AfterMath



Not Relevant? — Posted Thursday April 18, 2024
The subject of length (or distance) measurement is near and dear to me. Is an object's size an absolute characteristic of its existence, or does it depend on the observer? Einstein's special theory of relativity says it does indeed depend on the observer, and that size, length, distance or whatever you want to call it depends on the observer's frame of reference (this also applies to areas and volumes).

My PhD research focused on the size of particles and their statistical distribution. For massive particles, I determined that they often follow a log-normal distribution, much like the observed distribution of truly massive systems of galaxy pairs. But observations of size and distance all depend on the observer, and relativistically this has no objective meaning, This is what led me to Weyl's 1918 gravity theory, which is invariant with respect to such things. This new Scientific American article provides a little more depth into the matter, which I found relevant.

Hossenfelder Flips Again? — Posted Thursday April 18, 2024
German physicist Sabine Hossenfelder has gone back and forth a few times on the issue of whether dark matter exists or if a modified version of Einstein's 1915 gravity theory more correctly explains what is perhaps the most puzzling problem in cosmology today. In her latest video, she seems to give modified gravity theory a little more credit:

Here's a puzzle for my more educated readers. If you consider the nearly-conformal action $$ S = \int\!\! \sqrt{-g}\,R^2\, d^4x $$ for free space, its extremalization provides exactly the same predictions as Einstein's original theory, but with a purely geometric nod toward an explanation of dark matter. What today is known as pure \(R^2\) (or quadratic) gravity theory was first proposed by the German mathematical physicist Hermann Weyl back in 1918 (whose story is surely known to those who've followed my website).

The paper Hossenfelder cites in her video is from Dr. John Moffat of Canada's Perimeter Institute. It's a short, readable paper, but the author's argument relies on the existence of arbitrary scalar and vector fields having nothing to do with \(R^2\) gravity theory.

Rambling—Why Einsteinian Gravity is Not Wrong, Just Incomplete — Posted Tuesday April 9, 2024
Einstein's 1915 gravity theory is grounded in Riemannian geometry, a branch of differential geometry that includes non-Euclidean geometry (think of warped lengths, surfaces and volumes). It was developed in 1851 by the great German mathematician Bernhard Riemann (1826-1866), whose brilliant career was tragically cut short at the age of 39 by tuberculosis. Riemann's geometry was valid in any spacial dimension, but other than certain purely mathematical aspects the geometry remained grounded in the usual three dimensions of space. However, if Riemann had only thought of time as a fourth dimension, he might have been led to Einstein's gravity theory at least sixty years before Einstein published his monumental work in November 1915.

A key element of Riemannian geometry is that its elements are coordinate-independent, meaning that the geometry is applicable to any arbitrary coordinate system. Coordinate invariance means that non-inertial coordinate systems (accelerated systems) could be handled as well as inertial systems, an importsnt factor in Einstein's gravity theory. Einstein also recognized that time could be considered a fourth coordiinate (turning space into spactime), and the dimensionality invariance of Riemannian geometry was also key to the theory, which is four-dimensional.

Some background:

Nearly all physical theories are expressed in mathematical terms that specify a particular coordinate system. High schoolers usually learn about the \(x,y,z \,\) Cartesian coordinate system (the simplest), and slightly later they learn about the polar coordinate system \(r, \theta, \phi\). The mathematics of physical theories based in one system often look completely different in another, leading to confusion and/or disagreement over which system is the best (or easiest) one to use—it's really just a matter of preference or convenience. But physics cannot be dependent on which coordinate system is applied—that is, the predictions of a physical theory cannot change if the coordinate system is changed.

The importance of coordinate invariance was recognized by Riemann, and a number of other mathematicians set out to formalize his ideas. The Italian mathematician Gregorio Ricci (1853-1925) developed the absolute differential calculus (more commonly known as tensor calculus), which is in use today. Tensors are just mathematical quantities that don't rely on any particular coordinate system, and can be used to express any physical theory in tensor language. Concurrently, another Italian mathematician named Luigi Bianchi (1956-1926) derived fundamental mathematical relationships between certain important tensors.

When Einstein was trying to develop his general theory of relativity (gravity), the difference between inertial and non-inertial systems meant that coordinate invariance would be fundamental to the theory. But Einstein did not know how to proceed, so he turned to his close friend and colleague Marcel Grossmann, a mathematician conversant in tensor calculus. Grossmann essentially taught Einstein the formalism, and after many ups and downs over the period 1912 to 1915 Einstein finally completed his gravity theory in November of that year. It is a testament to the beauty, elegance and truth of Einstein's theory that it has not experienced a single failure in over 100 years of astronomical and cosmological observation.


However, despite the success of Einstein's gravity theory it presents several problems. For one, the theory is not conformally invariant, which means that it is fundamentally inconsistent with Maxwell's equations (although electrodynamics can be forced into theory). Another problem is that it appears to be incompatible with quantum field theory (which is conformally invariant). Still another problem is that it cannot be derived from any known fundamental principle. True, the free-space form of Einstein's theory can be deriived by extremalizing the Einstein-Hilbert action $$ S = \int\!\! \sqrt{-g}\, R\, d^4 x \tag{1} $$ (where \(R\) is the twice-contracted form of the Riemann curvature tensor \(R_{\mu\nu\alpha\beta} \rightarrow R_{\mu\nu} \rightarrow R\), but then this is just an ad hoc quantity that happens to work. In addition, the action principle in physics traditionally includes a kinetic energy term and a potential energy term, and these are missing in (1). Furthermore, adding a straightforward, principle-based energy-momentum term to the action is elusive (Einstein also had issues with this), so sources of matter and energy (mass, electromagntic fields, etc.) that give rise to gravity in the first place have to be artificially tacked on.

