Infinite information density is impossible

New paper:

An argument for an indeterministic interpretation of classical physics (i.e., Newton's mechanics and Maxwell's electrodynamics) was put forth by Gisin and Del Santo in [1] (see also [2] [3] [4] and [6] ). They maintained that although classical physics has traditionally been construed as deterministic (i.e., the physical laws determine a unique definite future (and past) state of a physical system once its current state is fixed, as famously revealed in the scenario of "Laplace's Demon"), it is not necessarily the case. There are metaphysical assumptions behind the traditional deterministic interpretation, and it is possible to give an alternative indeterministic interpretation by revising those assumptions, they contended. In particular, the usual practice that real numbers are used to represent physical quantities was held to be problematic, because this would lead to the unacceptable consequence of "infinite information density" (as related to the infinite string of digits following the decimal point of a real number) in the relevant physical space, according to them.

The paper does not agree with these conclusions, but I do.

I have argued here that classical mechanics is not really deterministic. Calculations always have error bars, just like any other part of science. Laplace's Demon is just a big straw man, like Schroedinger's cat.

Almost all real numbers have infinite information content, and such things are not observable.

Two quantum paradoxes about entanglement

This post is an explanation of a couple of points about entanglement that others get wrong. Part of the confusion is to mix two distinct paradoxes, so I separate them. (Remember a paradox is an apparent contradiction or confusing issue. Valid theories can have paradoxes.)

Uncertainty principle. A core tenet of quantum mechanics is that you cannot measure a particle's position and momentum at the same time. This is because particles are not really particles, and have wave-like properties that prevent having definite values for position and momentum.

Quantum mechanics enforces this uncertainty by using non-commuting observables. Measuring position then momentum is different from momentum then position. Other pairs of observables have this same property, such as Spin-X and Spin-Y.

This is an essential part of quantum mechanics, and was well-understood and non-controversial by about 1927.

Quantum twin paradox. If a system emits two equal and opposite particles, then properties of one can be deduced by measuring the other. For example, since momentum is conserved, the momentum of one will be opposite the other.

If the two particles are far apart, then knowledge about one seemingly has a spooky effect on our knowlegde about the other. This paradox occurs in either classical or quantum mechanics. It doesn't really violate the principle that there can be no action at a distance.

Combining these two paradoxes gives the EPR paradox. The idea is that you can measure the position of particle A and deduce the position of particle B, or you can measure the momentum of particle A and deduce the momentum of particle B, but you cannot measure the position and momentum at the same time.

Einstein argued in the 1935 EPR paper that this makes the theory of quantum mechanics incomplete. That is, you can deduce a particle's position and momentum by measuring its twin, but you cannot measure both at the same time. A complete theory would tell you both at the same time.

Bohm and Bell explain EPR with Spin-X and Spin-Y. You could use any noncommuting variables, as they all satisfy the uncertainty principle. Bohm proposed a nonlocal theory where a particle has a well-defined position and momentum all the time, but those variables might have nothing to do with what is observed. Bell proposed a classical theory of local hidden variables, but those theories have been refuted by experiments.

The EPR-Bohm-Bell followers will tell you that their argument is more subtle than just saying that the uncertainty principle makes quantum mechanics incomplete. That is because the position and momentum (or Spin-X and Spin-Y) are both predictable by measuring the twin particle. But you can't measure both at once in the twin particle, so you cannot predict both at once.

If you are bothered by the uncertainty principle, then you are going to be bothered by any theory were electrons have wave properties. Electrons are observed to have wave properties. If you are bothered by the quantum twin paradox, then you are also going to bothered by classical theories where someone might have info at a distance.

If you are not bothered by either paradox, then it is not clear why you would be bothered by the EPR paradox, because that is just putting the two paradoxes together. But there is a long list of intelligent physicists, from Einstein to Sean M. Carroll, who are tremendously confused by this combination.

Carroll on many-worlds and entanglement

Physicist Sean M. Carroll has a new video explaining entanglement.

