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.