But perhaps the biggest problem is that Einstein's gravity theory cannot be generalized in any satisfactory way that can provide for conformal invariance and mass-energy, which should somehow be incorporated into the action. The most fundamental quantity in gravity theory is the Riemann curvature tensor \(R_{\mu\nu\alpha\beta}\), which is identically zero in empty space. In non-empty space is is not, and should therefore be related to matter and energy (if it is not indeed the very source of matter and energy). But the Riemann curvature tensor is all there is, and there are some (including me) that think it should be the basis of all physical reality. By comparison, in quantum theory one has all kinds of neat things, like operators, fields and the beautiful Dirac bra-ket formalism, along with mathematically consistent ways of describing everything. In that sense, gravity is a "poor" theory, because it has to rely on so little—just the contracted Riemann curvature tensor. The only thing missing in quantum theory is gravity, which seems incapable of being jammed in—hence, the ongoing search for a quantum gravity theory, which may not even exist.

With quantum gravity, string theory and supersymmetry either going nowhere (and/or failing outright) as of today to incorporate gravity, it seems the only recourse is to generalize Einsteinian gravity. But despite ongoing efforts, including the use of scalar, vector, tensor and spinor quantities into the formalism, nothing has really worked regarding a solution to several remaining, perplexing problems like dark matter and dark energy. Meanwhile, Einstein's gravity theory remains eminently successful and unchallenged, despite its inability to be joined with quantum mechanics.

My dream of seeing a workable theory of quantum gravity in my lifetime will likely never be realized, and I'm now resigned to it.

A Waste of a Beautiful Mind — Posted Friday April 5, 2024
"Look at them, Smithers: goldbrickers, layabouts, slugabeds! (Not to mention Joe Sixpacks and Susie Housecoats) — C. Montgomery Burns


I was saddened while watching this new video from German-physicist-cum-YouTube-video-wrangler Sabine Hossenfelder, whose work, books and videos I've followed and admired for years. I noticed something going on with her a year ago, and in this personally painful video "confession" she reveals all.

For many more years I've followed Cornell University's arXiv.org site, which posts many thousands of freely downloadable, pre-peer-reviewed scientific papers on dozens of academic subjects. But over the last few years I've noticed an inabiity on my part to even comprehend the paper titles on the site, much less their contents. However, my initial fear of the onset of dementia was allayed when I and many others came to the realization that 99%+ of the papers are garbage ("bullsh*t," as Hossenfelder rightly calls it). A glance at a sampling of the papers on the site's General Relativity and Quantum Cosmology section provides convincing evidence of this. As Hossenfelder notes, the vast majority of authors are post-docs, adjuncts and untenured faculty workers whose only hope for a normal, stable life and a tenured university position with decent pay and medical and retirement benefits is to crank out as many papers as possible in an unending effort to secure grants for their employers. My post-PhD son saw this early on and left academia, calling it "life sucking."

Being retired with a pension, I can write all I want about interesting stuff, but with 8 billion and counting humans on the planet now I wonder how many more unproductive wastrels and slugabeds like me will be forthcoming in a future promising far less retirement comforts.

What's the future of academia today? Would Einstein himself stand a chance in this world? Apparently not even a brilliant mind like Hossenfelder's has any hope of a decent future except to bail out and become a YouTube semi-celebrity. Watch and weep:


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Not "Why is there Anything?", but "Why is it so Consistent?" — Posted Friday April 5, 2024
Although he strictly avoids the subject of the existence of God, astrophysicist Ethan Siegel's latest article talks about one of the most profound aspects of our physical world—continuous mathematical symmetries and conservation laws. These symmetries underlie perhaps the most profound reality, which is that every physical (and probably biological) law of the universe arises from consistent and inviolable mathematical rules that could not have possibly resulted from chance or a random chaotic collection of particles and fields. I urge readers of this site to read the article, and try to figure out for themselves just how such consistency, beauty and truth could have resulted by chance alone, or even the possibility of of an infinite multitude of random parallel universes, each having it own set of chaotic characteristics.

Understanding (or at least appreciating) this in the early 1970s is what initially forced me believe that God exists. Why or how He exists is a subject for theologians.

Readers might also want to read Nobel physicist Eugene Wigner's famous 1960 essay The Unreasomable Effectiveness of Mathematics in the Natural Sciences. in which he also ponders the reality of "the ultimate truth".

Stupid Eclipse Thing — Posted Wednesday April 3, 2024
On April 8 (which would have been my late wife's 78th birthday), a total solar eclipse will pass over a large swath of the United States. Although many people are looking forward to it, Time Magazine is reporting its downside—major traffic jams in affected states.

The article reminded me of similar traffic problems during an eclipse from years ago, when CNN aired several interviews with people on the street. I'll never forget one woman's comment, which went something like "This eclipse thing is so stupid. I don't know why they're having it in the first place."

i am mad as hell — Posted Tuesday April 2, 2024

No, the title of this post is not from poet e.e. cummings, but from a book I read in high school entitled The Life and Times of Archy and Mehitabel, a collection of poems from 1920s writer Don Marquis and cleverly illustrated by period artist George Herriman of Krazy Kat fame. The post title comes from the "archy declares war" poem.

