Monday, June 24, 2024

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


  1. This comment has been removed by the author.

  2. Quantum mechanics alone cannot fully explain several fundamental phenomena, including the spin-statistics theorem, the Unruh effect (recently observed), the Casimir effect, self-interaction, superposition and entanglement. QFT handles all of these fine. In terms of entanglement, the field commutators vanish. It's an utter myth, from the poorly educated, that QFT is just a relativistic version of quantum mechanics. Quantum "states" (macro device readings) are just asymptotic regions of fields. You can violate Bell inequalities with chaotic balls, electromagnetism, Ising models, brownian motion and even water waves. Fields are trivially nonlocal. Nothing mysterious or instantly nonlocal is happening. People trapped in abstractions from the 1920s have mystified our physics.