Does E=mc^2 Require Relativity?

Physicist Tony Rothman has a new paper arguing that one can get the famous Einstein mass-energy equivalience E = mc² before Einstein's 1905 paper, and without relativity. In particular, it appears in a 1900 Poincare paper.

Many physicists, for instance, are under the impression that ℰ=m⁢c² can be established by employing the four-vector formalism of special relativity. An early draft of Wikipedia’s page on mass-energy equivalence in fact offered exactly such a “derivation.” Four-vectors, however, are defined in order to be consistent with ℰ=m⁢c²; consequently any argument based on them to prove the relationship is circular. ...

A universal, assumption-free proof of ℰ=m⁢c² is no more attainable than a universal proof of conservation of energy or momentum, and the very idea that all physics can be derived from a master Lagrangian without experimental input must be doomed to failure. For that reason, all demonstrations of mass-energy equivalence rely on specific assumptions and approximations. The closest thing that exists to a general proof of ℰ=m⁢c² is the Laue-Klein theorem [16, 17, 18] of 1911 and 1918, which in essence states that if ℰ=m⁢c² holds for a point mass, then it also holds for an extended closed system, under specified boundary conditions. If radiation can escape to infinity, for example, the boundary conditions are evaded.

Einstein was aware of the inadequacies of his 1905 article and attempted to correct them in six further papers, but as Ohanian argues [19], none is free of errors and inconsistencies. Physicists who have actually read the 1905 paper know that the dubious step is the final one, in which Einstein relies on the Newtonian value for the kinetic energy. ...

Can one arrive at ℰ=m⁢c² in a consistent and plausible manner using only Galilean mechanics and “perhaps Maxwellian” electrodynamics?

Okay, but Maxwellian electrodynamics is a fully relativistic theory, if interpreted correctly. The whole theory of special relativity is mostly a recognition of that fact.

Another Misreading of Bell's Theorem

There is a steady stream of crackpot papers that misrepresent Bell's Theorem. The Wikipedia description is adequate:

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement.

It does not say anything about reality, or quantum mechanics, except that we cannot replace QM with a local hidden variable theory.

Here is a new paper that gets it wrong:

Allori, Valia (2024) “Hidden Variables and Bell’s Theorem: Local or Not?”. [Preprint] ...

Equation (2) might misleadingly suggest that Bell’s reasoning only applies to hidden variable theories. This is not the case, as discussed later: Bell has shown that all quantum theories, not just hidden variable ones, must be nonlocal. ...

To summarize the result of the previous section, Bell’s theorem shows that, assuming locality, the perfect (anti)correlations can only be explained by non-contextual hidden variables; however, non-contextual hidden variable theories have been empirically falsified by the violation of Bell’s inequality, when seen as a constrain that such theories need to obey to. Therefore, they only other option to explain the perfect (anti)correlations is to assume that there are nonlocal interactions. ...

Some have argued that Bell’s nonlocality result is unacceptable and have tried to get around it. One possibility which has recently received attention is to reject a hidden assumption called statistical independence. ...

Let’s grant that Bell’s theorem has proven that reality is nonlocal. One theory which respects this theorem is the pilot-wave theory, a hidden variable theory which is explicitly nonlocal. ...

It has been argued that retaining locality would be a desideratum for making quantum mechanics and relativity compatible. However, since locality has to come together with superdeterminism, it is not going to help with much at all.

No. Bell's reasoning does only apply to hidden variable theories. It only gives reasons to accept QM, and reject Bohm's theory and superdeterminism.

The main point of this paper is to argue that superdeterminism is no better than Bohm's theory. As opposed to people like Sabine Hossenfelder who argue for superdeterminism.

A lot of people, like Sean M. Carroll, were hoping that the 2022 Nobel Prize would endorse Bell nonlocality. But it pointedly did not.

The Wikipedia article occasionally has someone inserting text that Bell figured out how to get rid of the hidden variable hypothesis, and apply the theorem to all theories. But that is nonsense, of course.

New video: The 'spooky' side of quantum physics | Tim Maudlin on astonishment and fear in #quantumphysics.

Maudlin admits at 10:30 that you get a similarly spooky and incomplete theory if you tear a dollar bill in two, and send the halves to Alice and Bob. When Alice opens the envelope, she immediately knows what Bob got.

