Monday, September 25, 2023

The Essence of Relativity

Some say the essence of relativity is the Lorentz transformation, or the Minkowski metric, or the Michelson-Morley experiment, or the Einstein postulates. Here is my brief version.

Relativity is the study of the geometry of events in spacetime. An event is a position in three-dimensional space, along with a time. Euclidean geometry describes that space, but time is very different, as you can go back to the same position but not the same time. Relativity puts a non-euclidean geometry on spacetime that limits the speed of causality. Events can only affect nearby events if a light signal or slower signal can travel from one event to the other.

The first relativistic theory was devised by Maxwell in 1865. His electromagnetism theory used fields that propagate at the speed of light. This was in contrast to gravity, where similar inverse-square laws seem to act at a distance. He wondered whether this theory could detect the motion of the Earth. The Michelson-Morley experiment failed to do that in 1887, and seemed to show that the speed of light and the rest of Maxwell's theory was the same under inertial motion. Lorentz explained this by showing that motion modifies how we measure space and time.

Poincare and Minkowski showed in 1905-7 that there is a non-euclidean geometry on spacetime that underlies Maxwell's theory and explains the experiments. The theory can be expressed in equations that are covariant under the geometric symmetries. That geometric view came to dominate XX century Physics. It was important because it changed our understanding of space and time.

Einstein's chief contribution was to show that the Lorentz transformations could be derived from the principles that Lorentz and Poincare deduced from Maxwell and experiments. He never really accepted the geometric view.

Special relativity is the infinitesimal version of general relativity. Like a tangent line is the infinitesimal version of a smooth curve. In special relativity, the spatial part of spacetime is Euclidean, ie flat. Spacetime is curved in general relativity, and the Ricci curvature tensor is essentially the mass-energy.

When people say that relativity is non-euclidean, they usually mean that spacetime is curved from the gravity of mass. But the flat no-gravity tangents are also non-euclidean, because of the causality speed limit.

In my opinion, this non-euclidean geometry of flat special relativity spacetime is the true essence of relativity. It was what Minkowski explained in his wildly popular 1908 paper. That paper, along with experimental confirmations, is what sold physicists on relativity theory. Poincare's 1905 papers also had it, but were probably only understood by Minkowski and a few other mathematicians.

Most relativity historians ignore this essence, but see The Non-Euclidean Style of Minkowskian Relativity, by Scott Walter. It explains how Planck, Wien, Laub, Sommerfeld, Einstein, and German Physics journals all rejected the non-euclidean geometry approach around 1910-12. By then, Poincare and Minkowski were dead, and the biggest champion of it was Varicak.

General relativity was the natural generalization of special relativity, once the tools of Riemannian geometry were developed. Einstein's main contribution was to calculate the deflection of starlight during a solar eclipse, and the precession of Mercury's orbit.

The geometric view was accepted by most mathematical physicists from 1907 on, but rejected by Einstein and some later physicists, such as Steve Weinberg.

Thursday, September 21, 2023

Number 57 is Prime

So says the world's most famous mathematician, in a new paper. See page 27 where the authors apply their theory to example primes, 53 and 57. 53 is prime, but 57 is 19*3.

Apparently it is an inside joke among mathematicians to say 57 is prime, as if they cannot be bothered to check. See the Wikipedia article, where 57 is called the Grothendieck prime, as a math joke about the most famous abstract-thinking mathematician.

Monday, September 18, 2023

Big Oil Sued for Studying Uncertainty

There are lawsuits against Big Oil for supposedly deceiving us about climage change.

The London Guardian reports:

xxonMobil executives privately sought to undermine climate science even after the oil and gas giant publicly acknowledged the link between fossil fuel emissions and climate change, according to previously unreported documents revealed by the Wall Street Journal.

The new revelations are based on previously unreported documents subpoenaed by New York’s attorney general as part of an investigation into the company announced in 2015. They add to a slew of documents that record a decades-long misinformation campaign waged by Exxon, which are cited in a growing number of state and municipal lawsuits against big oil. ...

In 2008, Exxon pledged to stop funding climate-denier groups. But that very same year, company leadership said it would support the company in directing a scientist to help the nation’s top oil and gas lobbying group write a paper about the “uncertainty” of measuring greenhouse gas emissions.