Archy is a large cockroach whose soul transmigrated from an undated poet, but presumably from Shakespeare's time. He lives in an office, subsisting on stale library paste, and at night when the office is vacant he laboriously loads a typwriter with paper and composes his poems by painfully leaping upon the keys. He is unable to operate the CAPS key, so all his work is in lower case.

Archy has a friend, a scroungy female alley cat named Mehitabel (which means "God rejoices" in Hebrew). He is accompanied by an assortment of other odd characters whose activities he records in his poetry.

Archy also manages to visit nearby venues, including a museum and a radio facility, where he communicates with Mars. Perhaps the best poem results from his visit with an Egyptian pharaoh's mummy at the museum ("archy interviews a pharaoh"). After many millennia, the pharaoh reveals a dying thirst for beer, but Archy has to tell him "my reverend juicelessness this is a beerless country," as this is the Prohibition Era (1920-1933).

I recently found the free online book on the above link and fondly recounted how much of it I remembered verbatim after 57 years. I hope you'll enjoy it as well.

The Greatest Commandment — Posted Thursday March 21, 2024
When asked what the greatest commandment is in the Law, Jesus replied:
"Love the Lord your God with all your heart and with all your soul and with all your mind." This is the first and greatest commandment. And the second is like it: "Love your neighbor as yourself." All the Law and the Prophets hang on these two commandments. — Matthew 22:37-40
That second one is the harder of the two, at least for me, and it's probably true for the entire human race. From time immemorial, people have persecuted and slaughtered one another despite enormous advances in knowledge, technology, education and communication and despite all of our collective so-called intelligence, and we're not only no better off today but poised on the brink of global self-destruction. Why? Because we allow ourselves to be deluded by deep-rooted hatreds and biases, fed by egomaniacal, power-hungry demagogues from Alexander the Great to Vladimir Putin, Donald Trump, Kim Jong Un and their morally corrupt ilk today. Recently, Trump's son-in-law advocated kicking all Palestinians out of Gaza into the Negev Desert to allow Israel to bulldoze the region so that investors like himself could make fortunes building luxury ocean front communities, not for returning Gazans but for Israeli settlers.

I'm in despair today. How am I expected to love these monsters and their insane followers, and to follow Christ's related command that we love our enemies and do good to those who hate us? (Luke 6:27)

I dare readers of this site to watch this non-religious 15-minute After Skool video on why education and intelligence do not necessarily lead to wisdom, and how they can actually feed our destructive delusions.

All Black Holes Rotate — Posted Thursday March 21, 2024
In German physicist Sabine Hossenfelder's latest video, she tries to explain several anomalous aspects of Sag A\(^*\), the supermassive black hole at the center of our Milky Way galaxy. She claims that the rotation rate of a black hole is limited by the speed of light, but this isn't strictly true.

For a non-rotating black hole, the first two terms in its metric (the famous Schwarzschild solution, discovered in 1916 by Karl Schwarzschild) are given by $$ ds^2 = \left( 1 - 2 m/r \right)\, c^2 dt^2 - \frac{1}{1 - 2 m/r}\, dr^2 $$ so that, at \(r = 2 m \), the second term goes to infinity. This is the Schwarzschild radius, which defines the black hole's event horizon, from which nothing can escape. (Similarly, \(r = 0\) also takes things to infinity, which defines the hole's central singularity.) However, the Schwarzschild black hole is a convenient fiction, because all black holes rotate to some extent. The same two terms in the metric of a rotating black hole (discovered by New Zealand physiciat Roy Kerr in 1963) are given by $$ ds^2 = \left( 1 - \frac{2m r}{r^2 - a^2 \cos^2\theta} \right)\, c^2 dt^2 - \left( \frac{r^2 - a^2 \cos^2\theta}{r^2 + a^2 - 2m r} \right) dr^2 $$ where \(a\) is proportional to the hole's rotational angular momentum. Oddly enough, the point \(r = 0\) is no longer a problem, but setting the denominator of the second term to zero we have the point $$ r = m \pm \sqrt{m^2 - a^2} \tag{1} $$ which takes that term to infinity. (Note that for \(a = 0\), we recover the Schwarzschild problem points \(r = 2m\) and \(r = 0\).) From (1), it's obvious that it's not possible for \(a \gt m\), so that \(a = m\) defines the maximum rotation rate of a physical black hole (no black holes observed to date have been shown to exceed this limit). I can't see how the speed of light has anything to do with this limit.

The full Kerr metric is very complicated, and its implications for distinquished regions near the black hole are nothing short of amazing. (I suppose, however, that the limiting speed of light is buried somewhere in both metrics, so Hossenfelder may be right after all.)

Gravitons from Protons? — Posted Tuesday March 19, 2024
Really?!

This recent Quanta article talks about new research into the structure of protons.

Although protons are conventionally thought to be composed of three quarks (two up and one down) connected by gluons, it has become apparent that the internal workings are more like a zoo of quarks, gluons and virtual particles that respond to typical high-energy observations as though just three quarks existed. But by slamming protons much more forcefully with electrons, new features appear that seem to indicate that the interior of a proton is subject to truly enormous forces and pressures.

