## Sunday, June 16, 2019

### Bell only proved a null result

Peter Woit has closed comments on Bell locality without responding to a lot of sharp criticism, so I am not sure where he stands.

Marty Tysanner wrote:
While I may understand their rationale, it still dismays me that so many people have thrown locality “under the bus” (so to speak). Locality isn’t like the 19th century ether that was invented to explain certain physical phenomena; it’s at the core of relativity, electromagnetism, classical mechanics, and even QM evolution up to the time of measurement. I can’t think of anywhere else in all of fundamental physics – outside QM entanglement – where locality is in question. Moreover, there are obvious conceptual issues with non-local influences/communication between entangled particles at space-like separation: How do the particles “find” each other within the entire universe, so they can “communicate” (other than tautalogically or some other version of “it just happens; don’t ask how”); and why don’t we see nonlocality in other contexts if it’s a truly fundamental aspect of nature? ...

Given the centrality of locality in physics, I think we should “fight to the death” to preserve it in a fundamental theory.
That part of Tysanner's comment is correct. Locality is at the core of nearly all of Physics, including quantum field theory (QFT). If it were false, we would expect to see some convincing evidence, and then do some radical rethinking of out theories.

We do see the Bell test experiments, but they only negate the combination of locality and counterfactual definiteness. You can preserve locality by rejecting counterfactual definiteness. That is what mainstream physicists have done for 90 years.

Tim Maudlin disagrees with Woit and writes:
You do experiments in two (or three: GHZ) labs. You get results of those experiments. Those results display correlations that no local theory (in the precise sense defined by Bell) can predict. Ergo, no local theory can be the correct theory of the actual universe. I.e. actual physics is not local (in Bell’s sense).
Bell defined a local theory as a classical theory of local hidden variables. In later papers, he called them beables, and gave some philosophical arguments for believing in them, but the definition of locality is the same.

Quantum mechanics uses non-commuting observables. By the uncertainty principle, they cannot have simultaneous values. That remains true if you call them beables instead of observables. If you create a model in which they do have simultaneous, but maybe unknown values, then you get predictions that contradict experiment. That is what Bell and his followers have shown.

The only conclusion is the null result: No reason to reject quantum mechanics. Any other conclusion is an error.

Update: Lubos Motl completely agrees with me about Bell. Bell proved a nice little theorem in 1964 that supports locally causal quantum mechanics. Then he wrote some later papers that did nothing but confuse people who refuse to accept quantum mechanics:
In this later paper, Bell coined the new terms "local beables" and "local causality" which have turned his writing into complete mess combining outright wrong statements with totally illogical definitions. He also tried to retroactively rewrite what he did in 1964. While in 1964, as I said, he was rather clear that he made two main assumptions about the theory, namely that it is local and it is classical (although he wasn't a sufficiently clearly thinking physicist to actually use the word "classical"), in the 1976 paper, he already tried to claim that he had only made one assumption, "local causality". ...

There only exists one physically meaningful notion of locality or local causality – and it's what holds whenever the special theory of relativity (or its Lorentz invariance) is correct. The probabilities of measurements done purely in region A are determined by the prehistory of A – and don't depend on further data in the region B although it may contain objects previously in contact with the objects in A. There may exist correlations between measurements in A and B but all of those are calculable from the conditions in the past when A,B were a part of a single system AB. What's important is that people's decisions (e.g. what to measure), nuclear explosions, and other random events in region B don't cause changes to the system A. ...

The claim by Bell, Eric Cavalcanti, and this whole stupid cult that quantum mechanical theories cannot be "Bell locally causal" is wrong ...

People who talk about "beables" in quantum mechanics are doing an equally silly mistake as a molecular geneticist who builds his science on the seven days of creation.
This is correct. The term "beables" is just a goofy term for local hidden variables in a classical theory. Talking about them is just expressing a religious objection to quantum mechanics.

1. You write, "No reason to reject quantum mechanics. Any other conclusion is an error."

Yes! All experimental tests have supported quantum mechanics.

Of course Woit closed his blog. Woit's blog generally goes like this.