So the entanglement itself is not spooky or surprising. The only surprising part is that QM cannot be completed with local hidden variables. Maybe Maudlin explains that later. Reply

Epicycles are Real

A reader cites Carl Sagan's 1980 Cosmos a personal journey Ep. 3. Harmony of the Worlds (video, transcript).

This little machine shows Ptolemy’s model. The planets were imagined to go around the Earth, attached to perfect crystal spheres — but not attached directly to the spheres, but indirectly, through a kind of off-center wheel. The sphere turns, the little wheel rotates, and — as seen from the Earth — Mars does its loop-the-loop. This model permitted reasonably accurate predictions of planetary motion: where a planet would be on a given day. Certainly good enough predictions for the precision of measurement in Ptolemy’s time and much later. Supported by the church through the Dark Ages, Ptolemy’s model effectively prevented the advance of astronomy for 1,500 years.

Finally, in 1543, a quite different explanation of the apparent motion of the planets was published by a Polish cleric named Nicolaus Copernicus. Its most daring feature was the proposition that the sun, not the Earth, was the center of the universe. The Earth was demoted to just one of the planets. The retrograde (or loop-the-loop) motion happens as the Earth overtakes Mars in its orbit. You can see that, from the standpoint of the Earth, Mars is now going slightly backwards and now it is going in its original direction. This Copernican model worked at least as well as Ptolemy’s crystal spheres, but it annoyed an awful lot of people. The Catholic Church later put Copernicus’s work on its list of forbidden books.

So Ptolemy developed a reasonably accurate model, but it was somehow used by the Catholic Church to keep everyone in the Dark Ages?

No, this is mostly nonsense. The Church only objected to nine sentences in the Copernicus book, and not to publication of the model. Ptolemy did not require crystal spheres.

The Wikipedia article on epicycles is much more sensible:

Epicycles worked very well and were highly accurate, because, as Fourier analysis later showed, any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles. However, they fell out of favor with the discovery that planetary motions were largely elliptical from a heliocentric frame of reference, which led to the discovery that gravity obeying a simple inverse square law could better explain all planetary motions.

The first Ptolemy epicycle for each planet is the orbit of the Earth, and is used to explain the retrograde modtion. People can argue that this epicycle is not real, because Mars never really goes backwards. But Mars does go backwards, as viewed from the Earth, and that is what Ptolemy was modeling.

Subsequent epicycles were used to model variations in speed and direction from uniform circular motion. The Copernicus model did not need the first epicycle, as the Earth had its own orbit, but needed the subseqent epicycles, as deviations from uniform circular motion was observable at the time.

As Sagan later explained, Tycho Brahe made the observations that enabled models superior to Ptolemy's. Astronomy was not held back by epicycles, but by a lack of more precise data. That data came from Tycho, and later the invention of the telescope

Sagan pushes his anti-religion beliefs, but all these advances took places in Christendom, and not elsewhere.

Situational Awareness

The AI world is buzzing with the predictions of Leopold Aschenbrenner. It has some overlap with the AI doomsayers who say AGI superintelligence will take over the world, except that he has inside knowledge from OpenAI, and he has specific arguments how it is all going to happen in the next five years.

Scott Aaronson raves about the analysis.

Interestingly, Aschenbrenner sees his fellow AI researchers as being among the first to be put out of work by the new superintelligence. There is a global arms race to create the best AI, and by 2030, the winner will be doing its own research to improve itself. No humans needed, except to keep mounting Nvidia computers into server farms.

Update: Sabine Hossenfelder posts her critique. She agrees with some of it, but gets off the bus with the wild predictions of scientific progress.

Carroll tries to defend Many-Worlds again

Physicis Sean M. Carroll tries to answer this question:

Joel remok says if we can't access any of the many worlds, what 2:31:07 is the purpose of studying it, when there are still many discoveries to be investigated in the reality we exist in?

Good question. There is no point in talking about parallel worlds that we can never see or know anthing about.

The transcript of his answer:

2:31:13 look I've said before I don't care about the other worlds I care about the laws of physics the question is we have 2:31:20 problems with quantum mechanics as it is taught it is not a sensible rigorous coherent Theory. we make things up like 2:31:28 observations and wave function collapse that aren't rigorously defined. many worlds is a well-defined theory that 2:31:37 replaces the ill defined Copenhagen interpretation and lets us actually do science with it. the point of many worlds 2:31:44 is not the other worlds. it's that we've answered the question of what is a measurement, why do you get probability, 2:31:50 and things like that, and equally importantly there's the fact that we don't know the fundamental laws of 2:31:56 physics. we're not done with physics yet we're trying to build better laws of physics and I strongly think that taking 2:32:02 quantum mechanics seriously and thinking about what is the correct foundational version of quantum mechanics will be 2:32:09 useful to that program. so again it's not about the worlds. people who really 2:32:15 obsess about the other worlds are the ones who haven't really internalized many world worlds many worlds is just 2:32:22 it's always obeying the Sher equation that's the essence of the theory

No, this is nonsense on every level.