The Quanta article raises the question of how the energy-momentum tensor of these forces and pressures plays a role in proton structure and internal behavior. The energy-momentum tensor is usually reresented by a symmetric, ten-component \(4 \times 4\) matrix denoted by \(T^{\mu\nu}\), where the components represent energy density and momentum. The appearance of this tensor in particle physics studies seems very odd to me, since it usually appears only in the ten Einstein field equations of gravity expressed by $$ R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} \, R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu} $$ The gravitational force is always ignored in particle physics, mainly because particle masses are so small that their gravitational effects can be ignored. However, like mass-energy, pressure and force exert their own forms of energy, and if these are as truly enormous as indicated in the Quanta article, it's possible that gravity may play an important role in the structure of protons, especially considering the tiny distances involved. Recall that gravitational force \(F\) in Newtonian physics is given by $$ F = - \frac{G\,M\,m}{r^2} $$ where \(r\) is the distance between the two masses \(M\) and \(m\). For a proton, constituent distances are likely on the order of \(10^{-20}\) meters or smaller which, coupled with massive forces and pressures, might mean that gravity does indeed play a role.

Although the Newtonian force law has been verified down to sub-millimeter distances and sub-milligram masses, it's probable that it doesn't hold within truly tiny structures like protons and neutrons.

The Quanta article raises the possibility that high-energy electron-proton collisions can interact via the appearance of a graviton, the as-yet undetected force carrier of gravity, again promoting the (highly unlikely) possibility that gravity plays a role in particle physics.

The Butterfly Effect — Posted Tuesday March 12, 2024
Isaac Newton once stated that if one knew the precise position and momentum of every particle in the universe, then his Newtonian physics would be capable of predicting exactly how the universe was in the past and would be in the future.

In her latest video, German physicist Sabine Hossenfelder discusses why the Butterfly Effect effectively destroys Newton's claim, because the flapping of the wings of a certain lepidopteran insect in the Amazon forest might have an effect on the likelihood of a tornado in Laredo, Texas. Hossenfelder cites the work of the late mathematician Edward Lorenz on chaos theory, which posits that the initial conditions of a physical system, unless they're known exactly, can have enormous indeterministic effects on the system at other times.

However, what Newton and Hossenfelder fail to mention is that the meaning of the word "precise" is an impossibility. The effect of a butterfly flapping its wings can be made tantamount to knowing the one-zillionth decimal in the as-yet unsolved Navier-Stokes equation, gross approximations of which are used today in weather forecasting.

Hossenfelder also notes that not only can a butterfly theoretically affect the weather many thousands of miles away, but so can the happenstance position and arrangement of simple molecules in the environment. I would go even further to say that random quantum fluctuations can have the same indeterministic effect.

In short, I'd prefer to say that if the zillionth decimal in an otherwise reliable forecasting equation is unknown, then chaos will reign and we'll never know how to forecast accurate physical systems.

"Here in Pasadena, it is like Paradise!" — Albert Einstein — Posted Tuesday March 12, 2024
Tomorrow night (March 13) Caltech will present "Einstein in Pasadena - Between Two Worlds," a talk by Diana Buchwald, Professor of History and Director of Caltech's Einstein Papers Project. The talk is sold out, but you can watch it on YouTube when it has been posted.

Einstein spent three winters here in Pasadena (1931, 1932 and 1933), following a tour given to him by Edwin Hubble at the 100-inch Mount Wilson Telescope high above Pasadena. In 1929, Hubble was the first astronomer to prove the expansion of the universe, although it had been predicted theoretically by Russian physicist Alexander Friedmann in 1922.

During his first visit, Einstein stayed in the modest home of a Pasadena couple at 707 S. Oakland Avenue, but crowds of local gawkers made the visit difficult, so later he resided at Caltech's Athenaeum (I posted a link to the house as it looks today on the menu of my website).

Years ago my next-door neighbor (then a retired professor of linguistics at USC) personally saw Einstein give a dedication talk for a new telescope facility at nearby Pasadena City College (he told me he tried to get an autograph of the famous physicist, but was unable due to the crowds). The college's telescope and building still stand.

At the time of Einstein's last visit in 1933, Caltech's then-president Robert Millikan offered Einstein a professorship at the school. But personal differences between the two (Millikan was notoriously conservative, and he privately detested Einstein's progressive views), and in late 1933 Einstein fled Hitler's Germany to take a position at the Institute of Advanced Study at Princeton in New Jersey.

By the way, the Caltech talk is being given a day before Einstein's 145th birthday. March 14 (3.14), which is also celebrated as Pi Day!

You can watch it here.

That Which Was Lost is Still Lost — Posted Saturday February 24, 2024
Popular German physicist Sabine Hossenfelder seems to have turned primarily to science reporting, with a new video coming out almost daily now. Of course, her videos invariably include sponsor ads at the end, which is okay because a professor's salary only goes so far nowadays.

In her latest video she talks about the non-conservation of energy, something that conflicts with what every high-schooler is taught. It seems to arise only because the universe is capable of expanding or contracting according to the laws of general relativity. For example, every photon in the universe has a specific frequency \(\omega\) that endows the photon with an energy given by \(E = \hbar \omega \), However in an expanding universe the photon's wavelength (which is inversely proportional to frequency) gets stretched, which effectively reduces the photon's energy. Where does this energy go? According to Hossenfelder and most physicists, the energy is simply lost.