The company’s preoccupation with climate uncertainty continued. Before one meeting with company scientists in 2012, one researcher expressed an interest in finding “‘skeptic’ arguments that we consider to be not yet disproven”.

Wow, there is some confusion here on what science is all about.

There cannot be anything wrong with an oil company hiring a scientist to write a paper on the uncertainty of measurements. Every science paper should estimate the uncertainty of whatever is being measured. And they should all examine skeptic arguments.

Of course industry-sponsored research may not agree with environmentalist-sponsored research. It should all be published anyway.

Thursday, September 14, 2023

White Males no longer welcome in Academia

Physicist Larry Krauss has the story:
Let’s start at the top. Six of the eight Ivy League universities—Harvard, Brown, Penn, Cornell, Dartmouth, and Columbia—now have female presidents, as do UC Berkeley and MIT.

MIT is a particularly striking case. Despite comprising many traditionally male-dominated STEM disciplines, its upper management team is largely female. The head of the MIT Corporation, the President, the Director of Research, the Provost, the Chancellor, and the Dean of Science are all women. The Institute’s core discipline, the School of Engineering, consists of eight departments, five of which are led by women. This is clearly not a coincidence, nor is it likely, given the demographics of the place, that this is simply the result of choosing the best people for those jobs. ...

We can see the results of this in the California State universities: the undergraduate student body at Cal State Los Angeles is 59 percent female, and 67 percent of its graduate students are female; Sonoma State is 63 percent female; San Diego State is 57 percent female; Humboldt State is 58 percent female; Cal State East Bay is 61 percent female. Nationwide, around 60 percent of students are female. ...

It is no surprise to see a high prevalence of Indian and Chinese students among this group, as East and South Asians have been outperforming white students for some time. What is perhaps more surprising is that the finalists included only one young Caucasian male.

A century ago, there were top-level respected female scientists, like Marie Curie and Emmy Noether. Supposedly women dropped out to have babies in the 1950s. By the 1970s, top colleges were aggressively recruiting female stusents and faculty. Now, 50 years later, there is no need.

Monday, September 11, 2023

Ehrenfest paradox and the Psychological Contraction

The Ehrenfest paradox was to apply special relativity to a rotating disc, and finding some geometrical oddities. It requires non-Euclidean geometry to resolve it. It is a good test of how well early physicists understood relativity. Einstein wrote about it many times.

Einstein historian Tilman Sauer wrote in 2007 about Einstein correspondence with Vladimir Varićak:

These were rebutted by Einstein in a response of 28 February 1910 in which he also, with reference to Ehrenfest’s paradox, referred to the rigidly rotating disk as the “most interesting problem” that the theory of relativity would presently have to offer. In his next two letters, dated 5 and 11 April 1910 respectively, Einstein argued against the existence of rigid bodies invoking the impossibility of superluminal signalling, and also discussed the rigidly rotating disk. A resolution of Ehrenfest’s paradox, suggested by Vari´cak, in terms of a distortion of the radial lines so as to preserve the ratio of π with the Lorentz contracted circumference, was called interesting but not viable. The radial and tangential lines would not be orthogonal in spite of the fact that an inertial observer comoving with a circumferential point would only see a pure rotation of the disk’s neighborhood.

About a year later, Einstein and Vari´cak corresponded once more. Vari´cak had contributed to the polemic between Ehrenfest and von Ignatowsky by suggesting a distinction between ‘real’ and ‘apparent’ length contraction. The reality of relativistic length contraction was discussed in terms of Ehrenfest’s tracing paper experiment, but for linear relative motion. According to Vari´cak, the experiment would show that the contraction is only a psychological effect whereas Einstein argued that the effect will be observable in the distance of the recorded marker positions. When Vari´cak published his note, Einstein responded with a brief rebuttal.17

Sauer is trying to be favorable to Einstein. Varicak wrote several papers on applying non-Euclidean geometry to special relativity, and Einstein rejected this approach. Varicak's explanation was viable, and better than Einstein's.

The idea that the Lorentz contraction was "psychological" appears to have originated in this 1909 American article:

Let us emphasize once more, that these changes in the units of time and length, as well as the changes in the units of mass, force, and energy which we are about to discuss, possess in a certain sense a purely factitious significance; although, as we shall show, this is equally true of other universally accepted physical conceptions. We are only justified in speaking of a body in motion when we have in mind some definite though arbitrarily chosen point as a point of rest. The distortion of a moving body is not a physical change in the body itself, but is a scientific fiction.