Towards the end, he tells us that he likes the many-worlds interpretation (MWI), but admits that it has two major problems. It doesn't explain anything about the macroscopic world, and it doesn't predict anything.

He does give a tortured argument for assigning probabilities that is supposed to match the Born rule, but he rejected any frequentist interpretation that allows checking the probabilities against experiment.

The MWI is just nuts. Just listen to the advocates try to make sense of it. They are completely unable to make any scientific sense.

I am actually more disturbed by his explanation of entanglement. That is textbook stuff, and he gets it wrong. He says that he is writing an undergraduate quantum mechanics textbook under a contract with a publisher.

So far the quantum mechanics textbooks have been relatively free of the nonsense that Carroll peddles. I hate to think how many people are getting confused by him. I will post more on what he gets wrong about entanglement.

Update: I just listened to another Carroll Q&A. Most of his answers are correct and well-explained, but he sure has some peculiar views. Someone asked if some experiment could distinguish the Copenhagen and Many-Worlds interpretations.

He said no, because the Copenhagen interpretation is not well-defined! He said that no one knows what a measurement is, or any of the other things to make sense out of it.

This is completely crazy. Every QM textbook uses Copenhagen. So do nearly all the research papers. We have trillions of dollars of industry based on QM, from semiconductors to lasers to video screens, and it all uses Copenhagen. None of it uses MWI.

MWI is not well-defined. No one can say what a splitting of universes is, or what a prediction is, or anything that relates to a real-world experiment. There is no experiment that has ever confirmed any aspect of MWI. The problem with an experimental test is that MWI does not make any predictions.

Samsung now makes quantum phones

ExtremeTech reportw:

However, you probably don’t have a quantum 5G phone. ...

The new Galaxy A Quantum is the first and only smartphone with a Quantum Random Number Generator (QRNG) inside. The device itself is based on the mid-range Galaxy A71 5G, which Samsung has already launched in numerous markets sans quantum technology. ...

According to Samsung, the Galaxy A Quantum is much more secure than other smartphones thanks to its QRNG hardware. This is completely separate from the SoC and other core hardware. It’s a tiny embedded chipset called the SKT IDQ S2Q000 that’s just 2.5mm square consisting of an LED and a CMOS sensor. The LED shines into the sensor to produce image noise, and the sensor interprets that as quantum randomness. These random noise patterns become the basis for truly random number strings.

The Galaxy A Quantum will go on sale May 22nd in South Korea for KRW 649,000. That’s about $530, which is a bit more than the A71 5G on which it is based.

Modern electronics uses quantum mechanics for all sorts of things, but this is not really quantum. It is just thermal noise.

Some of the promoters of quantum computing say that quantum computers could be used for random number generation, if nothing else. Of course, chips for reliable random number generation have been available for decades. Random numbers are needed for cryptography, but there are many ways to solve that with old technology.

Bishop excoriated for free will belief

I often attack physicists who preach some mystical view of the world, but I should also credit non-scientists who are completely rational. Here is evolution professor Jerry Coyne's latest rant:

Yesterday, reader Neil called my attention to a particularly galling homily given yesterday by the Right Reverend Dr. David Walker, the Bishop of Manchester. It especially irked me because it was about free will—his idea that we have it in the libertarian form. ...

Walker rejects determinism, claiming that if we have no “choice” whether or not to commit an offense (i.e., the future is preordained), then humans beings “have no moral responsibility for what we do.” ...

Now you may try to tortuously parse the good Reverend’s words to say what he really means is a compatibilistic free will that, deep down, accept determinism of our actions. But I think you’d be dead wrong, for Walker states at the outset that he clearly rejects the mathematically-based determinism of science. No, he’s talking about pure libertarian free will—the kind that his sheep accept.

I’m surprised that, in a country where—although there’s a state church—Christianity is on a precipitous decline, the BBC still emits a “thought for the day” that is invariably religious. Seriously, my UK friends, why does this persist? ...

Sorry, but I can’t happily ignore it. Broadcasting it would be illegal in the U.S. You can happily ignore it, but I’m afraid that I’m not in that boat with you. It enables faith and religion and stupidity. It’s just as if they had an “astrology of the day” thought!