However, there is a kind of energy conservation law in Einstein's field equations, which are given by $$ R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu} $$ where \(T^{\mu\nu}\) is called the energy-momentum tensor. which is a measure of the total energy of a source of mass and/or radiation. Einstein's energy conservation law is given by the divergence quantity $$ \nabla_\nu T^{\mu\nu} = 0 $$ where \(\nabla_\nu \) stands for covariant differentiation. But strict energy conservation would be given by $$ \partial_\nu T^{\mu\nu} = 0 $$ in which \(\partial_\nu \) is the ordinary partial derivative. Try as he might, Einstein was never able to massage his gravity equations so that this latter divergence held. Consequently, energy is not conserved in our universe.

At the 5:08 point in Hossenfelder's video, she cites a recent paper by Russian researchers who try a form of modified gravity to answer the non-conservation issue. Hossenfelder is not crazy about the paper, but gives it some credit according to its innovative approach. However, I got nowhere with the paper, which you can download here. Good luck.

Meanwhile, here's Hossenfelder's informative video:


That Which Was Lost is Now Found — Posted Wednesday February 7, 2024
Imagine you're a librarian working in the ancient Roman resort city of Herculaneum in August of the year 70 AD. It's evening, and you've just finished rolling up scrolls of books that patrons have been reading. After placing the scrolls carefully on their shelves, you lock the place up and go home. That night you hear ominous sounds, followed by strong earth tremors. Then Mount Vesuvius explodes, sending fiery ash down on the town. You don't know whether to run or stay in your house, hoping the eruption will subside, as this has happened before. But the mountain explodes again, and this time it sends a pyroclastic flow of molten rock and fiery debris down on the town. Now you run, but you don't get far, as the air is hot and unbreathable. Your last thought is of your friends and family, and of course the fate of your beloved books. You end up under 20 feet of smoldering ash, your vaporized body becoming a hollowed-out cast.

The fate of those books was to end up as charred and blackened lumps too, but with each scroll still preserving its rolled-up shape. Modern investigators discover their remains, and a few efforts are made to unroll them to see what they have recorded. But those attempts fail, as the charred books simply fall apart into tiny bits of unreadable blackened soot.

For decades researchers have hoped that future technology would find a way to safely unwrap the scrolls, or at least provide a way of peering inside them so that they could be read. X-rays didn't work, and neither did MRI. But now machine-learning algorithms trained on the scrolls has partially revealed the Greek writing within, and artificial intelligence promises vastly greater success in virtually unwrapping the scrolls.

As reported in this new Scientific American, some several hundreds of blackened Herculaneum scrolls are being viewed as potentially important glimpses into the ancient world of Roman and Greek civilization. Perhaps some new mathematical discovery by Archimedes will be discovered, but at the present all we have is "Epicurus thinks his friend Philodemus is a know-nothing jerk." (My translation.)

That Was Then — Posted Monday February 5, 2024
We're getting record-setting tons of rain here in Southern California, so I have nothing to do but sit here and read, watch a little TV and reminisce. In my last post I mentioned how the quality of songs at live rock concert performances tended to be lousy compared with their recorded variants, but that ELO was a notible exception. Another exception was a high school performance put on by the long-extinct 1960s rock band The Bobby Fuller Four. which came to Duarte High School (California) in early 1966. Their only hit song that I recall was "I Fought the Law," a great song that still has no equal from the time as far as I'm concerned. The band performed it perfectly in our high school auditorium, and I still recall the girls (SHE in particular) going nuts over the band members, the late Bobby Fuller in particular.

The 1960s was a strange time for popular music in the sense that conventional rock music (the Rolling Stones' Get Off My Cloud, for example) could be heard on rock radio stations along with insipid niche tunes like They're Coming to Take Me Away and Baby Elephant Walk. There was no song vulgarity allowed in those days, of course, and I recall that when the Stones appeared on the Ed Sullivan Show to perform "Let's Spend the Night Together," the über-conservative Sullivan insisted that they sing it as "Let's spend some time together," a demand that the group ignored anyway, surely to Sullivan's dismay.

Here's a related photo from my 1966 high school yearbook. Upper left is Joey Paige, who sang "Goodnight My Love," followed by catcalls from the class audience to "Get a haircut!" To the right is our Senior Class President Chick Mangan welcoming Dick Biondi, a popular DJ from the radio station KRLA (he passed away in 2023). [I last saw Mangan in 1976 when he was a bailiff at a courthouse where I was a juror.] Lower left is The Deuces Wild, who performed something or other, and at the lower right is a stock publicity photo of The Bobby Fuller Four. You can read Page 9 of this old issue of KRLA Beat Magazine for more information, which indicates the bands came to Duarte High School in April 1966.

While it was nice of our high school president John McGrew to allow long-haired rock bands into the school, I never realized how preposterously conservative the school was at the time, along with most of its students and the town itself. The town's newspapers (The Duartean and The Daily News-Post) were very conservative news outlets, fully supportive of the Vietnam War, and they reported notoriously on several minor race riots the high school experienced involving attacks by whites against its few black students ("Hello" to my old friend Dumas M.!)

I suppose all that's nothing compared to what's going on in high schools today, with auditorium performances possibly involving half-naked twerking and gyrating performers. Sad.