1. Woit posts silly statement/confused account of some well-known physical fact.
2. Some rabble rushes in to correct him, while others rush in to confuse the issue, both giving Woit the attention he desires.
3. Woit shuts down the comments, stating, "I don't won't to host a discussion on my silly comments/confusion."

Then wait a few days and it all begins again.

It must be admitted, that over the past couple decades, no notable physics nor maths hath emerged from any of the blogs, nor their pop-sci books either.

2. lol Woit shut down the comments with "All,
I’m closing comments on this posting. This has gotten to the point where zero light is being shed on the Bell-nonlocality issue, and I’ve lost the patience needed to try and sensibly moderate a general discussion that people want to take in other directions."

lol! There exists several decades of literature on the EPR/Bell issues, and Woit thinks that his comment section of his blog is the place for enlightenment.

You and Woit should read some books and original papers, beginning with this one:
Quantum Theory and Measurement (Princeton Series in Physics)
by John Archibald Wheeler and Wojciech Hubert Zurek

"The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum theory, overarching principle of twentieth-century physics, appear to many to prefigure a new revolution in science.

Originally published in 1983."

As Woit never contributed to nor advanced physics, perhaps a better place to turn so as to learn about quantum mechanics would be to the founding father's papers. Enjoy!

3. Dear Roger,

Consider a photon as it crosses between two mirrors one light year apart. In its own frame, how far has the photon moved? In its own frame, how much has the photon aged?

4. Dear Roger,

you write, "We do see the Bell test experiments, but they only negate the combination of locality and counterfactual definiteness. You can preserve locality by rejecting counterfactual definiteness. That is what mainstream physicists have done for 90 years."

In all the founding fathers' papers on quantum mechanics, including Bohr, Born, Fermi, Dirac, Einstein, Planck, Heisenberg, et al., I never once came across your term, "counterfactual definiteness." Could you please cite the paper or place you got the term from?

Or perhaps your phrase "counterfactual definiteness" is a strawman for you to attack, without any existence in the vast literature of foundational quantum mechanics?

5. Dear Roger,

Do you still insist that the wavefunction of a single photon is local?

Consider a photon passing through two slits at once.

Does that photon exist as a local entity, or a nonlocal entity, in your opinion?

1. Dear GNR,

In the Schrodinger formalism, there is no wavefunction for photons, only for electrons.

Believing that there would be a wavefunction for photons is a very common and easy-to-make mistake. I made it too, and in fact continued believing so for a long time, even for a while after my PhD.

Researchers have tried developing a formalism that has a wavefunction for photons, but they have not succeeded. The basic reason behind their failure, I guess, could be that the photon number is not conserved, whereas any \Psi-based formalism requires conservation of |\Psi|^2.

However, inapplicability of \Psi for photons, in a direct way, is a rather technical point. You can always take the spatio-temporal change suffered by the system wavefunction during the process of emission or absorption of a photon, as representing the wavefunction-side of the photon. That would be entirely correct.

QM physicists are quick to point out that there is no \Psi for photon, but they never do tell you this part. But it is correct.

So, mathematically, you can always say (though most books don't mention it) that:
\Psi_{\gamma} = \Psi_{before emission} - \Psi_{after emission}
where the equality sign means is defined as.'' However, you still have to be careful in using \Psi_{\gamma}. To cut a long story short, the definition stays valid only during emission and absorption, and not in any other context.

The \Psi always exists everywhere in the universe, and also suffers changes which always occur only simultaneously everywhere (just as is the case for the gravitational field in the Newtonian gravity, or for the potential in a molecular dynamics simulation). So, it is non-local. Hence, a difference between two of its states also is non-local. In this respect, it is non-local.

However, also note, the two \Psi states being used in talking about photons have a restriction: they must be anchored in definite point-positions of nuclei. It is atoms that create or absorb photons. So, even if the wavefunction-changes associated with a photon are spread out everywhere in space, the changes begin and end in spatially definite, localized regions. In this sense, they also have a character of locality.

Hope this helps.

Best,

--Ajit

6. ear Roger,

Do you still insist that the wavefunction of a single photon is local?

Consider a photon passing through two slits at once.

Does that photon exist as a local entity, or a nonlocal entity, in your opinion?

