Abstract
It is shown that any hidden variable model that reproduces quantum mechanics for a single particle must either be nonlocal or violate conservation of momentum. This is established by deriving an inequality which must hold in any local, momentum-conserving hidden variable model for a modified form of the double-slit experiment. It is then shown that any hidden variable model that reproduces quantum mechanics must violate the inequality. The inconsistency between the classical and quantum views of the world is therefore demonstrated in a new way.
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Note that this does not contradict Ehrenfest's theorem. Ehrenfest's theorem shows that conservation of momentum holds for theexpectation value of momentum. It is still possible, in a hidden variable theory, for conservation of momentum at the hidden variables level to be violated, yet at the statistical level of many events for the expectation value of momentum to be conserved.
Ref. 13, pp. 176ff.
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Rice, D.A. Nonlocality and conservation laws in hidden variable theories. Found Phys 27, 1345–1353 (1997). https://doi.org/10.1007/BF02551516
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DOI: https://doi.org/10.1007/BF02551516