How Einstein learned about general covariance

Quanta mag reports:

Albert Einstein released his general theory of relativity at the end of 1915. He should have finished it two years earlier. When scholars look at his notebooks from the period, they see the completed equations, minus just a detail or two. “That really should have been the final theory,” said John Norton, an Einstein expert and a historian of science at the University of Pittsburgh.

But Einstein made a critical last-second error that set him on an odyssey of doubt and discovery — one that nearly cost him his greatest scientific achievement. The consequences of his decision continue to reverberate in math and physics today.

Here’s the error. General relativity was meant to supplant Newtonian gravity. This meant it had to explain all the same physical phenomena Newton’s equations could, plus other phenomena that Newton’s equations couldn’t. Yet in mid-1913, Einstein convinced himself, incorrectly, that his new theory couldn’t account for scenarios where the force of gravity was weak — scenarios that Newtonian gravity handled well. “In retrospect, this is just a bizarre mistake,” said Norton.

To correct this perceived flaw, Einstein thought he had to abandon what had been one of the central features of his emerging theory. ...

Einstein initially wanted his equations to be coordinate-independent (a property he called “general covariance”), meaning they’d produce correct, consistent descriptions of the universe regardless of which coordinate system you happened to be using. But Einstein convinced himself that in order to fix the error he thought he’d made, he had to abandon general covariance.

Not only did he fail at this, he doubled down on his error: He tried to show that coordinate independence was not a property that his theory could have, even in principle, because it would violate the laws of cause and effect. As one study of Einstein put it, “Nothing is easier for a first-rate mind than to form plausible arguments that what it cannot do cannot be done.”

Einstein pulled out of this dive just in time. By late 1915 he knew that the influential German mathematician David Hilbert was close to finalizing a theory of general relativity himself. In a few feverish weeks in November 1915, Einstein reverted to the equations of general relativity he’d had in hand for more than two years and applied the finishing touches.

Norton is an Einstein idolizer who makes this all about Einstein.

The problem was that Einstein did not understand general covariance. He only ever settled on it because of persuasion from Levi-Civita, Grossmann, and Hilbert. It was Grossmann who had the correct equations in 1913, that the Ricci tensor is zero. Einstein did not even know about the Ricci tensor.

The problem stems from Einstein not properly understanding special relativity in the first place. The core of the theory, and Poincare explained in 1905 and Minkowski in 1907, was that Maxwell's equations were covariant under Lorentz transformations. Einstein's 1905 paper only had the weaker principle of corresponding states that Lorentz published in 1895. Even as Einstein wrote later review papers on relativity, he never showed that he understood that Poincare and Minkowski proved covariance, or even the definition or importance of covariance.

The article makes it sound as if Einstein was competing with Hilbert, but actually they were collaborating.

The "completed equations", as applied to the solar system, were just Ricci = 0. Ricci is the covariant curvature tensor of the appropriate rank. I would credit the guys who figured out covariance and the Ricci tensor. With the discovery of dark energy, this equation is modified to say that Ricci is a small multiple of the metric tensor.

For details, see a scholarly account of the history of general relativity. One can debate which are the crucial ideas, but general covariance was not Einstein’s.

Difficult birth of Many Worlds

SciAm reports:

The Difficult Birth of the "Many Worlds" Interpretation of Quantum Mechanics
Hugh Everett, creator of this radical idea during a drunken debate more than 60 years ago, died before he could see his theory gain widespread popularity ...

To solve the problem of superposition, Everett proposed something truly radical, seemingly more appropriate for the pulp sci-fi novels he read in his spare time: he said that quantum physics actually implied an infinite number of near-identical parallel universes, continually splitting off from each other whenever a quantum experiment was performed. This bizarre idea that Everett found lurking in the mathematics of quantum physics came to be known as the “many-worlds” interpretation.

The many-worlds interpretation hit a roadblock almost immediately in the person of Everett’s PhD advisor at Princeton, the eminent physicist John Wheeler. Wheeler was a physicist’s physicist; ...

Wheeler also was very open to wacky ideas. Eg, he promoted "it from bit", that information is somehow more fundamental than fields or matter.

There is a good reason why Everett could not convince Wheeler or Bohr or anyone else. He idea is unscientific nonsense.

The work of DeWitt, Deutsch, and others led the many-worlds interpretation to become much more popular over the ensuing decades. But Everett didn’t live to see the many-worlds interpretation achieve its current status as the most prominent rival to the Copenhagen interpretation. He died of a massive heart attack in 1982, at the age of 51.

If Everett were correct, then he would be still alive in some of those parallel universes. Not even this SciAm story can go as far as to endorse such nuttiness.

The article gives the impression that Everett's idea was so radical that the world was slow to see the genius in it.