Side Note: I just noticed the writer of the Page 9 article, one Marlyn S. Some of my fellow high school grads will definitely remember her:


I WANNA GO BACK! — Posted Monday February 5, 2024
In 1981 the Electric Light Orchestra released its futuristic rock music album Time, which included Here is the News. The song parodied likely news reports from a dysfunctional future Earth, all of them doom-laden. The album's songs reference the year 2095, far enough away from 1981 to lend the songs possible credence and yet portraying a frightening world sadly closer to our own time.

ELO is my favorite band, with lead singer/composer/guitarist Jeff Lynne taking top credits for the band's many hits of the 1970s through the 1990s. The Beatle's Paul McCartney was highly impressed with Lynne's innovative music, which combined rock with classical orchestral instruments, noting that had the Beatles stayed together their music would likely have pursued the same genre.

I have all of ELO's albums along with videos of the many live performances they made over the years. I was not, however, aware that music videos (remember them?) were also made of some of the lesser-known songs. "Here is the News" is one of them, featuring Lynne and his band members portraying news reporters. The lip-syncing is not great, but the song is. Enjoy.

Side Note: The music at most live rock concerts tends to sound far inferior to what you might hear on the radio or on CDs. One of the great things about ELO is the songs in their live performances sound almost exactly like their commercial recordings. I attended my first rock concert on July 5, 1968, when the Doors performed at the Hollywood Bowl, and they truly sounded awful.

Is AI Next? — Posted Saturday February 3, 2024
"**Gasp** I ... I've become radioactive!"

In the second episode of Season 7 of The Simpsons, Bart and his pals get their hands on an extremely rare copy of Radioactive Man No. 1, which details the events leading up to the main character's becoming radioactive and subsequently a superhero. Like Peter Parker being bitten by a radioactive spider and becoming Spider Man (yet another unlikely superhero), the comics are replete with such fortunate transformations thanks to radioactivity (I can name other examples from a misspent youth of reading comic books, but I won't). But in reality, most radioactive materials are highly dangerous, having the ability to irreparably damage cellular DNA, leading to fatal cancers, not superheroes.

In her latest video, physicist Sabine Hossenfelder recalls how x-ray radiation was discovered by the German physicist Wilhelm Roentgen. The discovery didn't involve radioactive materials, but x-rays quickly found favor with merchandisers and medical quacks who figured they must be beneficial to human health. With the exception of medical imaging, x-rays were found to be also damaging to human tissue in even moderate doses. In 1898, French chemist and physicist Marie Curie and her physicist husband discovered the radioactive element radium, which also quickly garnered favor with merchandisers and medical quacks. But unlike x-rays, the unregulated public use of radium (including direct ingestion to increase "vigor") proved to have tragic consequences.

Because radium glows green in the dark due to its radioactive decay, watch makers found it useful as a means of making luminous watch dials and numerals visible in the dark. Paint infused with radium was employed for this purpose, applied by lowly-paid female factory workers who used finely-tipped brushes. To maintain the brush tip, they routinely pressed the brush between their moistened lips, which inadvertently transferred radium into their mouths. This use of radium faded within several years, when many radium girls developed oral deformalities and fatal cancers. To my knowledge, none became superheroes.

Predicably, watch factory owners and radium paint manufacturers fought vigorously for many years against legal charges that their products were causing any harm. The story is detailed in the informative and entertaining 2018 film Radium Girls.

Also interesting in the same vein was the popular 1920s practice of grafting monkey and goat glands into men's testicles to increase virility. (I understand the practice is still popular among far-right Republicans and Trump worshipers.)

"Remember Amalek" — Netanyahu — Posted Thursday February 1, 2024
My dear late Egyptian wife Munira was a devout Christian, and while she did not hold any enmity against Israel she always believed that Israel's primary goal was to annex the entire region, including Gaza and the West Bank, leaving Palestinians to either get out, starve to death or be eliminated Nazi-style. By rejecting any possibility of a future two-state solution, Israeli prime minister Benyamin Netanyahu seems to have adopted that "solution" instead.

For years since Israel's politically-based foundation in 1948, Israeli settlers have encroached onto disputed lands, kicking out generations-long Palestinian property owners and establishing militarily-protected kibbutzim and similar collective settlements in lands once owned by Palestinians. The ongoing Gaza War is now providing additional opportunities for land grabs by Israeli settlers in the West Bank, and in recognition of this President Biden has issued an Executive Order focused on violence committed by Israelis seeking to take advantage of the Gaza War.

Since Israel does not recognize any US legitimacy in the West Bank, I say good luck, Mr Biden. Meanwhile, America yawns.

Hossenfelder Dumps Dark Matter — Posted Thursday February 1, 2024
German physicist Sabine Hossenfelder has apparently left the dark matter fold, admitting that she no longer believes it exists. She briefly supported the idea that some kind of universal "superfluid" was responsible, but to me the only viable option left is modified gravity. Einstein himself stated that his 1915 gravity theory (still the standard) would be shown to be only an approximation of the truth, but dark matter advocates have insisted that an undetected, unproven and hypothetical dark matter particle could be explained by other undetected, unproven and hypothetical particles, wasting billions of dollars in experimental efforts over the past 40 years. Perhaps now pen and paper will ultimately prove dark matter will go the way of the luminiferous aether, polywater, pixie dust and the unicorn.


Is Energy Actually Conserved? — Posted Friday January 19, 2024
On occasion, a stable and electrically neutral atom will emit an electron in a process known as beta decay, which occurs when a neutron in the atomic nucleus spontaneously turns into a postively charged proton. Electrical neutrality is conserved, however, with the creation and emission of the electron.