I listened to the podcast, and I cannot find any fault with it. It is consistent with our best scientific theories.

Free will is a philosophical question, so I don't mind if Coyne has a different opinion from mine. But he goes farther, and seeks to censor alternate views, under the guise of purging unscientific thought.

I believe in free will, as I believe that personal experience in favor of it is compelling. If science had somehow proved determinism, I would have to reconsider, but the evidence is just the opposite. All the scientific evidence is against determinism.

Free will is essential to Christian ideas about moral responsibility, and to scientific underpinnings of experimentalism.

The determinist objectors to free will tend to degenerate into discussions like this:

{Responsive comment] To be fair to him, it’s not as though the Bishop could have chosen NOT to believe in libertarian free will.

[Coyne] And I could not have chosen not to excoriate him.

[Another comment] cannot argue with that…even if I so desired.

In my opinion, this is just philosophical silliness, and doesn't address what the Bishop said.

Physicists promoting fashionable nonsense

Jean Bricmont, Sheldon Goldstein, and Douglas Hemmick write in a new paper:

Hence, said EPR, in one of the most misunderstood, yet simple, arguments in the history of physics, the quantum state is an incomplete description of physical reality. It does predict the correct statistics, but does not describe completely the physical state of individual systems. Stated more precisely, it says that we must describe this pair of particles not only by their joint quantum state but also by other variables, often called "hidden," that determine the behavior of those particles when one measures their spin in a given direction.

What could be wrong with this conclusion? In 1964, John Bell showed that simply assuming the existence of these variables leads to a contradiction with the quantum predictions for the results of measuring the spin of those particles in different directions, one for the first particle and another for the second one (see [17] for a simple proof of this contradiction). Those predictions have been amply verified after Bell's publication (see ([21] for a review).

But what does this imply? That we have no choice but to accept the analogue of the second branch of the alternative proposed about the coin tosses of Alice and Bob: that the measurement of the spin on one side affects instantaneously (if the measurements on both sides are made simultaneously), in some way, the result on the other side. This is what is called nonlocality or "action at a distance."

This is nuts. How do respectable academics get away with writing voodoo papers?

Jean Bricmont wrote a book with Alan Sokal criticizing Fashionable Nonsense, meaning academics citing pseudoscience to support wacky ideas. Bricmont himself is a prime example of this nonsense.

He is entitled to his opinion, of course, but he is just wrong when he says that no other view exist. Here is how they start the paper:

Let us start with a physically classical situation: consider the proverbial Alice and Bob, situated far away from each other, and simultaneoulsy tossing coins, over and over. One would expect the results on both sides to be random and uncorrelated. But suppose that the results appear indeed random but are also perfectly correlated: each time Alice's toss results in heads, Bob's toss also results in heads and similarly for tails.

Obviously such a strange situation would cry out for an explanation. One possibility is the following. First, Alice and Bob are able to manipulate their coin tosses so as to obtain whichever results they desire and second, they agree in advance on an apparently random sequence of results and manipulate their coin tosses so as to both obtain that sequence when they toss their coins.

This looks extravagant, but is there any other possibility? Well, yes, there exists an even more extravagant one: that when Alice tosses her coin, she instantly affects the trajectory of Bob's coin, so that Bob's coin falls on the same side as Alice's coin.

Of course, this looks even more incredible than the previous scenario. But we may still ask: is there a third possibility? We don't see any and we will assume from now on that the reader agrees with us on that point.

No, I do not agree. The third possibility is that Alice's and Bob's coin tosses have a common cause.

That is, someone tosses a coin, duplicates it, and hands one copy each to Alice and Bob. Then Alice and Bob each appear to be getting random tosses, except that the outcomes are correlated.

This is what happens in the EPR experiments. Two distant particles are measured, but they were both emitted from the same source simultaneously.