On the contrary, theoretical physics ran out of good ideas in about 1980. Professors got desperate for ideas, so they started recycling stupid ideas from the past.

When I attack MWI, I am not just attacking a straw man. As you can see, it is the most prominent rival to Copenhagen.

Von Neumann believed in Church's Thesis

John von Neumann is regarded by many as the smartest man of the XX century. Two of his areas of expertise were the foundations of quantum mechanics, and computability theory. He wrote the first QM textbook that clearly explain how observations yield collapse of the wave function, 1932. He was one of the first in the mainstream mathematical community to recognize the significance of Goedel's work on the computability of proofs.

The Church–Turing thesis of the 1930s was the physically computable functions were those defined by Goedel, Church, and Turing.

Not until around 1985 did anyone argue that von Neumann's QM is in direct contradiction to the Church-Turing thesis, and that quantum computers will be able to create computable functions that are beyond what can be done with Turing machines.

How was von Neumann so stupid as to not notice this?

Von Neumann did a lot of work to build early computers, and yet he never commented that with quantum mechanics, he could outdo a Turing machine. Why?

And why didn't anyone else notice it either?

I say that the answer is that there is no such contradiction. The foundations of quantum mechanics do not imply a violation of Church's thesis. It is a myth.

QM says that if you have a system with a |0> state and a |1> state, and if you cannot predict which will be the result of a future measurement, then the formalism represents it as a cat-state, where either is possible. It is like the Schroedinger cat that might be alive or dead, until you open the box and look.

The theory works great, and I don't question it.

But the quantum computing enthusiasts claim that you can some use your uncertainty to do a super-Turing computation. This is like putting a cat in a box, generating some uncertainty about whether the cat is alive, and they trying to use that uncertainty to do a super-Turing computation. At the end, you might open the box to find that the cat was alive all along, but the intervening uncertainty somehow magicly does some super-natural computation.

I don't believe it. The conventional wisdom should be in the validity of Church's thesis, unless someone convincing demonstrates otherwise.

Argument that science, like religion, requires faith

Evolutionary biologist Jerry Coyne attacks a video saying this:

For the second half of the 20th century, the best philosophers of science, philosophers like Sir Karl Popper, Thomas Kuhn, Imre Lakatos and Paul Feyerabend, attempted to explain what science consists in and how it differs from myths and religion. And no matter how hard they tried, eventually, the debate died out their realization that science, much like religion, requires faith. To choose one scientific theory over another, is simply a matter of aesthetics in the hope that this theory and all to the other is going to work out.

But there is no way to disprove or prove in theory. And since there is no way to prove it or disprove it, then there is no point where it becomes irrational for a scientist to stay with a failing theory.

Coyne is right to criticize this, but the video is essentially correct that modern philosophers have abandoned the idea that science discovers objective truths. Popper was one of the last to believe that theories could be disproved, even if they could not be proved true, but his ideas are rejected today.

I used to say that physicists are still believers in hard science, and had not succumbed to philosophers nonsense. But now too many physicists teach the multiverse and all sorts other ideas that have no scientific support at all.

So, the best example of this is the case of heliocentricism. Heliocentricism was first put forward about 2,000 years ago. And for about 1,600 years, it was a failing theory. However, at some point, Kepler and Galileo decided to take it up. And even though it was failing for 1,600 years, they managed to convert it in a very successful theory. The choice, however, to do so, was not because the theory was a good one — since obviously it was failing for a long time — but simply because they liked it and for some reason they had faith in it. So scientists choose to stay, we the few, simply because they have faith in it. So both science and religion seem to require faith, which means that it is not so easy to distinguish between creationism and evolutionary biology.

This example is what convinced Kuhn that scientific revolutions, aka paradigm shifts, are driven by scientists who had an irrational faith (Kuhn preferred the term arational), and other scientists jumping on the bandwagon like a big fad.

As ridiculous as this is, it is the dominant view among philosophers of science today. Even physicists echo this nonsense when it suits them getting papers published.

Coyne replies:

Kepler and Galileo “converted” heliocentrism to a good explanation because of OBSERVATIONS, you moron! It was not because they had “faith” that the Sun was the locus of the solar system.

That is only partially true. Kepler admitted that he could not prove that the Earth goes around the Sun.

Galileo made some excellent observations with his telescope, but his biggest argument for the motion of the Earth was with the daily tides. Galileo claimed that it caused one tide a day, which is nonsense because there are two tides a day, and they are caused by gravity, not motion.

Coyne blames religious influences for undermining views of what science is all about. I am sure that is true in many cases, but the overwhelming attacks on science in academia come from philosophers who hate religious almost as much as he does.