When first studied in 1930, it was noticed that the outgoing electron did not have sufficient kinetic energy for the conservation of energy of the entire system. The famous physicist Niels Bohr was ready to believe that energy conservation was violated in beta decay, but the equally brilliant Wolfgang Pauli postulated that an unseen particle was also emitted with sufficient energy to maintain overall energy conservation. Pauli called this particle a "neutron," but when the actual neutron was discovered in 1932 Pauli's particle was renamed the neutrino, meaning "little neutral one."

Pauli's postulated neutrino remained undetected until 1956, but zillions of neutrinos are now routinely manufactured in linear accelerators, and they're copiously produced in the core of our Sun. Today, the neutrino is an honored member of the Standard Model of physics.

The law of energy conservation is a foundation of physics, but when Einstein announced his gravitation theory in 1915 (and when the expansion of the universe was discovered in 1929) physicists noted that both discoveries seemed to violate energy conservation. Or at least, so it seemed.

There is undeed a foundational aspect of the conservation of energy and momentum in Einstein's theory, but there is a hitch. It involves the divergence of the energy-momentum tensor \(T^{\mu\nu}\), but this divergence is a covariant one, not one involving ordinary partial differentiation. Try as he might, Einstein was not able to break down the covariant divergence into an ordinary one, and to this day it remains a key reason why a gravity-filled, expanding universe does not appear to conserve energy.

Most physicists today believe that the law of energy conservation is simply not applicable to our universe, but many beg to differ. One is the astrophysicist Ethan Siegel, who kind of waffles on the subject in the linked article. His argument is based in part on the fact that universal expansion stretches the wavelengths of photons, which decreases their energy. Where does this energy go? Siegel posits that it may power the expansion of the universe itself, but he also indicates that it might simply be lost, and that the energy budget of the universe is not conserved.

By stretching the wavelength of photons, the notion of tension (which ia kind of force) enters the picture. A stretched photon involves an increase in its "length," and tension times length is equivalent to energy. I once believed that the lost energy was taken up by the dark energy of space, but the vastness of photonic lost energy and its assumed uptake by dark energy do not seem to match, at least observationally.

This conundrum is at least partly responsible for why I believe Einstein's gravity theory needs to be modified. Einstein himself thought that his theory, likr that that of Newton's, was an approximation to the truth deserving of future modification, despite its seemingly unerring success for the past 109 years.

In 1918 the German mathematical physicist Hermann Weyl believed he had glimpsed a means of modifying Einstein's gravity theory, and in pursuing it he thought he had found a way to unify gravity and electrodynamics. I won't go into it, but it involves changing the way length, time and energy are accounted for, and it might still be a way of showing that the law of energy conservation in the universe it actually upheld. As a devotee of Weyl's work, I've struggled to find a mathematical way of resolving the problem, to no avail. Maybe some bright kid will.

So Sad — Posted Thursday January 11, 2024
Three weeks after some 1,200 Israeli civilians were murdered by Hamas in its horrific October 7, 2023 attack on Israel from Gaza, Israel's Prime Minister Benyamin Netanyahu defiantly addressed his nation. In addition to a pledge to destroy Hamas, Netanyahu asked his country to "Remember what Amalek did to you." This was a reference to Deuteronomy 25:17-19, in which Moses says
Remember what the Amalekites did to you along the way when you came out of Egypt. When you were weary and worn out, they met you on your journey and attacked all who were lagging behind; they had no fear of God. When the Lord your God gives you rest from all the enemies around you in the land he is giving you to possess as an inheritance, you shall blot out the name of Amalek from under heaven. Do not forget!
After the death of Moses, his chosen general Joshua proceeded to attack Canaan (the Promised Land). The first to fall was Jericho, with the death of all its inhabitants, and then Joshua marched against the city of Ai, in which all of its 12,000 inhabitants were killed, with only 36 Israelite fatalities. Upon completion, Israel's conquest of Canaan resulted in the deaths of perhaps 60,000 people, including all of its men, women, children, livestock and food supplies.

Israel's current reprisal war against Hamas in Gaza has so far resulted in the deaths of 24,000 Palestinian civilians. The ratio of civilian to Israeli deaths is only 20:1, far below that of the attack on Ai, but that ratio is expected to increase dramatically before Hamas is convincingly defeated as a terrorist organization.

The International Court of Justice (the Hague) is considering an accusation from member nation South Africa that Israel is committing genocide against Palestinians living in Gaza. That accusation is open to debate, but Israel's indiscriminate and widespread bombardment of Gaza is reminiscent of the total destruction that the Israelites visited upon the cities of Canaan more than three millennia ago.

Netanyahu's "Remember Amalek" remark is also chillingly reminiscent of Moses' Deuteronomy command, and Netanyahu's refusal to accept a ceasefire in Gaza appears to reflect the same determination that Joshua expressed in utterly destroying his enemies. In addition, with Gaza likely to be reduced to complete rubble, Palestinian survivors and refugees will have little recourse but to flee to Egypt's Sinai, leaving Gaza open to permanent Israeli occupation and lucrative ocean-front resorts after rebuilding.