Why won't you answer this simple, foundational question?

7. Dear Roger,

I think you fight in vain.

Your thinking here (and in the last post) notably comes couched in the Heisenberg formulation of QM, because the center-piece of your argument involves non-commutative observables. Regarding them, you say:

>> If you create a model in which they do have simultaneous, but maybe unknown values, then you get predictions that contradict experiment.''

Now this again becomes an issue of terminology, and not of basic physics.

Schrodinger's formalism says that not just a pair of non-commutative observables (like position and momentum), but in fact _all_ possibly measurable values of _all_ possible classical variables, regardless of _when_ they are measured (and even at all times when they are _not_ being measured), are to be seen as only different aspects of the \Psi field. For instance, \vec{p} \propto \nabla \Psi.

If you take Schrodinger's formalism as a model, then what you say is wrong. After all, \Psi always exists and always undergoes evolution as governed by Schrodinger's equation. \Psi (together with all its attributes) exists even at the times when the system is not being measured.

If you interpret \Psi as just a device of calculations (as epistemic, not ontic), you are just not giving the context of the differential equations-based paradigm of physics enough of a cognitive respect.

Who knows, but that might possibly be because you don't understand why and how physics at all uses differential equations---how the terms in any DE are to be interpreted, as far the physical existence issue is concerned.

Alternatively, you don't take \Psi as existing (as a _non_-classical object) simply because you were charmed by the beautiful structure of Heisenberg's abstract matrices and their non-commutative algebra, and so, you go ahead and also buy his more irrational philosophic positions. And, may be, having done that, you try to figure out what their counterparts in the DE-based formalism of Schrodinger's might be. And that's how begin to either deny \Psi reality, or try to portray it as if to accept the reality of \Psi is to impart a classicality to it---the kind of classicality which QM (and hence Bell) denied. (Motl has been expertly pursuing this track.)

You know best as to what is true. I take the Schrodinger equation firmly in the same paradigm as for the other DEs of physics---but with the proviso that \Psi is a non-classical object (an attribute of the background object, in fact; cf. my Outline document).

Needless to add, the Schrodinger formalism in fact is the basis of making predictions---which never have been contradicted in an experiment.

The Heisenberg formalism has always been dicey in the sense that it allows you to grow misconceptions such as the one just discussed, very fast.

What Bell's theorem involves is not a fundamental theory of quantum phenomenon, but an interesting implication of it. The terminology here is right. Bell's is a _theorem_, not a postulate.

It is futile to regard Bell's theorem as if it were a postulate (or the postulate) of QM, though admirers of his work often go overboard, and project it as such. From what I gather, Bell himself was far better than such admirers of his.

Best,

--Ajit

8. Here is how Roger works it seems:

1.Ignore all the original papers by Bohr, Dirac, Schrodinger, Fermi, Einstein, Planck, and Heisenberg
2. Read up on some Bayesian statistics that were and are irrelevant to quantum mechanics
3. Declare that the wavefunction is entirely local. Declare that the photon is entirely local. Declare that quantum probabilities are not physically real.

I think I'll be sticking with the published research belonging to Bohr, Dirac, Schrodinger, Fermi, Einstein, Planck, Heisenberg, et al., instead of Roger's bizarre proclamations.

9. Golden: I am defending the mainstream understanding of QM that has be taught in textbooks for 90 years. Yes, Einstein had a different view, but the consensus is that Einstein was wrong.

For mathematics, I rely on the mathematicians.

I don't know why you say "Declare that the wavefunction is entirely local." What I said was: "I guess you could say that the wavefunction is nonlocal as it represents spatially distinct points at the same time."

10. Dear Roger,

Just a protip--most physicists don't begin their sentences "Well I guess you could say. .. ."

For instance, Newton didn't say, "Well I guess you could say F=ma." Einstein didn't say "Well I guess you could say E=mc^2."

The wavefunction in quantum mechanics IS nonlocal.

Photons of light have nonlocal properties.

This isn't just things we say.

There are things that are.

Such is our physical reality.

11. Newton was definite about F=ma, but not so sure about whether gravity is nonlocal.