At least the religious folks are up-front about saying that their beliefs are based on faith.

Trashing the many-worlds interpretation

Lubos Motl trashes the Many Worlds Interpretation:

Bohr told Wheeler that it was a pile of crap because it was a pile of crap. In particular, the "splitting of the worlds" made no sense. Even today, in 2018, it makes absolutely no sense and no fan of these Everett ideas can tell you anything whatsoever about the question whether the worlds split at all, when they split, why they split, how many branches there are. You may suggest several answers to each questions, none of them can be completed to a convincing let alone quantitative theory, and in fact, none of them has a significantly greater support among the Everett fans than others. They don't seem to care. ...

On top of that, even if you solved these problems in some way, the many worlds theory will have nothing to do with science – with predictions. All predictions of quantum mechanics have the form of probabilities, continuous numbers assigned to possible results of experiments, or their functions or functionals. And no Everett's fan has an idea how these probabilities could be written into the many worlds, or extracted from the many worlds. It's just not possible. If this many world theory predicts something, it's the wrong prediction that all probabilities should be rational – the number of worlds would be the denominator because if several worlds obviously exist, they should be "equally likely". Well, the actual outcomes in quantum mechanics are not. It just doesn't make the slightest sense. And all predictions in quantum mechanics are functions of these continuous probabilities. Because the many worlds philosophy can't be reconciled with the continuous probabilities at all (or it seems to predict wrong probabilities), it can't be reconciled with the predictions as such – it cannot possibly have anything to do with science within the quantum mechanical framework.

Motl is correct. I think a lot of people have the misconception that MWI has some way of calculating which worlds or outcomes are more probable, but it has nothing of the kind. MWI does not make any testable predictions.

Peter Woit writes:

The calculation [of the spectrum of the hydrogen atom] in Many Worlds is exactly the same textbook calculation as in Copenhagen. It’s the same Schrodinger equation and you solve for its energy eigenvalues the same way. That is the problem: there’s no difference from the standard QM textbook.

This is just wrong. There is no known way to do a MWI calculation that matches some real world object like a hydrogen atom.

Jim Baggott says:

All this really shouldn’t detract from the main point. The formalism is the formalism and we know it works (and we know furthermore that it doesn’t accommodate local or crypto non-local hidden variables). The formalism is, for now, empirically unassailable. All *interpretations* of the formalism are then exercises in metaphysics, based on different preconceptions of how we think reality could or should be, such as deterministic (‘God does not play dice’). Of course, the aim of such speculations is to open up the possibility that we might learn something new, and I believe extensions which seek to make the ‘collapse’ physical, through spacetime curvature and/or decoherence, are well motivated.

But until such time as one interpretation or extension can be demonstrated to be better than the other through empirical evidence, the debate (in my opinion) is a philosophical one. I’m just disappointed (and rather frustrated) by the apparent rise of a new breed of Many Worlds Taliban who claim – quite without any scientific justification – that the MWI is the only way and the one true faith.

... this endless debate over interpretation is really a philosophical debate, driven by everybody’s very different views on what ‘reality’ ought to be like. And, as such, we’re unlikely to see a resolution anytime soon…

In a sense, this is correct. If an interpretation reproduces all the calculations used to test the theory, then whether to accept it is a philosophical issue, not an empirical one.

For example, the solar system has geocentric and heliocentric interpretation, and preference for heliocentric is philosophical, not scientific.

The trouble with this is that most of these QM interpretations are not really interpretations. MWI does not reproduce any calculations of QM, and does not have any empirical support.

MWI is just like QM except for (1) MWI has no way of making quantitative predictions (like the Born rule), and (2) MWI postulates parallel worlds where all possibilities exist and no world has an effect on any other world.

These two properties make MWI completely disconnected from any scientific analysis. With no predictions, it cannot be tested. And the parallel worlds are just subjective fantasies, with no relation to our world.

More and more, I see physicists argue that the MWI is the only scientific interpretation of QM, because the Copenhagen interpretation somehow fails to solve the "measurement problem" or to define what is "real". Whatever you might think to be shortcomings of the CI, the MWI does not solve any of them, and does not even qualify as a scientific theory. It is a mystery how otherwise-smart physicists could fall for something so ridiculous.

Tim Maudlin attacks Woit:

It is a bit hard to know how to comment on a discussion of a book called “What is Real?” when it has been asserted that

“I’d rather do almost anything with my time than try and moderate a discussion of what is “real” and what isn’t.

Any further discussion of ontology will be ruthlessly suppressed.”