The hoped-for "Two-State Solution" is all but dead now, having been replaced by Netanyahu as a contiguous Israel. Perhaps next to go will be the West Bank Palestinians, and then the phrase "From the River to the Sea" (i.e., from the Jordan River to the Mediterranean Sea) will have a more ominous meaning than what pro-Palestinian demonstrators were hoping for.

Is it 67, 73 or Something Else? — Posted Thursday January 11, 2024
In my post of 4 December last year I pondered the possibility that a fuzzier or grainier aspect of the Cosmological Principle might account for the so-called Hubble tension in modern cosmology. With the possible exceptions of dark matter and quantum gravity, the Hubble tension represents cosmology's most perplexing mystery today.

The Hubble parameter is a description of the current rate of the expansion of the universe. The two main contenders for the parameter are based on measurements of the cosmic microwave background (CMB) and the cosmic distance ladder (CDL). The former gives a value of about 67 kilometers per second per megaparsec (km/s/Mpc), while the latter is about 9% higher at 73 km/s/Mpc. The uncertainties in the data do not overlap, resulting in the tension. One or both of the figures must therefore be wrong.

The cosmological principle is based on the assumption that—on average—the disribution of matter and energy in the universe is perfectly homogeneous and isotropic. This assumption is necessary if Einstein's gravitational field equations are to be capable of describing the universe, as any lumpiness (either locally or non-locally) is strictly incapable of being modeled. Nevertheless, the cosmological principle has been remarkably successful in predicting the evolution and probable fate of the universe and all manner of many astronomical observations.

In the latest episode of PBS Spacetime, astrophysicist Matt Dowd raises the possibility that non-uniformity may be the reason for the Hubble tension, at least on the local level of our galaxy. For one thing, it is known that our Milky Way Galaxy is located in a large relative void of matter, and this void might be affecting certain astronomical observations (mainly associated with Cepheid variables) giving an apparent overestimate of the Hubble parameter for the CDL approach. In one of the papers Dowd mentions, accounting for this void would lower the Hubble figure to about 69, in closer agreement with the CMB approach. On the hand, it is also known that the Milky Way is a member of a supercluster of some 100,000 neighboring galaxies called Laniakea, a Hawaiian word meaning "immense heaven." Some researchers believe this supercluster might have the oppsite effect on astronomical observations, making the actual Hubble papameter closer to the CDL approach.

The other three papers mentioned in Dowd's talk can be found here, here and here. While readable, extensive scattering of currently available astronomical data forces the papers' authors to use complicated statistical analyses that themselves are difficult to follow. Good luck.

It's 2981 — Posted Tuesday January 2, 2024
The recreational math website MindYourDecisions posted this fascinating puzzle today:

A clever wife, tired of her husband's spending habits, gives him free access to her private ATM account pending his ability to find the pin code, which is hidden in the solution to this integral:

Like me, hubby first resorts to Wolfram Alpha, which fails\(^*\). Noticing that the denominator can be factored, he then tries a solution using partial fractions, but this too goes nowhere. He then tries to do the integral by throwing thousands of random Monte Carlo points at the plot given at 5:40 in the video, hoping that the normalized area under the curve can provide the answer. When this also fails, he then just waits for the video to provide the answer.

But to his dismay, wifey has already changed the pin code. He, like me, has wasted several hours of his life for nothing.

\(^*\) Actually, Wolfram Alpha works just fine; I simply punched it in wrong the first time:


1924 — Posted Tuesday January 2, 2024
You have to be of a certain age if you've subscribed to Classmates.com, a free social networking website founded in 1995 (has the Internet really been around that long?) that displays photos and stories from past high school graduates and attendees. I signed up sometime after retiring in 2002 mainly to see what it was all about, but there wasn't much on it back then. Today, the site has nearly 100 million subscribers.

There are several other such classmate websites, and in 2006 I saw one post from an elderly graduate of the 1924 Quincy (Illinois) High School. As best as I can remember now, she wrote "I graduated from QHS in 1924 and am now almost 100 years old. My grandson is writing this for me. Is anyone from my class still out there?" I somehow contacted the woman's family, but I never got a response. She most likely passed on shortly after her inquiry.

Struck by the pathos of her post, that same year I added my father to the Classmates site (even though he died in 1981) to find out if there was anyone still alive from his graduation class. He too graduated from QHS in 1924, and I have his rather tattered graduation yearbook, which turns 100 years old in June (I bought the yearbook from eBay in 2007). Dad was 19 years old at the time, a year older than most high school graduates of today, but very common for kids at the time (graduation from high school back then was somewhat equivalent to graduating with an undergraduate college degree today).

I occasionally get messages from Classmates saying "Hello Ogden Straub! People want to see how you look today!" (No, they do not! 😜)


My father, from his 1924 yearbook

I'm now 75, and my high school graduation took place in 1967, going on 57 years ago. The yearbook sits on my bookshelf, and I wonder where it will end up when I'm long gone.

2024 — Posted Monday January 1, 2024
I'm praying for a happier, more peaceful and saner New Year, but I can't help but feel pessimistic. Two major wars are ongoing, with the possibility of expanding into regional, multi-country disasters, while at home the spectre of a Trump reelection will determine if America remains a democracy or a dictatorship.

Meanwhile, I just turned 75, and while I feel okay there's no denying that my body is now three-quarters of a century old. Ugh.
I feel old, Starbuck, and bowed. As though I were Adam, staggering beneath the pile of centuries since Paradise.
— Captain Ahab, Moby-Dick