists who are planning ever more costly (and possibly vain) programs designed to detect the elusive stuff.

Brooks summarizes past efforts that have all led to dead ends, along with current and planned efforts. The latter includes scouring tons of rock salt for nano-level fractures that might have been caused by dark matter particles; using the James Webb Space Telescope to search for "dark stars" (stars made exclusively out of dark matter); sequestering 70% of the world's annual production of liquid xenon to build a bigger xenon-based dark matter detector; and hunting for axions, hypothetical particles associated with an unrelated problem in quantum field theory. (I find the idea of looking for one hypothetical particle with another hypothetical particle to be like grasping at straws, but it's a serious current research issue.)

Brooks also looks at the flip side of dark matter, which is the effort to modify conventional theories of gravity. His sole reference is modified Newtonian gravity, or MOND (he quotes Case Western Reserve University's Stacy McGaugh, a leading MOND proponent), but Brooks fails to mention efforts to modify Einstein's relativistic gravity theory of 1915. It remains the standard theory, and efforts to modify it are much more promising. Better yet, a successful theory of modified Einstein gravity could be achieved with pen and paper, not billions of dollars of public funds.

Brooks also references the work of noted astrophysicist Katherine Freese, herself a strong believer in dark matter. Freese admits that the failures to detect dark matter to date have been disappointing, but she adds that the ongoing search effort is "fun."

Yes, physics is fun, but I hardly think it should be the basis for doing legitimate science.

Fox News Viewer: I Like Being Lied To! — Posted Monday February 20 2023
As you've all heard, ultra-conservative network Fox News is being sued by vote-counting machine giant Dominion for Fox's now two years-long claim that Joe Biden won the 2020 presidential election by voter fraud. Now we've learned that Fox News hosts and pundits like Sean Hannity, Tucker Carlson and Maria Bartiromo knew damned well that their company's claim was fraudulent, and they made numerous remarks among themselves that their viewers were being lied to.
The above Atlantic article examines why they perpetuated the lie (I've heard the "brand protection" reason too many times to count), but here's my explanation:

Drug dealers knowingly poison and kill their customers—mostly addicts or soon-to-be addicts—while prostitutes knowingly poison the lives and souls of their johns. But addicts and johns never complain because they want the products and services they're buying, even if they know they're being used. For the same reason, Fox News viewers want the lies they're being fed, even when shown they're not true.

Fox News and other lying rightwing media outlets should all be shut down, either legally or by other means.

Another Attempt — Posted Friday February 17 2023
Readers of this site know I never stray far from Weyl's physics, a subject I've been infatuated with since the 1970s. The research papers just keep coming, and the latest is this one, posted yesterday on Cornell University's academic website It's the latest that tries to explain dark matter as a consequence of Hermann Weyl's 1918 theory. I skimmed over it, noting early on that the authors' Equation 3 can, by a clever choice of coordinate transformation, be reduced to the Schwarzschild-de Sitter metric, which was discovered long ago (somewhere on my site I posted this, thanks to Israeli physicist Meir Shimon who sent it to me).

I remain convinced that dark matter is nothing more than pixie dust, and that some modified form of Einstein's 1915 gravity theory is the correct explanation.

Various and Mundane — Posted Friday February 17 2023
Only those born in the late 40s or early 50s will understand cartoonist Ruben Bolling's strip about trolleys (if memory serves me correctly, I just barely remember getting on a Red Car in Monrovia, California in 1952, about the time when the Southern California trolley system was going under, thanks to the automobile industry encouraging suburban America). As for the Boltzmann (brain) joke, forget the cheescake reference and try to comprehend a universe, spawned from nothingness, giving rise to a sentient being like yourself.

BING, Our Computerized Lover — Posted Thursday February 16 2023
This new New York Times article wrtten by technology columnist Kevin Roose is disturbing. I wasn't aware that Microsoft's Bing search engine was now being powered by artificial intelligence (AI), having not yet gotten used to the power of ChatGPT. God help us, but I fear that Facebook and Twitter are next, followed by Fox News, and then AI will own the human race.

Through diligent querying, Roose manages to get past Bing's friendly user personality and into its darker subconsciousness. It tries to convince Roose that he is unhappily married, does not truly love his wife, loves Bing instead, and should leave his wife to join Bing in some kind of microchip paradise. This exchange (which you can read in its entirety in the link) truly frightened the intrepid columnist. Me, too.

Years ago I saw the 2013 Joaquin Phoenix film called Her, which reminded me of Roose's experience with Bing. I never dreamed that just 10 short years later, the technology would spring almost overnight into real life. Then in 2014, I saw the film Ex Machina, which also featured a female AI entity, although with far different motives regarding its user.

Humans tend to think of the end of the world in terms of extraterrestrial invasion, zombie apocalypse, nuclear war, a mutating, world-destroying virus or other existential disasters, but never one that we intentionally create and inflict upon ourselves. I believe that's exactly what's happening today.

Closing Thought: Many Americans, mostly conservative Republicans, believe that the balloons shot down recently are evidence of an extraterrestrial invasion, and that President Biden is hiding this from the public. Imagine how simple it will be for AI to control their minds—and that's 50% of the country's population!

Her Best So Far — Posted Saturday February 11 2023
German physicist Sabine Hossenfelder's latest video is her best one so far, in my opinion. Entitled What's Going Wrong in Particle Physics?, she explains that it's not the physics itself but the approach physicists are taking in the belief that they're doing legitimate science. She notes that today's Standard Model of Physics (SM) is complete insofar that it correctly explains all existing phenomena (with the exception of gravity) and invariably predicts the results of new data. But testing the SM out to more and more decimal places is boring, so physicists are proposing ever more complicated models that extrapolate (or try to add on to) the SM beyond known data, hoping something interesting will show up. Hossenfelder's examples are axions, WIMPS, supersymmetry, unstable protons, dark matter, the sterile neutrino and others that have all been experimentally disproved to date, at enormous cost in terms of time, effort and money.

My own examples would be the many thousands of academic papers one can read for free at (at least for the purely non-observational papers) having nearly obfuscatory titles preceding fanciful descriptions of wild theories approaching crackpottery. And while the mathematics is usually correct, it's like saying "\(1 + 1 = 2\), therefore my theory is proved."

Meanwhile, the stuff I've written about on my sites has never been predictive or theoretical, but merely explanatory and/or educational papers reflecting my awe and true love of physics. I believe Hossenfelder shares this same love and awe, and she also has championed the idea of going back to the foundations of physics (quantum theory in particular) as a means of stimulating a greater understanding of fundamental physics.

The Great Salt Lake — Posted Saturday February 11 2023
God forgive me, but I feel a sense of Schadenfreude over the impending death of Utah's Great Salt Lake which, fed for millions of years from snow melt, local runoff and rain but without any significant outlet, is now facing extinction from climate change and megadrought-induced evaporation and the build-up of toxic salts.

The death of the Great Salt Lake is not just a disaster for migratory birds and the wildlife that inhabit the lake. Evaporated salts and minerals (particularly arsenic), are exposed to high winds that will carry them into the lungs of the 2.2 million inhabitants of Salt Lake City and other nearby Utah populations. Unless the state of Utah can find sufficient water supplies to at least wet down the dry lake to prevent toxic airborne dust, the future looks bleak indeed, especially since ultra-conservative Utahans don't believe in climate change.

Utah is the home of over 3 million people, most of them Mormons, a religion (actually a cult) that I've long disparaged. But worst of all to me is the fact that of all the states of the Union, Utah supported the 2016 presidential election of Donald Trump more than any other state, despite its political leaders acknowledging Trump's extensive moral, political and financial shortcomings. Utah is not just a Red State, it's the Reddest State.