When Lorentz first advanced the idea that an electron, or in fact any moving body, is shortened in the line of its motion, he pictured a real ​distortion of the body in consequence of a real motion through a stationary ether, and his theory has aroused considerable discussion as to the nature of the forces which would be necessary to produce such a deformation. The point of view first advanced by Einstein, which we have here adopted, is radically different. Absolute motion has no significance. Imagine an electron and a number of observers moving in different directions with respect to it. To each observer, naïvely considering himself to be at rest, the electron will appear shortened in a different direction and by a different amount; but the physical condition of the electron obviously does not depend upon the state of mind of the observers.

Although these changes in the units of space and time appear in a certain sense psychological, we adopt them rather than abandon completely the fundamental conceptions of space, time, and velocity, upon which the science of physics now rests. At present there appears no other alternative.

This is all completely correct, but rejected by Einstein. Based on this paper, Varicak attributes the new view of space and time to Einstein, but Einstein published a rebuttal denying that his viewpoint was any different from Lorentz's.

The issue here is: Do rigid bodies really contract, or is the apparent contraction just an artifact of the non-euclidean geometry of spacetime?

Lorentz would say the former, while Minkowski proposed the latter in 1907 and that has been the preferred interpretation in textbooks ever since.

Poincare also proposed the latter in 1905, but said that the views were mathematically equivalent, so he would say that they were both correct. In his view, the contraction is "only apparent, something which would be due to our methods of ​measurement".

What would Einstein say? The latter view seemed to be attributed to him in the above 1909 paper, and repeated by Varicak in his 1911 paper on the Ehrenfest paradox, which says, "contraction is only an apparent, subjective phenomenon, caused by the manner of our clock-regulation and length-measurement." We can be pretty sure the attribution is incorrect, because Einstein published a rebuttal to that 1911 paper. Einstein corresponded with Varicak and was fascinated by the subject, so I think he was clearly favoring Lorentz's view during 1905-1911, at least. He could have accepted credit for the geometrical view, but he vigorously denied it.

This is the clearest evidence that Einstein did not understand and accept special relativity, as it has been explained by Minkowski in 1907 and every textbook since.

Marco Giovanelli has written a new paper on Appearance and Reality: Einstein and the Early Debate on the Reality of Length Contraction. It has a lot of historical info on this issue.

In Einstein’s theory, length contraction is a kinematic effect that depends on the definition of simultaneity; however, it is just as real as length contraction in Lorentz’s theory, where it is conceived as a dynamic effect due to the motion of a rod through the ether. The two theories derive the same quantitative measure for the contraction through different routes. To explain this point, Einstein resorts to his beloved comparison between relativity theory and thermodynamics:
One cannot ask whether the contraction should be understood as a consequence of the modification of molecular forces caused by motion or as a kinematic consequence arising from the foundations of the theory of relativity. Both points of view are justified. [letter to Varicak, 1911]
He also relates it to Bell's spaceship paradox.

Einstein is correct that different points of view about the contraction are justified. The first view, "a consequence of the modification of molecular forces caused by motion", is usually attributed to Lorentz. The second view refers to Einstein's 1905 two-postulate approach. Einstein appears to say that it is meaningless to say which is better.

The approaches were logically equivalent. Lorentz started from the Michelson-Morley experiment and Maxwell's equations, and deduced the contraction. Einstein postulated the constant speed of light and the Poincare relativity principle, and made the same deductions. Neither really analyzed the molecular forces. Lorentz did correctly believe that the forces were electromagnetic, and hence subject to his transformations.

What is missing from Einstein's 1911 comments is any recognition of the non-euclidean geometry view put forward by Poincare in 1905 and Minkowski in 1907.

