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Can Leggett-Garg inequality be used to falsify superdeterminism, Bohmian mechanics and other realist interpretations of quantum mechanics?

https://en.wikipedia.org/wiki/Leggett_inequality https://en.wikipedia.org/wiki/Leggett%E2%80%93Garg_inequality

Since many people are still working on those interpretations, i am doubtful it can, but i still don't understand the reason. Furthermore,why are these two inequalities different from Bell's??

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    $\begingroup$ There seem to be two questions here, one is about the falsifiability of Leggett's inequalities and the other is the meaning of realism in quantum physics. Please edit one out as these are very different questions. $\endgroup$
    – Mauricio
    Commented Jan 24 at 17:19
  • $\begingroup$ Duplicate? (no accepted answer): physics.stackexchange.com/questions/96643/… $\endgroup$
    – Mauricio
    Commented Jan 24 at 17:26
  • $\begingroup$ I expect a simplier answer that the one provided by the link you commented. I'll try my best to edit the question to include the Leggett's inequality part only. Thank you $\endgroup$
    – Marco Fabbri
    Commented Jan 24 at 17:31
  • $\begingroup$ If you aren't trying to model reality with your physical theory, what exactly is it that you're trying to model? $\endgroup$
    – Travis
    Commented Jan 25 at 18:29

1 Answer 1

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Leggett and Garg's stated assumptions are

(A1) Macroscopic realism: A macroscopic system with two or more macroscopically distinct states available to it will at all times be in one or the other of these states.

(A2) Noninvasive measurability at the macroscopic level: It is possible, in principle, to determine the state of the system with arbitrarily small perturbation on its subsequent dynamics.

If you ignore the "macroscopic" part of the assumptions, whose meaning is unclear (as the authors admit), hidden variable theories violate (A2) by definition (the unmeasurability of hidden variables is what makes them "hidden"), so the argument doesn't rule out any hidden variable theory. The paper doesn't claim otherwise; there's no mention of Bohmian mechanics or hidden variables in it.

As for superdeterminism: "It is possible [...] to determine the state of the system with arbitrarily small perturbation on its subsequent dynamics" means that there is only a small difference between the future of the system if you do measure it and the future of the system if you don't. In a superdeterministic world, one of those futures is inconsistent with the laws of physics (the one that doesn't happen), so the comparison doesn't make sense. I would say that superdeterminism violates an implicit assumption of this argument (and most scientific arguments) that counterfactual reasoning makes sense, so the argument doesn't apply to superdeterminism either.

Bell's argument has nothing like assumption (A2) in it. In Bell's experiment, the measurements on each prepared system are spacelike separated, so the (local) effect of the measurement on the system doesn't matter. Also, in Bell's argument, there is no assumption that measurements reveal the "true" state of the system.

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