From a purely mathematical standpoint, does Bell Inequality favor De Broglie-Bohm over other interpretations of QM?

I have a superficial understanding of all this but it seems to me that Bell Inequality is about non-locality and entanglement which are some of the key features of de Broglie-Bohm.

"Moreover, a hidden variable interpretation of elementary quantum theory (5) has been explicitly constructed. That particular interpretation has indeed s grossly nonlocal structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces the quantum mechanical predictions."

ref: '5'. D. Bohm. Phys Rev 85, 166 and 180 (1952). http://www.drchinese.com/David/Bell_Compact.pdf https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory

  • $\begingroup$ The Bell Inequality is a recipe for making an experimental determination about which of two classes of possible quantum theories are consistent with physical reality. As with all pieces of pure theory it only tells you anything in conjunction with experimental evidence. $\endgroup$ – dmckee Sep 28 '17 at 18:01
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    $\begingroup$ de Broglie-Bohm, as an interpretation of quantum mechanics, needs to be completely consistent with QM, and as far as experimental observables go, it is competen synonymous with the latter - exactly like all the other interpretations. There is no result within QM that can provide support to one interpretation over another, by definition of the term. The observed violations of Bell inequalities are entirely consistent with QM so they are blind to any such issues. $\endgroup$ – Emilio Pisanty Sep 28 '17 at 19:39
  • $\begingroup$ edited the question, hopefully for clarity $\endgroup$ – allwind Sep 28 '17 at 20:22

No, Bell inequalities do not favour Bohmian mechanics over other interpretations of QM. However, the experimental violations of Bell inequalities rule out any hidden variable theory that does not share some of the key features of Bohmian mechanics, indeed, first and foremost the non-locality.

With a bit more details, Bell inequalities are theorems which apply to hidden variable theories. Consider the famous experiments with entangled pairs of particles: when one member of the pair is observed with a spin +1, the other is always observed with a spin -1. There are two premises to demonstrate Bell inequalities: (i) each pair is produced in a well-defined state and keeps that state until measurement (i.e. one particle has a spin +1 and the other one has a spin -1, always), and (ii) the measurement on one particle is totally independent from the measurement on the other particle. Since Bell inequalities have been observed to be violated, either (i) or (ii), or both, are false. Those people who are attached to the metaphysical concept of a reality independent of our observing it definitively want to keep (i) and therefore they have to accept that (ii) is false. But then Bohmian mechanics precisely provide such an escape. Bell himself wrote that he felt vindicated when he read Bohm's seminal article, actually.

On the other hand, interpretation of QM are just that interpretations: they make the exact same predictions and they share common features essential to derive those predictions. Non-locality is one of them: it is inescapable and Bohmian mechanics is non-local in exactly the same way as the Copenhaguen interpretation since in both cases the non-locality comes from the wave function dependence on the positions, spins, etc of all the particles in the system under scrutiny. There is really no difference at that level between both interpretation.

  • $\begingroup$ "experiments on Bell's Inequality rule out [...]" FTFY. Bell's work shows the (hugely important) fact that you can distinguish at least two classes of proposed theories, but it doesn't pick one until you have the data. $\endgroup$ – dmckee Sep 28 '17 at 19:07
  • $\begingroup$ This is clarified later but you are right, if somebody only reads the first paragraph… $\endgroup$ – user154997 Sep 28 '17 at 19:19

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