The question “What is real?” just is the question “What exists?” which is in turn just the question “What is the true physical ontology?” which is identical to the question “Which physical theory is true?”. Peter Woit begins by writing “Ever since my high school days, the topic of quantum mechanics and what it really means has been a source of deep fascination to me…”. But that just is the question: What might the empirical success of the quantum formalism imply about what is real? or What exists? or What is the ontology of the world? To say you are interested in understanding the implications of quantum mechanics for physical reality but then ruthlessly suppress discussions of ontology is either to be flatly self-contradictory or to misunderstand the meaning of “ontology” or of “real”. That is also reflected in the quite explicit rejection of any discussion of two of the three possible solutions to the Measurement Problem: pilot wave theories and objective collapse theories.

No, when quantum philosophers ask "what is real?", they are not asking about existence or physical consequences. They are usually searching for a nonlocal hidden variable theory that is supposed to match their nonlocal intuition. They subscribe to a belief that QM is defective, and a hidden variable theory would be better.

At least Maudlin is not defending MWI. But pilot wave theories are nonlocal, and objective collapse theories are hard to reconcile with experiment.

Hawking also had unsupported beliefs

Evolutionary biologist atheist Jerry Coyne writes:

Stephen Hawking’s body was barely cold (or rather, his ashes were barely cold) when the religionists came muscling in with their tut-tutting and caveats about his accomplishments. For Father Raymond de Souza, a Canadian priest in Ontario (and Catholic Chaplain of Queen’s University), he did his kvetching in yesterday’s National Post. His column, as you see below, claims that “Hawking’s world was rather small.” Really? Why?

Well, because Hawking, while he made big advances in cosmology, couldn’t answer the BIG QUESTIONS about the Universe: namely, why does it exist? Why is there something rather than nothing? ...

But God is de Souza’s answer to this big question, and, further, the priest says that that answer is compatible with science. ...

Those are some questions for Father de Souza, but I have more:

What’s your evidence for God? And why do you adhere to the Catholic conception of God rather than the Muslim conception, which sees Jesus as a prophet but not a divine being? Why aren’t you a polytheist, like Hindus?
If God created the Big Bang, who created God?
If you say that God didn’t need a creator because He was eternal, why couldn’t the Universe be eternal?
And if God was, for some reason, eternal, what was he doing before he created the Universe? And why did he bother to create the Universe? Was he bored?

These questions aren’t original with me; they’re a staple of religious doubters. And of course Father de Souza can’t answer them except by spouting theological nonsense.

The Catholic Church does have all sort of beliefs that are grounded in faith and revelation, not scientific evidence. But so did Hawking, and the physicists that Coyne relies on, like Sean M. Carroll.

Hawking was a proponent of the multiverse and string theory. Hawking spent much of his life arguing about issues that cannot be resolved by any scientific observation.

Most of Coyne's questions, above, are not really scientific questions. There is no known scientific meaning to discussing what preceded the big bang, if anything. It is not clear that such questions make any sense.

Coyne sometimes questions the motives of his fellow humans. If he cannot necessarily figure out human motives, how can he expect to figure out God's motives?

I suspect that priest could give a good explanation for why he is not a Muslim, and not a polytheist.

I don't mind atheists calling out religious believers for having beliefs that are merely compatible with science, but not directly supported by evidence. But why are those atheists so supporting of physicists who do the same thing, with string theory, the multiverse, and black hole information?

The blockchain is not efficient

Nature mag reports:

Dexter Hadley thinks that artificial intelligence (AI) could do a far better job at detecting breast cancer than doctors do — if screening algorithms could be trained on millions of mammograms. The problem is getting access to such massive quantities of data. Because of privacy laws in many countries, sensitive medical information remains largely off-limits to researchers and technology companies.

So Hadley, a physician and computational biologist at the University of California, San Francisco, is trying a radical solution. He and his colleagues are building a system that allows people to share their medical data with researchers easily and securely — and retain control over it. Their method, which is based on the blockchain technology that underlies the cryptocurrency Bitcoin, will soon be put to the test. By May, Hadley and his colleagues will launch a study to train their AI algorithm to detect cancer using mammograms that they hope to obtain from between three million and five million US women.

The team joins a growing number of academic scientists and start-ups who are using blockchain to make sharing medical scans, hospital records and genetic data more attractive — and more efficient. Some projects will even pay people to use their information. The ultimate goal of many teams is to train AI algorithms on the data they solicit using the blockchain systems.

No the blockchain is not efficient, and does not offer any advantage to a project like this.

The blockchain is surely the least efficient algorithm ever widely deployed. Today it consumes energy equivalent to the usage of a small country, to maintain what would otherwise be a fairly trivial database.

It appears that someone got some grant money by adding some fashionable buzzwords: AI, blockchain, women's health.

The blockchain does not offer any confidentiality, or give patients any control over their data. This is all a big scam. It is amazing that a leading science journal could be so gullible.