In the writings of those years, Einstein appears to have still been reluctant to embrace Minkowski’s (1909) reduction of kinematics to geometry. Indeed, he presented the key result of relativity as the distinction between the geometric and the kinematic configuration of a body (Einstein, 1908, 1910, 1911a).29 (In modern terms, the distinction between the proper and the coordinate shape of a body.)
Einstein would often argue that his approach was not ad hoc. and hence superior to Lorentz's.
Lorentz complained that, in a popular article, Einstein had referred to the Lorentz-Fitzgerald contraction as a “hypotheses invented ad hoc” (Einstein, 1915, 707) to neutralize Michelson’s result (Lorentz to Einstein, Jan. 1, 1915; CPAE, Vol. 8, Doc. 43). Lorentz argued that such an objection might have applied to his first formulation of the contraction hypothesis. At a later stage, however, reacting to Poincaré’s criticism, Lorentz provided a coherent theory of matter from which length contraction can be derived as a consequence. Lorentz regretted not having stressed this more, as it would have left less of an impression of being an ad hoc hypothesis (Lorentz to Einstein, Jan. 1, 1915; CPAE, Vol. 8, Doc. 43).

Lorentz argued that Einstein’s approach was somewhat misleading from a “didactical” point of view (Lorentz to Einstein, Jan. 1, 1915; CPAE, Vol. 8, Doc. 43). If the contrac- tion is derived as a consequence of the new kinematics “and nothing more is added in commentary”, it could give rise to the suspicion that “only ‘apparent’ [scheinbare] things were involved here and not a real [wirkliche] physical phenomenon” (Lorentz to Einstein, Jan. 1, 1915; CPAE, Vol. 8, Doc. 43). ...

Once again, Einstein replied by alluding to a more subtle dialectic between the real and the apparent:

... Regarding the erroneous view that the Lorentz contraction was ‘merely apparent,’ [scheinbar] I am not free from guilt, without ever having myself lapsed into that error. It is real [wirklich], i.e., measurable with rods and clocks, and at the same time apparent [scheinbar] to the extent that it is not present for the co-moving observers.39 (Einstein to Lorentz, Jan. 23, 1915; CPAE, Vol. 8, Doc. 47)

So Einstein's differences with Lorentz were slight, and mostly have to do with Einstein trying to take credit for what Lorentz had already done. Einstein never says Lorentz was wrong, but he does say that the geometrical view is wrong:
Perhaps Mr. Varičak might admit—and thus in a way retract his assertion—that the Lorentz contraction is a ‘subjective phenomenon.’ But perhaps he might cling to the view that the Lorentz contraction has its roots solely in the arbitrary stipulations about the ‘manner of our clock regulation and length measurement.’ The following thought experiment shows the extent to which this view cannot be maintained. (Einstein, 1911d, 509)
Einstein is wrong here. The modern view is that our manner of clock regulation and length measurement corresponds to a non-euclidean geometry on spacetime. The contraction is subjective in the sense that it only shows up in the comparison between the true non-euclidean geometry and the more intuitive Euclidean geometry. That is what Poincare said in 1905, Minkowski in 1907, and Varicak in 1911. Einstein did not understand it.

I have posted many criticisms of Einstein's lack of originality. Many of these are not new, as Whittaker argued in a 1953 book that Lorentz and Poincare had all of special relativity. Lorentz said back in 1909 that Einstein just postulated what was previously proved. But I have not seen anyone else make the point I make here. That the modern geometrical view of relativity was explicitly rejected by Einstein as late as 1911.

Even when experts were starting to credit Einstein with the new geometrical view of relativity, he was adamantly denying it.

There are Einstein fans who claim that Lorentz and Poincare never really understood special relativity, based on post-1905 lectures or writings that supposedly showed confusion about fundamentals. Usually the argument is that Poincare occasionally chose an preferred reference frame. But of course choosing a preferred frame is not incorrect or contrary to modern thinking. Everyone chooses preferred frames all the time.

Einstein is not wrong either when he clings to a Lorentzian anti-geometry view. But he is contrary to modern thinking, and he was wrong to say that Varicak's "view cannot be maintained."

Einstein did eventually accept non-euclidean geometry, as Grossmann, Levi-Civita, and Hilbert convinced him that it was necessary for general relativity in 1913-1916. But he never really accepted the geometric view, and never accepted Varicak's argument.

If you are a physicist reading this, you might complain that I am a mathematician siding with other mathematicians -- Poincare, Varicak, Hilbert, Whittaker -- against the great physicist Einstein. Einstein's genius was in Physics, not Mathematics, and maybe it is unfair to judge him by mathematicians. Maybe so, but I am discussing the mathematical understanding of relativity, and Einstein's was deficient.

