Did Bell rule out all possible kinds of local determinism in the world?

Question

From what I can understand, Bell proved that a certain particle is expected to behave a certain way if there is a hidden variable that determines its eventual state beforehand. Because this doesn’t occur, modern physics supposedly rules out all local hidden variables.

My question is twofold.

A) How do you know how a particle would behave if a hidden variable was operating on it if you don’t know what that hidden variable is in the first place?

B) Did Bell rule out any and all local causes that may help determine the state? Isn’t this the philosophical equivalent of trying to prove a negative? How is this different from disproving that there’s some mysterious local invisible entity pushing things down every time which causes gravity? Sure, this sounds ludicrous, but almost no one would admit that this can actually be disproven.

Answer 1

Bell's theorem explains that if the evolution of a system is described by stochastic variables and measurement devices aren't correlated with whatever chooses the measurements you perform, then the degree to which it can be correlated with other systems is constrained to a particular form.

Quantum theory allows systems to have correlations that break this constraint. If you explain these correlations by assuming that the equations of motion of quantum theory describe reality, then the evolution of a system isn't described by stochastic variables, but rather by observables that are Hermitian operators that can be described by matrices. Reality as described by these matrices is more complicated than the world we see around us and looks approximately like a collection of parallel universes in the circumstances of everyday life as a result of a process called decoherence:

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/1111.2189

For some reason this is controversial and is called the many worlds interpretation of quantum theory (MWI).

Observables of different systems only affect one another when they interact. Since the relevant equations of motion are local so is the evolution of quantum systems. In experiments to test the Bell inequalities, locally inaccessible information is carried in decoherent systems and this information causes the correlations when the results of measurements interact and not before:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

So there is a local explanation of Bell correlations.

There are other accounts of physical reality that are called interpretations of quantum theory despite the fact that they contradict unmodified quantum theory (that is the MWI) in ways that can in principle be tested experimentally:

https://arxiv.org/abs/1906.10761

https://arxiv.org/abs/2310.14969

https://arxiv.org/abs/2003.11989

https://arxiv.org/abs/2003.12195

Some of these may be local, such as superdeterminism, which violates the assumption that measurement devices aren't correlated with whatever chooses the measurements you perform, but collapse and pilot wave theories are non-local.

Answer 2

There is a clear loophole in Bell's theorem that it requires the experimentalists to freely decide in which orientation they perform a measurement. Strictly speaking the experimentalists are expected to be described by the same unitary evolution describing the particles that they are measuring. Therefore there is no choice on the experimentalists side and their choices of measurements could be correlated with the hidden variable values of the particles they are measuring.

On the other hand it would be very strange for this kind of correlations to consistently occur. It would be hard to imagine a process that consistently causes correlations between the neurons in an experimentalists brain, making them decide on performing the experiments one way or another, and the very particles they are measuring.

See also https://physics.stackexchange.com/a/633651/130040

Answer 3

How a particular interpretation deals with bells theorem is a fundamental aspect of understanding that interpretation - it's one of the questions any interpretation has to answer.

One interpretation which is (arguably, I suppose) locally deterministic is Many Worlds, and bell himself expressed that he didn't like many worlds as an idea very much but he did think it gave a novel solution to bells theorem.

So as far as "loopholes" in Bells theorem go, breaking the assumption that there's a single world with a single experimental result is a loophole in bells theorem that allows for a certain kind of local casualty.

Answer 4

Bell's theorem applies generally- it doesn't single-out any specific type of potential local cause. To use your example, suppose the outcomes of measurements on electron spins are the result of a 'mysterious local entity' or an invisible pink rabbit, or whatever, the point is that if you have a pair of entangled electrons, one of which is in New York and the other is in Timbuktu, then the mysterious local entity in New York would have to be communicating with the mysterious local entity in Timbuktu faster than the speed of light in order to be able to explain the results of the experiments.

As an aside, there is an argument you can make to say that the Copenhagen interpretation of quantum mechanics is inherently non local in any case. For example, the wave function of an electron can be spread over a vast volume of space, but when you measure the electron's location with some degree of precision, the wave function is taken to change instantaneously everywhere.