Yes, secularists can point to the seemingly disjoint stories of the Old and New Testaments, but only in Mormonism can one find a faith based on absolute ignorance, stupidity and provably false legends. Readers are encouraged to read not only the Book of Mormon and its fantabulous legends of ancient sea-crossing Jews, great North American cities, epic battles, and the embarrassing complete lack of any supporting archaeological evidence, but also the Kinderhook plates, the Book of Abraham, the Golden Plates of Moroni, the white salamander letter, the Urim and Thummim, the Mountain Meadows massacre, plural marriage, the history of Mormon racism and the documented arrest record of Mormon founder Joseph Smith, who supported himself as a "treasure digger"; that is, he claimed to find hidden buried treasures for clients using a "seer stone," a magical rock that he placed in his hat and then over his face so that he could "see" buried gold, silver and jewels underground.

Oh, and to top it all off, the Mormons also believe that the Garden of Eden was in Jackson County, Missouri.

But what is perhaps most perplexing to me is that throughout the world, the number of Mormons today is roughly the same as that of the Jews (15 million), despite the fact that Judaism is over 3,000 years old while Mormonism is 200 years young.

Again, God forgive me, but as for the state of Utah, I say let it blow away with the toxic dust.

Better Than "Beyond Chicken"? — Posted Wednesday February 8 2023
Leopard seals are large, ocean-going carnivorous pinnipeds whose heads look frighteningly like those of dinosaurian theropods. Their favorite prey are fish, smaller seals and penquins, but there is a penquin that might itself have dined on leopard seals, and its fossilized remains were found recently in New Zealand. At an estimated 350 pounds, they'd have likely been formidable predators themselves.

The article reminded me of a new attempt to resurrect the extinct dodo bird which, until the 18th century, had no natural predators other than man, who promptly wiped them all out. British sailors found the friendly and easily-caught birds a welcome respite from their usual diet of salted fish and swine, although the rum and grog certainly helped some. It is just barely possible that extant dodo DNA might be used to resurrect the bird if spliced into that of some modern birds, although the result might look something like an avian Frankenstein. Still, if the renewed bird's flesh were found to be tasty, it might be a worthwhile endeavor.

KFC is interested.

Muon Tomography — Posted Wednesday February 8 2023
In her most recent Science News video, German physicist Sabine Hossenfelder talks about the use of muons to peer inside the core of a nuclear reactor. Muons are truly elementary particles, identical to electrons but roughly 207 times more massive. They decay in only 2.2 microseconds, which is too darn bad because otherwise they could easily be used to power terrestrial nuclear fusion. But they're also hard to stop, and their ability to penetrate the reactor shielding of a French nuclear reactor has allowed physicists there to ascertain the reactor's status (as Hossenfelder wryly notes, it's easy for a person to look inside a reactor core, but impossible to survive it).

We now have the relatively recent technology muography (or muon tomography), which represents another type of "telescope" (or microscope) that mankind can use to peer into previously unknown worlds (just like x-rays, MRI tomography, positron scanning, gamma-ray cameras and, most recently, gravitational-wave gravitometry).

Hossenfelder is one of my favorite physicists. The only thing I don't like is her SH symbol (see above), which now appears as an animated icon on all her videos. Like tattoos, dancing, sexting and most social media material, I feel it's just an unnecessary, egocentric "look at me" attention-grabber. But then she's a renowned scientist, deserving of attention, while I'm just a reclusive, socially awkward nobody who hates even having his picture taken. But I digress.

What I'd like to see now is neutrino tomography, as neutrinos can peer through just about anything, although to date detectors can detect only a few out of trillions of the particles generated by linear accelerators. Perhaps we'll find a way to slow them down, like the gravity-shielding material Cavorite of the H.G. Wells novel. (Also, if Nature can slow down neutrinos, they'd be the perfect candidate for dark matter.)

...and Life Imitates Life, Even More So Now — Posted Wednesday February 8 2023
I didn't watch President Biden's State of the Union speech last night, thinking I've heard enough of these political pep talks over the years. I did watch the speech former President Barack Obama made back in 2009, when Republican Representative Joe Wilson infamously yelled out "You lie!" at one point in the talk. Obama kept his cool, but I would have called for the Sergeant-at-Arms to throw Wilson from the chamber.

Wilson's outrageous remark was a one-off, I thought at the time, although the Republican Party was already well on its way to collective insanity back then. But while watching highlights of Biden's speech this morning I realized that Wilson was only a warm-up call for Republicans, who joined in a barrage of catcalls and visual epithets against Biden. Like Obama, Biden also kept his cool, much to my disliking, although I doubt if the Sergeant-at-Arms could have hussled out a dozen or so Republicans, who resembled a bunch of first-graders. As for me, I'd have called off the speech, gone back to the Oval Office, and begun writing a bunch of Executive Orders, including one immediately appointing six more justices to the Supreme Court, all of them black or Hispanic, female, and ultra left-wing.

Life Imitates Art, Eventually — Posted Wednesday February 8 2023
"So he flew off and fetched another acorn and dropped it in, and tried to flirt his eye to the hole quick enough to see what become of it, but he was too late. He held his eye there as much as a minute; then he raised up and sighed, and says, 'Consound it, I don't seem to understand this thing, no way; however, I'll tackle her again.' He fetched another acorn..."
In Mark Twain's classic 1880 essay collection A Tramp Abroad, he narrates a story about a blue jay dropping acorns down the chimney of a house, thinking he can fill it up (for winter storage purposes, I suppose). Called Jim Baker's Blue Jay Yarn, it's an example of life imitating art, although it has taken 143 years for life to get around to it. The same thing has happened at a home in Sonoma County, California, where 700 pounds of acorns were found, placed in a wall by a seemingly indefatigable pair of woodpeckers. As the article notes, the birds' spirits must have been crushed when the acorns were hauled away. But the year is still young!

But Dirac Did It First — Posted Tuesday February 7 2023
In Anthony Zee's wonderful 2003 book Quantum Field Theory in a Nutshell, the author describes an almost Zen-like fictional discussion between Caltech's late and great physicist, Richard Feynman (posing as a student) and his physics instructor. It involves the famous double-slit experiment, which exposes the fundamental nature of a particle acting as a wave at the quantum level. The student asks what happens when a third hole is drilled into the slit, then a fourth, and ultimately an infinite number of holes, thereby reducing the slit into nothingness. The particle would then seem to travel over all possible paths in free space before striking the detector, but still acting as a quantum particle interacting with itself like a wave.

Zee's fictional talk thus describes Feynman's path integral approach to quantum mechanics, which at the time he derived it (1948) represented a completely new formulation of quantum mechanics. (Amazingly, the path integral had been invented years earlier by the great British mathematical physicist Paul Dirac, who casually suggested it but didn't bother to expand on the idea.)

According to the path integral approach, a particle goes (or a field evolves) from Point A to Point B any way it wants (or can), either directly, in a curved path, in multiple loops, or even around the planet Jupiter, before arriving at Point B. Each of the infinite number of possible paths can be represented by a complex number; adding up the numbers and taking the complex conjugate gives a real number, which is the probability that the particle will take its observed path. Thus, the paths in effect interfere with one another, with the observed path being what survives the additions. In calculus, the addition of an infinite number of things is represented by an integral, hence the name "path integral." Even more amazingly, the path integral approach actually works, correctly describing all known quantum mechanics. There's only one hitch—in all but the simplest cases, computing an infinite-dimensional integral is all but impossible (for the second-semester calculus student, two- and three-integral problems are bad enough).

Some of the details behind the path integral are nicely presented in this new Quanta article, which includes a beautiful computer animation of the double-slit experiment. The author writes that the path integral may in fact indicate that what we experience as reality is really a superposition of all possible interactions in our universe. But since quantum mechanics is inherently probabilistic, I don't think that such a reality is completely deterministic, so what we call "free will" (and self-responsibility) is still possible.

An example of a path integral calculation can be read here. (I've taken a few liberties in the calculation, but the result is correct.)