Einstein's special relativity did not have anything physically new. The physical predictions were the same as Lorentz's, and physicists called it the Lorentz-Einstein theory. The only appeal was his mathematical derivation. So yes, I think it is fair to judge his mathematics by mathematical standards.

It is hard to understand just what Einstein's view was. Giovanelli writes:

What is clear is that in the following months, Einstein made the first published reference to Ehrenfest’s thought experiment in a paper on gravitation published in February, where he pointed out that the geometry of the rotating disk is non-Euclidean (Einstein, 1912a, 356). Since a rotating system is equivalent to a system at rest in a suitable gravitational field, Einstein (1912b, 1064) soon began to realize that the traditional physical interpretation of coordinates as readings on rods and clocks could not be maintained in the presence of gravitation (see Stachel, 1989, for more detail).

After returning to Zurich, Einstein famously found a solution to the conundrum with the help of his friend Marcel Grossman. However, his struggles with the meaning of coordinates in physics continued during the Berlin period (Giovanelli, 2021).

In modern terminology, spacetime is a 4-dimensional manifold, with many coordinate systems possible, not necessarily having physical significance. Grossmann and others tried to convince him to use covariant tensors, but during 1913-15 he was persuaded by his Hole Argument that such things were impossible. It appears that Hilbert enlightened him to use covariant equations.

In the Lorentzian view, bodies really contract. In the Poincare-Minkowski-Varicak mathematician view, the contraction is an artifact of using coordinates that do not match the geometry. Einstein did not seem to be fully in either camp, and saying only that the contraction is required by the kinematics.

Here is an argument from the above 1909 article:

If our ideas possess a certain degree of artificiality, this is also true of others which have long since been adopted into mechanics. The apparent change in rate of a moving clock, and the apparent change in length and mass of a moving body, are completely analogous to that apparent change in energy of a body in motion, which we have long been accustomed to call its kinetic energy.
An object at rest has no kinetic energy. If you watch it from a moving frame, all of a sudden it has kinetic energy. Where did that energy come from? The energy is not real. It is just an artifact of the coordinates being used. It is just psychological. Not imaginary. If a brick hits you in the head, your pain will be real. The energy is measurable.

The best way to make sense of this is to say spacetime is a manifold with a non-euclidean geometry.

Tuesday, September 5, 2023

Celebrating the Prize for Bell Experiments

A new paper starts:
The 2022 Physics Nobel Prize was not quite like any other. While the Nobel prizes in physics are always of interest to the physics community, by a rule, they are merely a matter of curiosity for the general public. However, the latest Nobel award should pertain to all of us, ir- respective of the profession, and remind us that it’s been a time to rethink our basic worldviews.
No, it did not change anyone's worldview. The experiments only confirmed what had been conventional wisdom since 1930.
While there might not be a consensus on whether it is the idea of separability (locality) or reality that should give in, or maybe that we live in countless parallel universes, there is an absolute consensus in contemporary physics that the hopes of ever returning to anything resembling classical physics are long over.
Again, classical physics has been rejected since 1930.
Einstein, who still believed that the universe is something akin to a huge deterministic clockwork mechanism, was essentially the sole exception among this elite – and his expectations in this context were, as we have seen, explicitly proven wrong.
That's right, Einstein was one of the last holdouts, clinging to classical ideas that everyone else had rejected.
And, finally, once it was experimentally established that Bell’s inequalities are indeed violated in our universe, we encountered a truly unique situation in the entire history of science. Never before has humanity been in the necessity to abandon an entire paradigm because of a proof of mathematical nature that could guarantee that our previous scientific view – in a quite broad sense – was plainly wrong. ... We are speaking of abandoning the entire scientific worldview that was absolutely dominant for a few centuries (at least in exact sciences). It was dominant to the extent that we, for the most part, tacitly understood it surely must be the correct one, so that rarely anyone even bothered to question it.
People were saying this in around 1930, as the pre-1925 classical physics had been abandoned on atomic scales.

The paper quotes historical physicists, and discusses a range of Bell issues from many-worlds to superdeterminism.

It is indeed remarkable that everyone accepted the new quantum theory between 1925 and 1930. Everyone but Einstein. But it is old news, as has been for 90 years. It is almost as if someone concocted a new way to test relativity theory, and then all the science journals published essays about the reality of time.