Abstract
This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.
Highlights
I published a series of papers which can be unified by the slogan “getting rid of nonlocality from quantum physics” [1,2,3,4,5]
Reduction of the wave function resulting from measurement retro-action; and the Heisenberg uncertainty principle. The latter was formulated as follows: “It is shown in quantum mechanics that, if the operators corresponding to two physical quantities, say A and B, do not commute, AB 6= BA, the precise knowledge of one of them precludes such knowledge of the other
The observational problem is free of any special intricacy since, in actual experiments, all observations are expressed by unambiguous statements referring, for instance, to the recording of the point at which an electron arrives at a photographic plate. Speaking in such a way is just suited to emphasize that the the appropriate physical interpretation of the symbolic quantum mechanical formalism amounts only to predictions, of determinate or statistical character, pertaining to individual phenomena appearing under conditions defined by classical physical concepts.”
Summary
I published a series of papers which can be unified by the slogan “getting rid of nonlocality from quantum physics” [1,2,3,4,5] ( see recent papers of References [6,7,8] for a discussion). The EPR-reasoning was, based on two basic quantum mechanical principles: reduction of the wave function (the projection postulate) resulting from measurement retro-action; and the Heisenberg uncertainty principle The latter was formulated as follows: “It is shown in quantum mechanics that, if the operators corresponding to two physical quantities, say A and B, do not commute, AB 6= BA, the precise knowledge of one of them precludes such knowledge of the other. Bohr wanted to say that if even for a single particle position and momentum are irreducibly coupled to corresponding experimental contexts, there is no reason to expect something cardinally different for a compound system of two particles This line of thinking is important for foundational analysis of the Bell-argument and experiments based on violation of the Bell type inequalities (see References [1,2,3,4,5]). It is not surprising that, as was shown in my recent paper, Reference [1], violation-satisfaction of the CHSH-inequality can be formulated in terms of noncommutativity-commutativity of operators representing local observables of Alice and Bob, respectively, as indicated above
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