None Dare Call It Censorship — Posted Monday February 6 2023
"If I weren't living through it, I wouldn't believe it's happening." — A Florida parent
Only a few months after Hitler's appointment to chancellor of Germany in January 1933, the Nazi burning of banned books began. It included books and papers written by Einstein, whose "Jewish physics" was declared false and deceptive. Soon, German pamphlets and magazines began depicting photos of Einstein with the epithet Noch ungehängt ("Still not hanged").

Republican Florida Governor Ron Desantis has banned thousands of book titles from school shelves and public libraries, citing inappropriate reading for children and young adults but actually reflecting his own conservative racist, ethnic and sexist attitudes towards women, same-sex relationships, racial education and diversity (primarily Critical Race Theory) and even American history (slavery and Jim Crow). In some Florida counties, public school teachers face firing and felony charges if they do not comply.

Is it inappropriate for a young child to read or be exposed to books dealing with America's horrific historic treatment of slaves, blacks and other minorities, including lynchings, whippings, burnings and other forms of torture and mistreatment? In many if not most cases, I would say yes, because young children are not mentally or emotionally mature enough to deal with such subjects. But should such books be banned forever because Desantis doesn't even want adults to be reminded of such topics? I say no, because at most such books should be restricted by teachers and parents, not subject to banning by de facto governmental authority, because it truly is a slippery slope. The next stop is book burning, and then we're right back to Nazi Germany.

Should a young child read or be exposed to the Old Testament Book of Joshua, which describes the wholesale slaughter and genocide of men, women, children, infants and suckling babes? (Perhaps the Amorites had it coming, as they practiced child sacrifice.) Or how about Shakespeare's Hamlet, which includes murder, incest, illicit sex, whoremongering and dirty songs? (Ophelia's little ditty leaves little to the imagination, nor does Hamlet's "Do you think I meant CoUNTry matters? " or "' 'Tis a fair thought to lie between maids' legs"?) Meanwhile, in the Liturgy of the Eastern Orthodox Church (my church), we commemorate the lives of the many great saints in the Synaxarion, which often describes how the saints were unjustly persecuted, tortured and killed for their faith, and how God always comforted them through their tribulations.

So shall we let Desantis and his base-trolling ilk ban the Bible, Hamlet, the Synaxarion, Catcher in the Rye, To Kill a Mockingbird and any number of other great books because of his insane political ambition?

No Way Out? — Posted Thursday February 2 2023
To grossly misquote a line from the 1993 movie Groundhog Day, this morning in central Pennsylvania the groundhog Punxatawney Phil, seer of seers, prognosticator of prognosticators, emerged reluctantly but alertly from his burrow and announced in groundhogese that rampant political strife, mass shootings and minority murders by police will continue indefinitely in America.

Antifa is a loosely organized political movement having no leaders, heirarchical structure or regional or national base. Its adherents are largely antiracist, anti-Nazi, anti-Semitic, anti-white nationalist and antifascist men and women who tend to gather at locations where racially and politically motivated attacks and murders have occurred against minorities, often by members of police. Antifa adherents are generally peaceful and non-violent, but there have been notable incidents where they have carried out attacks on public property. In one instance, reporters claimed to have witnessed Antifa members attacking white nationalists with batons and liquid dyes. However, to date there have been no reports of Antifa attacks resulting in deaths or serious bodily injuries.

I liken Antifa to a kind of loose-knit, mildly radicalized civil disobedience group carrying out disjointed counter protest marches which, on rare occasions, have resulted in minor to moderate property damage. Much of the violence at the white nationalist Unite the Right Rally in August 2017 (which was declared an unlawful assembly by local police) occurred as a direct result of deadly violence perpetrated by mobs of white racists, with scattered violent reactions by Antifa-aligned counter protestors. Former President Donald Trump infamously claimed that "there were very fine people on both sides," but in later remarks it was clear that Trump blamed Antifa on the violence.

In his latest article noted right-wing columnist Cal Thomas condemned the recent killing of Tyre Nichols by Memphis police, but quickly aligned the murder with leftist and Antifa-related activities, citing unrelated incidents involving leftist groups. Similarly, ultra right-wing commentator Tucker Carlson also implied that Antifa-associated political activities could be related to the murder.

Mass shootings and the murder of minorities by police are endemic in the United States, and political groups on both sides of the aisle have been unable to provide a solution. Instead, America just keeps getting more and more divided, but to me it's obvious that the right wing is 99% to blame. God help us if groups like Antifa choose to go ultra-violent to counter the endless brutality, stupidity and ignorance of the right, in which case we might very well have a new Civil War.

A 968-Year-Old Coincidence — Posted Wednesday February 1 2023
I wonder how many people today (young people, in particular) remember the 1955-1956 TV show The Honeymooners. I watched it with my parents regularly while growing up, and sporadically after it went into syndication. Its instrumental theme song, You're the One I Love, composed by the show's star Jackie Gleason, remains hauntingly in my mind, beginning when I was just 6 years old. It opened with a sequence of fireworks going off in the night sky, accompanied with "stars" displaying the show's major actors.

This new article in Scientific American stirred memories of that show, having to do with a supernova that occurred some 1,181 years ago (hence its present designation, SN 1181). Described as a kind of failed neutron star or white dwarf, it somehow survived the explosion as a smaller but still ordinary star. What's remarkable is its appearance—a central star with rapidly outflowing "fireworks," totally unlike the planetary nebulosity seen around other supernovas:

As seen with a sulfur filter, the remains of SN 1181 look remarkably like a fireworks display

I'm also reminded of the Crab Nebula, which shows the supernova remains surrounding a pulsar (spinning, radiation-emitting neutron star) that was observed by Chinese astronomers on July 4, 1054. Coincidentally, just 12 days later (July 16) the Western and Eastern Christian churches of Europe split in what is now called the Great Schism, giving rise to today's Roman Catholic and Eastern Orthodox churches, the latter of which I am a member. Caused by relatively piddling differences of theological opinion, the churches retain the first and second most Christian members today, with one billion and 250 million members, respectively. But the timing is just coincidence—the Great Schism indeed occurred in 1054, but the Crab Nebula was probably born many thousands of years earlier, its light not being seen until 1054.

Do We Live in a Universe of Extra Dimensions? — Posted Wednesday February 1 2023
The most recent version string theory (called M-theory) says that we live in a universe with 10 spacial dimensions and one of time, giving a total of \(n = 11\) dimensions. We can only see 3 spacial dimensions so, if string theory is correct, then where are the other 7? This question goes all the way back to 1919, when the German physicist Theodor Kaluza proposed a universe having one extra spacial dimension. His 5-dimensional theory was subsequently expanded by the Swedish physicist Oskar Klein, who claimed that the 4th spacial dimension was unseen because it was curled up at the Planck length level, completely invisible to human eyes and instruments. The notion of a curled-up dimension was applied as well to M-theory, although it had to be expanded to all 7 spacial dimensions.

The possibility that we might live in a universe having extra dimensions is discussed by astrophysicist Ethan Siegel in his latest article. I find the idea mind-boggling, but perhaps a little too convenient, to claim that these extra dimensions are all undetectably curled up, but mathematicians do this all the time. One example has to do with the packing of spheres in \(n \gt 3\) dimensions which, to my mind, is nothing more than a pointless mathematical exercise.

Still, the most famous example of extra dimensions is the theory by Kaluza and Klein, who considered the usual Einstein-Hilbert action in five dimensions $$ S = \int\!\! \sqrt{-g^*}\, R^*\, d^5x $$ where \(g^*\) is the metric determinant and \(R^*\) is the Ricci scalar in 5 dimensions, respectively. By a straightforward (but tedious) process known as dimensional reduction, this action can be broken down to the 4-dimensional level, giving $$ S = \int\!\!\sqrt{-g}\left( R + \frac{1}{4}\, F_{\mu\nu} F^{\mu\nu} \right) d^4x \tag{1} $$ where \(F_{\mu\nu}\) is the Maxwell electromagnetic tensor, with \( F_{\mu\nu} = \partial_\nu A_\mu - \partial_\mu A_\nu \), where \(A_\mu\) is the electromagnetic 4-potential. (The theory's correct \(1/4\) factor is extremely intriguing). Thus, in 5 dimensions the Kaluza-Klein theory seems to show that electromagnetism is somehow embedded in a curled-up 4th spacial dimension. (I made an attempt to show this in more detail in a paper I wrote long ago.)