Many-worlds does not answer the question of what is a measurement. It says that a measurement splits the worlds, but there is no explanation of how the worlds split, how many worlds there are, how you knowt he worlds have split, or anything. It is no better than how bohr explained it.

Many-words says nothing about how we get probabilities. The many-worlds folks do not even believe in probabilities.

Saying that Copenhagen is ill-defined to do science is backwards. Copenhagen has had successes worth trillions of dollars. No one has ever done any science with many-worlds.

I don't know how Carroll says this junk with a straight face. It is like saying Astrology is the only true science.

Here is the distinction. Copenhagen says you can predict an experiment, with probabilities for different outcomes. Once you observet the outcome, you discard the other possibilites as events that did not happen.

Many-worlds is just like that, except that there are no probabilities for the outcomes, because they all happen, and no world is any more likely than any other. Once you see an outcome, the parallel worlds with the other outcomes go out of reach. A prediction might seem true or false, but that is only because you are trapped on one of the worlds. It is not possible to do any science, because no prediction can ever be falsified.

Copenhagen makes sense and is scientific. Many-worlds is an unscientific fantasy.

AI Models will maintain String Research

Peter Woit reports that the top string theorists are retiring, and they are worried that the younger generation will not carry on as before.

Not to worry! One suggests that AI large language models like ChatGPT will come to the rescue, because they can

train an LLM with the very best papers written by the founding members, so that it can continue to set the trend of the community.

Okay, maybe this was a joke, but it is likely to happen anyway. We may have reached peak knowledge. Already journals are being tricked into publishing AI-generated articles. The LLMs of the future will be trained on the LLMs of the past.

There is no experimental data that has any bearing on string research. Ed Witten cannot live forever. Advanced AI LLMs may be able to carry on string papers indefinitely.

SciAm gets Trump Derangement Syndrome

Scientific American used to be the worlds greatest popular science magazine, but now it is filled with politics and pseudoscience.

Now it has this article from an Australian Politics professor:

Donald Trump is now leading in many polls and could retake the U.S. presidency, despite numerous scandals, indictments and erratic behavior. Explanations for his popularity focus on factors like white identity, right-wing authoritarianism, nationalism and populism.

U.S. politics has included people with these predilections for many decades, however, so the puzzle of Trump’s appeal remains. ...

We differentiated the most loyal Trump supporters from the rest of the American population, including those who merely voted for Trump and supported his policies, by measuring three aspects of Trump support: unquestioning credulity, exemplified by the belief that he was in fact the legitimate winner of the 2020 election; ...

Most strikingly, we find they are highly conscientious, a measure of self-reported characteristics including carefulness, dependability, orderliness and self-discipline. Conscientiousness is significantly associated with all the three cultlike aspects of Trump support.

Support for Pres. Trump is not so tricky to explain. Pres. Biden is one of the worst Presidents ever. He is responsible for foreign policy disasters in Afghanistan, Ukraine, and Gaza. His reckless spending has caused high inflation. He has allowed the USA to be invaded by millions of foreigners. He is too senile to do the job. His VP is even worse. He has pursued bogus prosecutions of his political enemics. He appoints incompetent leftist minorities. He supports the sexual mutilation of children.

Pres. Trump, on the other hand, presided over four years of peace and prosperity. He would have been re-elected, but for changed voting rules that allowed the collection of million of votes whose casting and counting could not be verified. Trump won a majority of the votes cast and counted on Election Day.

This professor even found that most Trump supporters had conscientiously examined the evidence, and found Trump to be the better man. But this article makes no mention of all the objective reasons for concluding that Trump was a better President than Biden. He blames authoritarianism, while Biden is much more authoritarian then Biden.

As an example, those who resisted covid vaccine mandates nearly all support Trump over Biden. This shows that Biden is the authoritarian, and his supporters like his authoritarianism. Also, only an auhoritarian would prosecute his political enemies.

The Scientific American of a few years ago would never have published such a trashy partisan and illogical article.