What are non-local hidden variables?

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Solution 1

Bell's theorem says the following. Suppose that each measurable quantity for a system is described by a stochastic variable - a single number picked out of a hat. The stochastic variable's value might depend in some way on other values you don't know about or can't measure - hidden variables. In order to match the predictions of quantum mechanics, the variables of spatially separated systems would have to influence one another non-locally - without any signal passing between them.

So Bell's theorem means that any other theory that reproduces the predictions of quantum mechanics either works by some means other than hidden variables or it is non-local. A non-local hidden variable theory would just say that there are hidden variables but they are non-local. Such a theory wouldn't get around Bell's inequality - it would claim that the inequality is correct and says that the laws of physics are non-local.

I would also say it seems strange to talk about getting past Bell's inequality. The inequality is either right or wrong. You should be clear about either accepting it or refuting it - getting past is a vague description that leaves your position unclear.

There are other responses to Bell's inequality that don't involve accepting that the world is non-local, such as trying to explain the outcomes of the relevant experiments by applying quantum mechanics instead of trying to find another theory that reproduces its predictions. Quantum mechanics doesn't have hidden variables - rather each system is described in terms of observables represented by Hermitian operators:

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

Solution 2

If you know what are local hidden variables, then any variables outside that is non-local variable.

Local variables (hidden or otherwise) is the information/plan stored inside the entangled particles at the time they depart. Whether hidden or not is a different question. I think they are called hidden because they would be stored in the entangled particles and not visible to outside observers.

Any other mechanism/plan/influence would be non-local.

Not necessarily true, but an example can be - Suppose the measurement of previous pairs somehow are remembered by the environment and that memory influences outcome of measurement of subsequent pairs in such a way that quantum predictions are matched. By environment, I mean one or more of - creation equipment, measuring equipment, space in the vicinity of the experiment.

This would be considered a non-local influence because it is not stored inside entangled particle at the time of creation. It would rather accumulate in the environment as we measure more and more entangled pairs and the accumulation would steer the overall outcome towards quantum predictions. This kind of influence does not need to act at FTL. Simple sub luminal speeds would be sufficient in such a mechanism as it has plenty of time to act over duration of experiment.

This phenomena is named as memory loophole. There can be other possibilities which can be given some other name. All non-local possibilities are called loopholes by QM community.

Allmost all entanglement experiments geared towards proving two things -

  1. Bell's inequality is violated
  2. All loopholes (non-local influences) are closed.

Any data sets that do not prove these two things, are discarded as erroneous data.

I am ready for the down votes:)

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Updated on July 14, 2021

Comments

  • A. C. A. C.
    A. C. A. C. about 1 year

    It is said that Bell's Inequality basically denies all possible local hidden variables theories as solutions to entanglement but what does a non-local hidden variable theory mean and how does it get around Bell's Inequality?

  • Admin
    Admin over 3 years
    I think it would be worth pointing out the consequences of non-local hidden variables ever becoming non-hidden: causality violation. So because hidden variable theories must be non-local by Bell's theorem, such hidden variables must (assuming we don't want causality violation) not be observable even in principle. That's a bit like the aether or something: this thing in the theory which can never be detected, and that makes many people pretty uncomfortable with such theories I think (certainly me).
  • user21820
    user21820 over 1 year
    @tfb: That's actually not right. We cannot observe non-local hidden variables in full, but that by no means implies that we cannot observe them at all. It's not conceptually any different from a wave-function, which we can never measure in full but can measure approximately at a chosen point.
  • CommaToast
    CommaToast about 1 year
    Non-local hidden variables could work like global variables in computers, where a single location in memory gets referred to from multiple different local scopes that don't share local variables. The existence of non-local hidden variables could weakly support the idea that the universe is a simulation.
  • alanf
    alanf about 1 year
  • CommaToast
    CommaToast about 1 year
    @alanf I'm not convinced by Deutsch's arguments or your summary of them. The Halting problem and Incompleteness Theorem are limits on the ability to make statements about things, however they don't block you from creating a full simulation because youtu.be/xP5-iIeKXE8 the Game of Life can run in the Game of Life without having to know if a given pattern ever halts. A simulation can be a full simulation without needing to be able to predict what will happen next in inside itself.
  • CommaToast
    CommaToast about 1 year
    @alanf Deutsch tried to torture Cantor's proof of the uncountability of the real numbers to make a claim about simulations but it's complete nonsense. I mean he completely hamfisted it. He says, "Suppose all possible environments produced by this generator can be laid out sequentially" but then his argument is that a finite generator is finite so therefore it's not "real VR" or some bullshit. Well what if the computer running the sim, itself grows in its own reality, as the simulated reality grows? Deutsch is an idiot (sorry).
  • CommaToast
    CommaToast about 1 year
    He says, "Suppose all possible environments produced by this generator can be laid out sequentially" but then he mentions "altering" these states, creating new states that are not in the sequence (which contradicts the first statement that says "all possible environments produced by this generator can be laid out sequentially". It's bogus AF.
  • alanf
    alanf about 1 year
    @CommaToast Your comments misstate Deutsch's position, so the arguments you present are irrelevant. For example, Deutsch claims that any physical system can be simulated by a universal computer, so your claim that he denies the idea that it would be possible to make a full simulation is false.
  • alanf
    alanf about 1 year
    There are other problems with what you write. For example, the point of supposing that there is a list of all possible environments and then showing there is an environment that isn't on the list is to show that supposing the existence of the list leads to a contradiction so no such list can exist. This kind of argument is called proof by contradiction: to understand it better see "Proof and the Art of Mathematics" by Joel David Hamkins, especially Chapters 1 and 13.
  • CommaToast
    CommaToast about 1 year
    I know that it's a contradiction but it doesn't prove anything. It does not support the point he was trying to make.
  • CommaToast
    CommaToast about 1 year
    Also I am not convinced that "any physical system" can be simulated on a classical computer. A Universal Turing machine has no way to simulate quantum randomness. The best it can do is to use a pseudorandom algorithm. It could use an external source of randomness, but if it does, then it's not really simulating randomness. Also, I'm skeptical a classical computer could simulate quantum non-local effects; I would be warmer to the idea of a simulation of our reality being possible on a quantum computer or hybrid.