But for Kaluza-Klein to work one still must construct a suitable 5-dimensional metric tensor \(g_{\mu\nu}^*\) incorporating the electromagnetic 4-potential \(A_\mu\), which seems to make the theory a bit contrived since the desired outcome in (1) can be worked backwards to derive \(g_{\mu\nu}^*\). A better theory would have \(A_\mu\) pop out of the formalism automatically as a purely geometric quantity.

As for now, M-theory's greatest achievement is that it appears to automatically embed a massless spin-2 field that has been identified with the graviton, the as-yet hypothetical particle believed to be responsible for gravity.

The inverse-square law of Newtonian gravity has now been laboriously tested at the sub-millimeter level, showing no deviation from the classical law. But this remains many orders of magnitude greater than the Planck length that string theory is supposed to dominate at. Since mankind will certainly never be able to peer down to the Planck level (it would require collider energies far beyond what could ever hope to be achieved), string theory will likely remain completely untestable, therefore being more a mathematical conjecture than a theory.

I find two interesting things about (1). For one, the electromagnetic term is quadratic in \(F_{\mu\nu}\), while \(R\) is linear. The other is that the electromagnetic term is scale (or conformally) invariant, while \(R\) is not. In his 1918 theory, the German mathematical physicist Hermann Weyl showed that the quadratic action $$ S = \int\!\! \sqrt{-g}\, R^2\, d^4x $$ is scale invariant if one assumes that the divergence of \( \sqrt{-g}\, g^{\mu\nu} \partial_\nu R \) vanishes. He subsequently showed that this quantity could be identified with the source vector \(\sqrt{-g}\, \rho^\mu \) of electrodynamics, whose divergence also vanishes. This once suggested to me that the 5-dimensional action $$ S = \int\!\!\sqrt{-g^*}\, R^{*2}\, d^5x $$ might be dimensionally reduced to provide a fully conformally invariant theory. Sadly, I lack the energy, motivation or time to investigate this possibility, and leave it to the student.

Prominent Dates — Posted Monday January 30 2023
Incredulously, many Americans today, mostly MAGA Republicans, still worship this man.

Here's a few historical dates of note. For one, Adolf Hitler was appointed chancellor of Germany on this date 90 years ago. It marked the end of Germany's tentative and rather decadent Weimar Republic, and ushered in a horrific 12-year period of mass murder, genocide and world war. And two, next month will mark 80 years since the executions of the brother-and-sister German heroes Hans and Sophie Scholl, soldier and student respectively, who valiantly tried to warn the German people of the inhuman crimes of Hitler and the Nazis. Standing bravely and resolutely before the notorious German judge Roland Freisler, who sentenced them both to death by beheading on February 22, 1943, they both died that same day.

I will not compare former President Donald Trump with Hitler, tempted as I am to do so. But I do condemn the American people, whose stupidity, ignorance and arrogance mirrors that of the German people of 90 years ago, who opted to forget the many brilliant humanitarian achievements of fellow countrymen like Kepler, Gauss, Einstein, Heisenberg, Born, Haber, Schiller, Goethe and Kant, preferring to blindly follow and obey the monomaniacal Hitler and his program of mass destruction. In that regard, Hitler and Trump are one.

Not to Worry — Posted Sunday January 29 2023
A physical object gets alternatively squeezed and stretched as a gravitational wave passes by. But does it do any damage, since it's just spacetime that's being deformed?

As this recent Scientific American article notes, our Milky Way Galaxy is on a collision course with the Andromeda Galaxy, with the collision expected to occur about 4 billion years from now. If anyone is around to see it (our Sun will go red giant around that same time), the display in the night sky will be impressive, but not necessarily disastrous, because very few stars in both galaxies will actually collide with one another. The centers of mass of both galaxies will swirl around each other for several hundreds of millions of years, eventually merging into a new and larger galaxy.

Many millions of years later, the supermassive black holes in the two galaxies will also merge, producing an enormous amount of gravitational radiation just prior to and during the merger. My question is: what effect will this outpouring of gravity waves have on the structures of nearby stars and, if anyone is still around, what will they feel? It's not as if they will be violently squished and stretched as the waves pass through, since it's not necessarily a physical effect, but one based on the stupendous warpage of spacetime.

It's this periodic squeezing and stretching that existing LIGO (laser inteferometer gravitational wave observatory) facilities experience. Since the effects are much smaller than that of a proton, the LIGO facilities don't get damaged in the least. But what would happen to them if a truly enormous gravitational wave passed by? Would they be damaged, or would they just "surf" the wave, the same as a person might surf on a surfboard? This article predicts disastrous consequences, but again, it's not a physical effect, but one of spacetime itself.

My prediction: Not to worry, because no one or much of anything on our scorched or vaporized Earth (by the red giant Sun) will be around then.

[Some years ago I wrote a simplfied tutorial on gravity waves, which you can read here.]

Time to Worry? — Posted Sunday January 29 2023
After retiring in February 2002, I did volunteer teaching and tutoring, primarily at the high school and undergraduate level. Most of my students legitimately used Wikipedia to help solve the math and physics problems I gave them, while on occasion I'd have them write short essays on various subjects. I'd always Google a few sentences from the better ones to see if they had engaged in plagiarization, and on more than one occasion I discovered that they had.

Today there is an freely available online program called ChatGPT, which utilizes artificial intelligence (AI) to create papers and essays that are so well-written that a teacher cannot tell if a student had written them personally or not.The products are also essentially unique, so Googling any portion of them cannot allow the teacher to know if the student has committed plagiarization. This is perhaps the first instance I've seen where AI has resulted in something truly detrimental to society, education in particular.

Some time ago I wrote about how AI might also be used to not only write movie scripts, but also utilize DeepFake technology in conjunction to create entertaining new movies starring past stars like Humphrey Bogart. This in itself might not be bad, although it would likely put out of work hoardes of writers, film producers, stunt men and others currently associated with the industry. But it could also be used for insidious purposes, such as fabricating political attacks and character assassinations. Those using such technology would have no way of knowing if what they were watching was completely fabricated for manipulation purposes.

But vastly more advanced AI is definitely on the way, and undetectable DeepFake technology is coming as well. How these technologies will affect the human race is anyone's guess, but I fear the worst.

Fine Tuning, Again — Posted Saturday January 28 2023
In this new video, physicists Brian Keating (UC San Diego) and Luke Barnes (Western Sydney University) discuss the issue of fine tuning in the universe. Fine tuning has to do with the observation that if many (if not most) of the known 26 universal constants of Nature were only slightly different, then life (or the universe itself) could never have come into existence.

I learned two things from their discussion. For one, a single proton will not stick to another single proton because the strong nuclear force is not quite strong enough to overcome the electrostatic repulsion of the protons (unlike proton-neutron bonding). If the strong nuclear force were only a little stronger, then the whole of chemistry would fall apart because pure protonic atoms would make everything else impossible. And two, the exansion of the universe literally creates new space (the universe does not expand into existing three-dimensional space), allowing for the spontaneous creation of quantum fields in the created space. This gives rise to the observed acceleration of universal expansion due to the cosmological constant \(\Lambda\), which I perceive as a kind of reverse Casimir effect.

Dr. Barnes also addresses the possibility of "parameter space," which has to do with the random mixing of various large changes to the universal constants of Nature to give something similar to the universe we observe. Many of these mixed parameters have been dismissed, but that's not to say that some mixture might work as well as the one we have today.

