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From the EPR article:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity."

I do not see how a local quantum theory violates this notion of realism. Would it not be more accurate to say that the option is between non-separable realism and separable non-realism?

Norbert Schuch
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A.D.
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Realism in this sense states that measurable things have a value, whether or not they are actually measured. This lends a sense of objective realism to the measured quantities in the sense that they don't need a subject observing them to have that value. It's trivial to build a patchwork quilt theory which gets the answer "right" for everything observed, but lacks a value for things which don't have a subject actively observing them.

The issues that arise with Bell's theorem appear when you try to define these values without creating contradictions.

Cort Ammon
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  • So is this realism in a broader sense than Einstein's operational definition of it? Can we have local realism if we take realism to be in Einstein's sense exclusively? – A.D. Dec 25 '20 at 07:30
  • I don't think so. I'm having trouble finding any reference that wants to pin down Einstein's definition of realism precisely enough. However, in a soft handwavy sense, its universally accepted that Bells inequalities forbid local realism, so I think its' reasonable to assume that nobody has found a loophole based on careful definition of realism. – Cort Ammon Dec 25 '20 at 07:37
  • @CortAmmon and why would local non-realism assumed to be capable of violating Bell Inequalities without using non local information?. The issue is not that we have local non realism left, it is that we only have non-locality left, as Bell believed. –  Dec 25 '20 at 08:07
  • @Wolphramjonny When you say "information", does this mean "realist variables"? – Norbert Schuch Dec 26 '20 at 18:52
  • @NorbertSchuch, I mean, for Alice's photon, at the time of Alice's measurement, knowledge of the orientation of the measurement apparatus of Bob, or viceversa, whoever measured last needs that info to bias the statistics. Or is it just magic? –  Dec 26 '20 at 19:07
  • @Wolphramjonny If by "magic" you mean "there is no realist explanation", then yes, it is magic. (Other than that, Alice needs to info about Bob's measurement to describe her experiment, nor will she obtain any information through her experiment.) – Norbert Schuch Dec 26 '20 at 19:20
  • @NorbertSchuch I know that, but the correlations cannot be generated without magic –  Dec 26 '20 at 19:50
  • @Wolphramjonny Sure, but this does not necessarily require non-locality, unless you insist on realism. – Norbert Schuch Dec 26 '20 at 22:44
  • @NorbertSchuch I guess the ethernal question will be answred when someone can make a nonrealist local model that works in a local computer –  Dec 26 '20 at 23:44
  • @NorbertSchuch wouldnt a simulated Markov chain be nonrealist? Perhaps I am confused in the meaning of nonrealism –  Dec 26 '20 at 23:46
  • @Wolphramjonny I'd say any model which works in a local computer can be replaced by a realist model, where all possible outcomes are determined at any point in time, and there is a complicated update mechanism to update the new states after each measurement. You can do this e.g. with arbitrary measurements on a qubit. (Which is some kind of Markov chain, I guess?) – Norbert Schuch Dec 26 '20 at 23:49
  • @NorbertSchuch I understand, thanks –  Dec 27 '20 at 00:17
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Realism means that there are hidden variables that can explain the statistical results in a deterministic way. A non realist theory has no hidden variables, and thus the value of the variable to be measured could not have a defined value until it is measured. Here the measurement result is randomly chosen (within some distribution) at the moment of the measurement.

Notice that non-realism, with its inherent randomness, should not have any advantage in being able to reproduce quantum correlations. What magical process would enable this? Without non-local information a non-real local algorithm should be as bad as a real local one in reproducing quantum correlations.

I have asked multiple times to colleagues about this issue, and also read quite a bit, and I could never find an argument about why non realism could get away with non-locality. In my opinion Bell's theorem really show that QM is non local, because local non-realism is becoming just a word to avoid saying "no-local".

PS: some give QM as an example of a local non-realist theory, but this argument is circular, because it explicitly assumes in advance that QM is local.

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    Can't upvote this enough! Non realism is hard to get exactly because it does not explain the correlation. I once tried to explain non realism in the "students & teachers" analogy of entanglement (https://physics.stackexchange.com/q/591578/276737). I ended up saying that we completely forget about the students (photons), which are just "part of the world". Later, somehow, the teachers (detectors/observables) are acted upon in a correlated way. – Cream Feb 04 '21 at 14:21