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"All quantum observables in a hidden-variables model must commute simultaneously" by James Malley

Abstract:

*Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show these these conditions are entirely equivalent to those later introduced by Bell, Kochen and Specker. As is it known that these conditions are also equivalent to those under which the Bell-Clauser-Horne inequalities are derived, we see that any experimental violations of the inequalities demonstrate only that quantum observables do not commute.The same conclusion applies to the collection of elegant inequality-free no-go proofs of Greenberger-Horne-Zeilinger, Mermin and Peres.*

In essence, this paper states that all hidden variable theories - local or non-local - must necessarily require that observables commute - which is empirically false. This conclusion makes sense to me, if for no other reason than it is another way of saying that reality is observer dependent (and which hidden variable theories are designed to negate).

Von Neumann's famous HV no-go proof of 1932, which was torn down by Bell, is also vindicated in a certain sense. (Although I would not call it a ironclad defense.)

It seems to me that as time passes, it will become clear that no Hidden Variable theory can be made which is both self-consistent and consistent with basic predictions of QM.