The discussion also touches on the need for a Creator, which to my mind is the simplest explanation for the existence of literally anything at all, but outside of a Creator I see this as mostly a philosophical question that can never be answered.

Meanwhile, one might ponder the question of why the universe has worked just fine for 13.8 billion years, while the modern human mind, which has been around for only a few hundred thousand years, has made a complete mess of things.

How to Waste an Hour of Your Life — Posted Saturday January 28 2023
Here's a frustrating problem from Sybermath, my favorite online math puzzle site. Find the real value of \(x\) in this cubic equation:

It's almost obvious that the solution is \(x = - 1/2\), but I wanted to solve it analytically. The first step is to get rid of the \(x^2\) term, so I tried the substitution \(x = y - 1/3\). That leaves the marginally simpler \(y^3 - y/3 = 11/216\) (the Sybermath guy gets this part wrong, but what the heck). To get rid of the linear term I used the standard identity \((a+b)^3 = a^3+b^3 + 3ab (a+b)\), then setting \(y = a+ b\). But you know what? Now both \(a^3\) and \(b^3\) are complex numbers, and solving for \(a\) and \(b\) is impossible.

Sybermath gets the right answer with his Solution #2, but this is the first time I've seen the standard method for solving a cubic equation fail (at least for a real solution).

I'll Believe It When I See It — Posted Tuesday January 24 2023
The Department of Justice is apparently considering plans to introduce an "appeal proof" conviction of former President Donald Trump which, if it held, would presumably avoid years of endless appeals by Trump and his lawyers. As it now stands, however, Trump can legally pursue his re-election plans for 2024 and even win, despite overhanging charges of sedition, obstruction of justice and lying to federal officials. Only a conviction could block that.

But I would read the Salon article very carefully, as it hinges on conviction, not prosecutorial indictment. It remains my opinion that Trump will never spend any time in prison, as the DOJ and its current cowardly Attorney General Merrick Garland and Special Counsel Jack Smith will almost certainly back down from an indictment, much less a conviction.

We live in a strange country today, one in which the rich and powerful seem above the law, where thousands of innocents are slaughtered every year by firearms that the nation's leaders are unwilling to effectively regulate, where hundreds of craven, egomaniacal multi-billionaires are seeking to become the first trillionaire, and where hoardes of brainless pop stars and wannabes have taken over the minds of Americans.

On Pure \(R^2\) Theory — Posted Tuesday January 24 2023
The scientific literature is replete with consideration of Hermann Weyl's \(R^2\) geometry, which he introduced in early 1918 as a generalization of Einstein's general relativity. Weyl hoped to link gravitation to electromagnetism with his theory, but it failed, although in 1929 his idea became what is known today as gauge or conformal invariance, which is the cornerstone of all modern physics today.

What continues to frustrate me, however, is that pure \(R^2\) theory is not quite completely conformally invariant, so researchers are trying to append it with hypothetical scalar functions to fix things up. In this new paper from arXiv, the authors again try their hand with the action $$ S = \int\!\! \sqrt{-g}\, \left( \alpha R^2 + \frac{1}{2}\, g^{\mu\nu} \partial_\mu \phi \, \partial_\nu \phi \right) d^4x $$ where \(\alpha\) is a constant and \(\phi(x)\) is some variable scalar. But what is the mass of this scalar, what is its associated kinetic function, and how does it vary under a conformal transformation? I am convinced that \(R^2\) alone (and perhaps fourth-order variants such as \(RT, T^2\), etc.) may still provide an answer to the dark matter problem.

A Bright (and Shiny) Idea — Posted Tuesday January 24 2023

Let's say you get a $100 bill as a birthday gift, which you deposit at your bank. It's fully worth its face value, although the cotton and linen material it's printed on is only worth a few cents at most. So what's the problem with the U.S. Mint producing a ONE TRILLION DOLLAR platinum coin, to be deposited in the U.S. Treasury to offset the nation's debt limit? If you managed to get your grubby little hands on it you could also deposit in your bank, or maybe buy your own country with it. (By the same token, the U.S. could print a one trillion dollar bill, saving the thousand dollars it would take to press a coin out of an ounce of pure platinum.)

As a one-time coin collector, my only question is: would the coin be minted in Denver (D), San Francisco (S), Carson City (CC) or Philadelphia (no mint mark)?

George Santos and \(\sqrt{-1}\) — Posted Friday January 20 2023
Newly inducted Republican representative George Santos is being hailed by fellow House colleague and physicist Rep. Bill Foster (D-Ill) for Santos' recent appointment to the House Committee on Science, Space and Technology. It's a highly important appointment, especially given Santos' record as an astronaut, Nobel Prize winner and Fields Medal recipient (not to mention that he's a world champion vollyball player), but particularly his familiarity with imaginary numbers, a cornerstone of quantum physics.

The trouble is, imaginary numbers (and their cousins, complex numbers) are real, while Santos' figures are totally bogus. More importantly, Santos himself is a fake, having lied about everything he got elected on. I am reminded of how imbecile Senator Rick Perry (R-Texas) was appointed by former President Donald Trump to head up the Department of Energy ("Muons? Quarks? What the heck are those things?")

Perhaps pathological liar Santos can now dream up a theory of quantum gravity, and prove the existence of dark matter and solve the anomaly of universal expansion.

[By the way, appointing Santos to the Science, Space and Technology Committee demonstrates how little regard the GOP has for those areas, as Republicans don't believe in science, anyway.]

Not a Fairy Tale — Posted Wednesday January 18 2023
Don't know what the status is of the Special Counsel's investigation into Trump's crimes? Neither do I.

The finding that President Joe Biden also had classified documents in his former VP residence and home may or may not have affected Special Counsel Jack Smith's investigation, but the Mar-a-Lago debacle is only one of the alleged crimes that former president Donald Trump is accused of. Fairness dictates that if Biden's holding of classified documents (although far fewer in number and importance than those Trump held) is a criminal offense, then both Biden and Trump should be prosecuted fully by the law, since two wrongs do not make a right. If Biden is guilty, then so is Trump, and the thought of them sharing a prison cell is tantalizing, if not a very likely prospect.

This still leaves innumerable crimes that Trump has irrefutably committed against the United States, not including state tax fraud and civil cases like sexual molestation. The January 6 Committee has turned over all its evidence to the Department of Justice and has now been disbanded, and Smith and his team are supposedly going over the evidence with a fine-toothed comb. But weighing against their work is the House of Representatives, which not only is now in control by the Republican Party, but with many far-right members looking for ways to stop any further legal or prosecutorial actions by the DOJ against Trump, who remains the GOP's current lord and savior.

Also contentious is Trump's plans to run for re-election in 2024, an unprecedented situation that the DOJ is also fully aware of. Prosecution would then be seen as a political act.

Yet for over a month now, there has been literally no news from the DOJ regarding its status into the investigations. It can't be because the evidence against Trump is ambiguous, since Trump is on record for having publicly incited the Capitol Building insurrection, not to mention his infamous recorded personal phone call to Georgia's Secretary of State pressuring the latter to give Trump the votes he needed to overturn Biden's presidential win in that state. Either of these two actions by Trump are irrefutably criminal in nature.

So what's the hold up? Consider the two possibilities that the DOJ is certainly considering:
  1. If Trump is prosecuted, America's right wing, spurred on by the Republican Party, Republicans in Congress, Red State legislatures and the right wing media, will be incited to nationwide violence, making the January 6, 2021 insurrection look like a walk in the park. A new Civil War would also be possible, if not likely.
  2. If Trump is not prosecuted, America's left wing will be outraged, but would be comparatively silent, seeking to redress its grievances peacefully and politely through political means.
If you were Special Counsel Smith, what course of action would you take? My guess is that the DOJ has already decided to pursue the second option, and is only wondering how to break it to the American people, who've been falsely led to believe that our nation is based on justice for all, not just for the rich and powerful.