The paper goes on to argue for Bohmian mechanics, as a nonlocal hidden variable theory. That theory agrees with quantum mechanics for some simple systems at least, so they are free to believe in it if they wish. But in all cases, local theories better job of explaining the data. They are just wrong to deny the possibility of local theories.

Bricmont previous wrote History of Quantum Mechanics or the Comedy of Errors:

The goal of this paper is to explain how the views of Albert Einstein, John Bell and others, about nonlocality and the conceptual issues raised by quantum mechanics, have been rather systematically misunderstood by the majority of physicists.

This paper argues that most physicists, textbooks, Nobel prizewinners, etc. are all wrong about quantum mechanics, because they do not believe in spooky action.

No, the textbooks are not wrong.

Bricmont quotes David Mermin:

To those for whom nonlocality is anathema, Bell’s Theorem finally spells the death of the hidden-variables program. ... Many people contend that Bell’s theorem demonstrates nonlocality independently of a hidden-variables program, but there is no general agreement about this.

That is correct. If you choose to believe in nonlocality, then it is possible to have a theory of nonlocal hidden variables like Bohm's. If you accept locality, then the hidden variables program is dead. A few physicists believe that Bell somehow proves nonlocality, but they are wrong.

The Dream Universe

Dr. Bee book review:

The Dream Universe is about “how theoretical physics is returning to its unscientific roots” and that physicists have come to believe

“As we investigate realms further and further from what we can see and what we can test, we must look to elegant, aesthetically pleasing equations to develop our conception of what reality is. As a result, much of theoretical physics today is something more akin to the philosophy of Plato than the science to which the physicists are heirs.”

He then classifies “fundamental physics today as a kind of philosophy” and explains it is now “less about a strictly rational understanding of the universe and more about finding a scenario that we deem intellectually respectable.” He sees no way out of this situation because “Observation, experiment, and fact-finding are no longer able to guide [researchers in fundamental physics], so they must set their path by other means, and they have decided that pure rationality and mathematical reasoning, along with a refined aesthetic sense, will do the job.”

I am sympathetic to Lindley’s take on the current status of research in the foundations of physics, but I think the conclusion that there is no way forward is not supported by his argument. The problem in modern physics is not the abundance of mathematical abstraction per se, but that physicists have forgotten mathematical abstraction is an end to a means, not an end unto itself. They may have lost sight of the goal, alright, but that doesn’t mean the goal has ceased existing.

I wrote a similar book several years ago, and I place the blame on Einstein worship, not math or theory.

While Einstein did much worthwhile work, he is largely idolized today by anti-positivists who believe that finding reality is based on finding aesthetically pleasing equations. You can see this most explicitly in how he is credited for relativity. He is almost never credited for what he actually did. He is either credited for the work of others, or for some anti-positivist philosophy.

Greene video pushes action-at-a-distance

Brian Greene has a series of educational physics video, and his latest is on Bell's theorem:

Albert Einstein and his colleagues Podolsky and Rosen proposed a simple way to rid quantum mechanics of its most disturbing feature--called non-locality--in which an action undertaken here can affect the result of a measurement undertaken there, even if here and there are far apart. John Bell came up with a way to test Einstein's vision of reality, ultimately showing that Einstein's vision was wrong.

That text is correct, but if you listen to the video, Greene says that the world was proved to be nonlocal. He says measuring the spin of a particle can have an effect on a distant particle.

Greene sees the big issue as to whether a spin measurement is a random event at the time of the measurement, or it is predetermined in advance.

Briefly, quantum mechanics is somewhat strange because electrons act like waves, and you cannot measure their position and momentum at the same time. Einstein and others had an idea for replacing quantum mechanics with a classical theory of hidden local variables, because that would be more compatible with his determinism prejudices. Bell and subsequent experiment proved that all those classical theories do not work. The world is quantum.

Bell did not show any nonlocality. He only helped show that the classical theories don't work. Almost everyone was convinced of that in 1930 anyway.

Watching this video will just get you confused. There is no action-at-a-distance.

Greene is very good at explaining a lot of physics, but he really goes off the rails when he talks about Bell's theorem, many-worlds, or string theory.