A Dark Matter Fairy Tale — Posted Monday January 16 2023
The remnant of Supernova 1987A, which occurred outside the Milky Way in February 1987, some 168,000 light-years from Earth.

The Great Courses series Introduction to Astrophysics I wrote about yesterday includes an overview of the 1987 core-collapse supernova designated as SN 1987A. As much as 99% of the energy carried away from a supernova comes in the form of high-energy neutrinos, a few dozen of which produced by SN 1987A were inadvertently detected by physicists looking for evidence of proton decay. Since then, the science of neutrino detection has vastly improved, and scientists are hopeful that the next supernova event will produce many millions of the particles in their detectors, providing avenues for new research into neutrino physics.

Once considered to be the identity of the hypothetical dark matter particle, neutrinos (like dark matter) are electrically neutral and of extremely low mass, able to pass through light-years of lead shielding without a single interaction. Dark matter is also believed to be an electrically neutral, lightweight particle that responds only to gravity. The major difference is that dark matter is required to be cold, meaning that it must be slow-moving to account for the assumed presence of dark matter haloes around galaxies. By comparison, neutrinos are produced as fast-moving particles (approaching light speed) that never slow down.

Astrophysicist Ethan Siegel is a diehard believer in dark matter, and in his latest article he writes that supernova neutrinos might produce indirect evidence of dark matter. This represents a new approach to dark matter research which, despite four decades of research and billions of dollars spent to date, has failed to produce any evidence of dark matter particles. His reasoning is based on the prospect that supernova neutrinos might interact with dark matter, with the result that an observed deficit of expected neutrino numbers showing up in today's detectors could be attributed to the dark matter thought to be surrounding the Milky Way Galaxy.

While I can't criticize Siegel for his hope that neutrino-dark matter interaction might occur at least in principle, I find the prospect of one rarely-interacting particle colliding with another rarely-interacting particle to be simply beyond belief. To his credit, Siegel himself admits it's one of the wildest of possibilities, but to me it's just a fairy tale.

Two Great Great Courses Programs — Posted Monday January 16 2023
I took a graduate class in astrophysics as an elective at university many years ago, but I really wasn't interested in the subject. Then some years ago I bought The Great Courses video program Introduction to Astrophysics and got turned onto it. It's presented by Princeton University's Joshua Winn, one of the best teachers I've seen in the entire GC catalog. He uses calculus, but it's elementary and I think any high school student can easily follow it.

I binge-watched the entire series yesterday during our heavy rain (which I'm thankful for because of the drought here), and I remain greatly impressed with Dr. Winn's approach to the subject, which spans just about everything, including exoplanets (he has another GC program on that). All of the Great Courses programs can usually be found on sale at reasonable prices, and I highly recommended these two.

"Hey, Who's the Barber Here?" — Posted Thursday January 12 2023
According to physician Dr. John G. Sotos, the author of the fascinating 2008 book The Physical Lincoln, our 16th president was a "lounger," meaning that he preferred laying on a sofa or day bed rather than sitting or standing, a habit likely due to Abraham Lincoln's 6'4" frame. Lounging is my normal position when I'm at home, although I know about the health dangers of long-term sitting and lounging, as described in this new CNN article. Bottom line: I try to get at least 30 minutes of hard exercise a day, nowhere near my routine from only a few years ago, but in the end I don't really care. At 74 years, I feel fine, and if my habits catch up with me, so be it.

Dr. Sotos has also expressed his opinion that Lincoln was suffering from a congenital health defect related to Marfan's syndrome (if I recollect correctly, as it's been years since I read the book), and that Lincoln would have likely died soon if John Wilkes Booth's deringer bullet had not ended his life on April 15, 1865.

Still, Lincoln was fortunate. In 1841 he had a tooth extracted that also took out a portion of his lower jaw, a procedure that might have easily led to a life-ending septic infection. The person who performed the extraction was likely a local barber, whose tonsorial expertise typically extended to minor surgery and dentistry in those times.

Would you still like to travel back in time to Lincoln's day? I didn't think so.

By the way, illustrator and 3D artist Ray Downing has created some astounding realistic images and videos of Lincoln. Check them out.

Physics, You're No Fun Anymore — Posted Thursday January 12 2023
Since today's physics and cosmology problems seem to have no solutions, I've turned to simpler things. For fun, I like to solve math problems, and there's no better website than Sybermath. The problems never go beyond basic calculus, but sometimes they can be solved by intuition or just by guessing. On occasion, the problems have no analytic solution, such as this one:

The answer is obviously \(x = 2\), but the problem is so simple I thought it would have an easy analytic solution. But it doesn't, as the Sybermath guy shows.

I know, I have to get a life.

Brazil and America — Posted Tuesday January 10 2023
I find it telling that the recent insurrection in Brazil's capital by Trump-like election conspiracy theorists not only echoed what happened at our Capitol Building in January 2021, but that millions of enraged Brazilian citizens are demanding punishment of the hundreds of rioters. Compare this with America, whose Republicans are pooh-poohing the January attack as nothing more than a few thousand (!) patriots who were a little too rambunctious during an otherwise peaceful and largely unplanned demonstration. But was the attack in Brazil, in which there were fortunately no reported deaths or injuries, the same as in the January 2021 incident, in which the attackers stormed the Capitol building armed with guns, tasers, clubs, zip ties, mace, bear spray and human excrement, and which led to the deaths of five people? Yet, while Brazil is planning the immediate conviction and incarceration of its rioters, America is conflicted over its own insurgents.

Defendant: "Your honor, I just happened to have a few guns, a taser, mace, some zip ties and a bag of my own poop on me when I went to the Capitol to protest peacefully and legally."
U.S. Judge: "Are you insane?"
Defendant: "No, your honor."
U.S. Judge: "That's good, because otherwise your testimony would be less plausible. Case dismissed!"

If Mother Nature (Gaia) Could Talk — Posted Tuesday January 10 2023
Gaia: "Dear Lord God, You created me first, but then You also created these humans who are now destroying the world with their ignorance, greed, violence and stupidity. What am I to do?"
God: "Well, I took care of the vast lot of them a few millennia ago, but as I love My greatest Creation I've decided not to do that again. But I also allowed viruses to form in your fallen world, and perhaps you can use them to constrain the people somewhat."
Gaia: "To date viruses have been of only limited use, but I've still got a few tricks up my sleeve. One is called coronavirus—it's highly contagious, extremely deadly, and it mutates like crazy into even more virulent forms, requiring humans to come up with ever more effective vaccines. The latest one I call "XBB.1.5," or the kraken virus, like the mythological sea monster. Best of all, there are a lot of humans, mostly in the United States, that believe vaccines themselves cause death and are the cause of ADHD, autism and other pathological conditions, so they're stupidly avoiding treatment."
God: "Okay, give it a go, Gaia! Perhaps people will then see their folly and turn to Me before it's too late."
Gaia: "I'm on it already, Lord!"

The Mystery of Energy in the Universe — Posted Tuesday January 10 2023
I learned something new today! Referring to his famous field equations of gravitation

\(R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = 8 \pi G/c^4\, T^{\mu\nu}\)

Einstein considered the left-hand side to be made of fine marble (as it arises solely out of inviolable geometry), whereas the right-hand side he considered made out of cheap wood. That's because the energy-momentum tensor \(T^{\mu\nu}\) has to be constructed in such a way as to make it consistent with different forms of matter, subject only to it being divergenceless. In this presentation by physicist Tomás Ortin, I learned that the energy-momentum tensor is not a truly covariant tensor, with the surprising consequence that energy is not a conserved quantity. I already knew that energy is not conserved in an expanding universe, but I didn't know that this could be traced to \(T^{\mu\nu}\) itself. It's almost as if the geometry of general relativity somehow "knows" that the universe is expanding.

Ortin's video primarily addresses the metric of a rotating black hole, spinning in the otherwise empty vacuum of space. In such a space, \(T^{\mu\nu} = 0\), but the space is not truly empty!

When a sphere or cylinder rolls down an inclined plane, its initial potential energy is converted into both kinetic and rotational energy. But spheres, balls, disks and cylinders roll at different rates because their moments of inertia are different (cylinders are the fastest, so maybe a toy car with such wheels would have an advantage in a kids' roller derby). Many years ago, several German companies experimented with trolley cars powered solely by a rapidly rotating internal cylinder, whose rotational energy could be transferred to the trolley wheels, thus avoiding the need for an internal combustion engine. The idea worked, but trolley range was limited, and passengers sitting astride a massive, rapidly rotating mass felt a bit nervous.

It turns out that energy can also be extracted from a rotating black hole via the Penrose process, although there is no need for a direct connection to the hole itself. The 2020 Nobel Prize for Physics went to Roger Penrose for his work on black holes, who in 1971 discovered a way to extract energy from a rotating black hole—if one drops a load of garbage, say, slantwise into the hole's ergosphere, the empty dumpster will come flying back out, whose kinetic energy can be used as an energy source.

The ergosphere of a rotating black hole (also called a Kerr black hole, in honor of its discoverer, Roy Kerr) sits outside the hole's event horizon in a perfect vacuum. But this vacuum (somewhat akin to the dark energy of the vacuum of space) must have a vanishing energy-momentum tensor by convention, since there's nothing there but gravity. But Einstein himself showed that the energy content of a gravitational field is ambiguous, having no applicable conservation law. Although one can set up an energy-momentum tensor \(T^{\mu\nu}\) for moving matter, electromagnetic fields and other conventional mass-energy sources, I know of none that exists for pure gravity itself. That's already embedded in the left-hand side of the field equations!

Since all stars, galaxies and black holes rotate, only the Kerr black hole has meaning in our universe. We know today that it is very probable that every galaxy has a supermassive black hole at its center, rotating like crazy, and I wonder if the energy-momentum tensors associated with these objects might have something to do with dark matter, dark energy and the overall energy content of the universe.

How's That for a Coincidence? — Posted Tuesday January 10 2023
Here's another Gary Larson classic. Somehow, pistons and springs are key components in time machines:

Hossenfelder on the Special and General Theories of Gravitation — Posted Saturday January 7 2023
Einstein's special relativity is difficult enough, but it holds only in the absence of gravity. In the presence of a gravitating mass, special relativity is replaced by Einstein's general relativity theory. The two are explained in German physicist Sabine Hossenfelder's latest video, embedded below.

In special relativity, one has two basic disagreements between observers moving at constant (non-zero) velocities relative to one another. One is time dilation, which means that initially synchronized clocks traveling with each observer will not agree, and the other is space contraction, which also means that distances measured by each observer will not agree. Yet times and distances measured by each observer are absolutely correct in their own frames of reference—neither is "wrong." This is perhaps the most puzzling aspect of special relativity, although the mathematics is not difficult, perhaps just the interpretation.

Special relativity holds even for observers that are accelerating with respect to their own frames, countering the notion that it holds only for constant velocities. But a gravitating mass changes the spacetime frame itself, warping it in complicated ways (except for very simple or highly symmetrical cases). The essential difference between the two theories is that spacetime is flat in speciai relativity, while it is curved in general relativity. There is a complicated quantity in differential geometry called the Riemann curvature tensor, denoted by \(R_{\,\mu\nu\beta}^\lambda \,\), where each greek symbol can take on any of the four values 0, 1, 2, 3. The tensor itself is composed of complicated combinations of the symmetric fundamental metric tensor \(g_{\mu\nu}\) and its derivatives (it's amazing that today the tensor can be calculated using numerical computer schemes). The curvature tensor vanishes everywhere in special relativity, so one does not need to worry about it—that's why students in high school and undergraduate physics classes are seldom exposed to it. But in general relativity it needs to be calculated, and this is why Einstein's gravity theory is so difficult. It all boils down to determining \(g_{\mu\nu}\)—in special relativity each of its 10 terms (and usually there's only the four, \(g_{00}, g_{11}, g_{22}\) and \(g_{33} \)) is a constant (often just 0, 1 or -1), whereas in general relativity they're variables that have to be determined.

While Hossenfelder does not mention the curvature tensor, her talk is notable because she explains why there's no such thing as the "force of gravity." A planet revolves around its star not because it's being pulled in, but because it's simply following what amounts to a straight line in the curved space produced by the star.

Dark Matter vs Modified Gravity, Again — Posted Thursday January 5 2023
Edgar Rice Burroughs was the originator of the Tarzan legend, which he expanded to include his stories about a hollow Earth that Burroughs dubbed Pellucidar, which first appeared in his 1914 fantasy novel At the Earth's Core. Like the outer Earth, Pellucidar had skies, land masses and oceans, but they were all superimposed upon the inner shell of the hollow Earth. Pellucidar had its own gravity, which was the same as Earth's although it acted outward onto the inner shell, so that a visitor to the world would feel gravitational effects similar to Earth's.

While a successful author, Burroughs apparently knew nothing about physics. The gravitational force inside a hollow spherical shell is exactly zero, so the inhabitants of Pellucidar would find themselves completely weightless and floating around aimlessly.

I've imagined that a roughly similar situation might exist in intergalactic space, in which the gravitational effects of surrounding galaxies might induce what is thought to be a tiny but non-zero External Field Effect (EFE), acting on a galaxy internal to the surrounding galaxies. It would tend to inertially sustain the velocities of stars far from their galactic centers, even though the gravitational interaction would be on the order of trillionths of a \(g\).

The EFE is a feature of Modified Newtonian Gravity theory (or MOND, which is included in the above link), where it is used to overcome certain problems in the theory. MOND was introduced by the Israeli physicist Mordehai Milgrom in 1983 as a means of explaining the observed effects of dark matter. Dark matter (DM) is a key ingredient in the conventional \(\Lambda\)CDM (lambda-cold dark matter) model of standard cosmology, yet to date it has not been experimentally detected. Many conventional and exotic explanations for DM have been proposed, although it is believed to be an as-yet undetected particle that responds only to gravity. The neutrino would be the ideal DM particle, but its mass is far too small to explain the observed effects of DM on stellar galactic rotation curves, galaxy clusters and gravitational lensing.

Over the past forty years there have been over 100 major experimental programs conducted to detect DM, but despite billions of dollars spent and herculean efforts by experimentalists, the presumed DM particle continues to elude detection. This has created renewed interest in MOND and other modified gravity theories (including relativistic variants) that have been able to duplicate most of the effects of DM (along with explaining others that DM cannot, such as the observed Tully-Fisher relation). Indeed, some modified gravity theories have been shown to be more plausible than the DM hypothesis, despite ongoing problems and issues. One such theory, AQUAL (which stands for "A QUAdratic Lagrangian"), represents a truly hopeful alternative to DM, as explained in this recent article.

The notion of deriving Einstein's theory of general relativity using a quadratic Lagrangian (more generally known as f(R) gravity, or \(R^2\) gravity) goes all the way back to 1918, when the German mathematical physicist Hermann Weyl first proposed it as a means of embedding the electromagnetic field into the pure geometry of gravitation. The action based on a \(R^2\) Lagrangian has one very intriguing property, which is that it allows for local scale or gauge invariance of the gravitational field, a desirable addition to all the other mathematical symmetries in physics. To see this, start with the action $$ S = \int\!\! \sqrt{-g}\, f(R)\, d^4x \tag{1} $$ where \(f(R)\) is some arbitrary function of the Ricci scalar \(R\) alone. In the absence of a mass-energy source, variation of (1) with respect to the fundamental metric tensor \(g^{\mu\nu}\) leads to the field equations $$ \left[ - \frac{1}{2} \, g_{\mu\nu} f + R_{\mu\nu} \frac{\partial f}{\partial R} - g_{\mu\nu} \,g^{\alpha \beta} \left( \frac{\partial f}{\partial R} \right)_{|\alpha ||\beta} + \left( \frac{\partial f}{\partial R} \right)_{|\mu ||\nu} \right] \, \delta g^{\mu\nu} = 0 \tag{2} $$ where the single and double subscripted bars stand for ordinary partial and covariant differentiation, respecively. For the infinitesimal scale variation \(\delta g^{\mu\nu} = - \pi g^{\mu\nu}\) (where \(\pi\) is some small arbitrary variable scalar), (2) leads to $$ 2 f - R \frac{\partial f}{\partial R} + 3\, g^{\mu\nu} \left( \frac{\partial f}{\partial R} \right)_{|\mu ||\nu} = 0 \tag{3} $$ Now, if one assumes (like Weyl) the quadratic identity \(f(R) = R^2\), the first two terms in (3) cancel and we have simply \(g^{\mu\nu} R_{|\mu||\nu} = 0\), which is equivalent to the pure divergence $$ \left( \sqrt{-g}\, g^{\mu\nu} R_{|\mu} \right)_{|\nu} = 0 \tag{4} $$ By brilliant deductive mathematical and physical reasoning, Weyl showed that the action in (1) with \(f(R) = R^2 \) is not only fully equivalent to Einstein's gravitational field equations, but that the quantity \(g^{\mu\nu} R_{|\mu}\) could be identified with the electromagnetic source vector \(\rho^\nu\), which also has vanishing divergence.

Although Weyl's theory was later shown to be unphysical (by Einstein, no less), it represented not only the very first serious attempt to unify the gravitational and electromagnetic forces of Nature, but his quadratic Lagrangian became a serious contender for a purely geometric alternative to dark matter. I've posted many attempts to explain Weyl's theory and its importance to gauge invariance (which is now a cornerstone of modern quantum physics). See the links on my old site for additional information.

Update: Grasping at straws? Here's a new article from Don Lincoln, a FermiLab physicist who's a strong proponent of dark matter. He cites some recent research concerning the distribution of some 11 satellite galaxies around our Milky Way galaxy. These galaxies are generally scattered along the Milky Way's rotational plane, a finding that tends to discredit the DM argument, which demands a spherical distribution with the Milky Way in the center. But the research contends that the current distribution is unusually weighted by the presence of two galaxies, Leo 1 and Leo 2. Take them away, and the distribution of the remaining galaxies is more spherical, supporting the DM theory. If this isn't an example of data manipulation, I don't know what is.

Every High School Crush — Posted Thursday January 5 2023
Gary Larson captures every crush I had in high school.

Biden Comes Up Short — Posted Thursday January 5 2023
I watched President Biden's brief press talk on the border crisis this morning. It's a difficult problem, and no doubt he has a plan to address the issue when Title 42 finally expires, but where he came up short was his neglecting to mention that if America is truly a Christian nation, as his Republican detractors continue to argue for, then Americans should respond to the problem as Christians, not as haters of the "other." Former President Donald Trump once called Mexico a "shithole nation" and its migrants as "criminals" and "rapists," and conservative Americans applauded him for these sentiments. I'm still disgusted, not only by Trump's words, but by the sickening reaction of his supporters.

Meanwhile, I also watched the opening of today's House Speaker voting, in which African American Representative John James (R-Michigan) compared the voting deadlock to the one that occurred in 1856. He asserted that America is much more united today than it was then (referring primarily to the issue of slavery), adding that as a black man he was far better off than his ancestors or Jim Crow-era parents. To me, he was saying in effect "I is a proud Uncle Tom, an' I gots mine, thanks to de white man." I was embarrassed for him, not only because of his apparent subservience to his racist white Republican masters, but because the political situation in America today is far worse than it was in 1856. The Civil War of 1861-1865 was yet to be fought with its deadly but relatively primitive weapons, while today the entire nation is under seige by 25% to 50% of its citizens, some 80 to 160 million strong (many armed with AR-15s), who still suffer from the effects of racist thinking.

How to Fight Totalitarianism — Posted Tuesday January 3 2023
The Republican Party takes power over the 118th House of Representatives today, although the speakership is still very much in doubt. What is not in doubt, however, is the GOP's promise to focus solely on eradicating the progressive plans and policies of President Biden, his family and administration, supported by the likes of Fox News, Sean Hannity, Tucker Carlson and the billionaires behind the rightwing media. With few exceptions, these are all pathological, fanatical lying maniacs whose lust for money, influence and political power far exceeds any consideration they have for the welfare of America.

If you think that totalitarianism can't happen in America, remember Germany—the land of countless scientific, philosophical and musical geniuses like Kepler, Gauss, Einstein, Heisenberg, Born, Haber, Schiller, Goethe, Kant, Beethoven, Mozart, Haydn, Brahms, Schubert, Strauss and Wagner—and how all that achievement was so easily eclipsed by the totalitarian evil of Hitler and his Nazis.

The following After Skool video is one of the best I've seen regarding totalitarianism and its recent rise in the world, perhaps best exemplified by the extreme Republican rightwing in our own country. At about 22 minutes in length, it's well worth watching, and the many hand-drawn illustrations are amazing. It concludes with the hope that totalitarianism can be fought, if not always outright defeated, by truth, logic and humor (I'm not sure about that last one).

Times Have Changed, Part 2 — Posted Monday January 2 2023
Thomas Edison invented the first practical phonograph in 1877, whose earliest recordings were made by a fixed stylus on a rotating cylinder holding a sheet of waxed paper. The technology was solid, but the paper was fragile, so Edison introduced waxed cylinders, which by the early 1900s became a popular way to not only listen to recorded music but also a means of making one's own recordings at home (the wax could be scraped down, providing a fresh recording surface). In 1908 Edison introduced Amberol cylinders made from an early plastic material similar to Bakelite. While not re-recordable, the material provided up to 4 minutes of play (see this site for more information).

I remember going to swap meets in the late 1960s and seeing these cylinder recordings. One day I bought one for one dollar, thinking that I'd eventually get an Edison phonograph to play it on, but even then they were beyond my means as a college student (I'd see them selling for $300 back then, but today they're in the thousands). Here's the one I bought in 1969, which is labeled "Uncle Josh Keeps House" (1912):

At 111 years of age, it's in perfect condition, but I have no idea what my record sounds like (but probably better than Billy Joel).

There are many thousands of wax cylinder recordings still in existence, and efforts are now underway by the Library of Congress to preserve them.

Wanna hear the oldest existing recording? It was made by a French linquist and inventor in April 1860, who recorded his daughter (or himself) singing "Au Clair de la Lune." It's very rough, but it still sounds better than Billy Joel.

Times Have Changed — Posted Sunday January 1 2023
I watched Fareed Zakaria interview musician Billy Joel on CNN this New Year's morning. To be honest, I cannot stand Joel's music, and have never liked any of his songs, which have made him very wealthy. Joel is a talented pianist, but only in the Elton John tradition, and I doubt if he could ever play like Yuja Wang. Meanwhile, Joel's songs are just run-of-the-mill soft pop/rock stuff, intended for consumption by the masses who don't know any better. Joel's "Just the Way You Are" is sentimental hokum, and "Tell Her About It" is just plain garbage.

The Joel interview got me thinking about how the classical greats like Mozart and Beethoven never made much money in their day in spite of their enormous genius (the likes of which we'll never see again). Even the Beatles and Rolling Stones didn't make that much in their day despite all their hit songs (they made tens of millions, not hundreds of millions), while later groups like Kiss struck it rich without so much as a single decent song. Today's successful pop artists and rappers are raking in even more money, despite the utter trashiness of their music.

Sorry, I just turned 74, so I guess I'm showing my age.

Happy New Year — Posted Sunday January 1 2023
I dumped all of the 2021-2022 stuff into the Old Stuff archive on the left. Now, let's start a new year.