A note on the locality of Gudder's hidden-variable theory

Wilhelm Ochs

David Böhm, Jeffrey Bub

Mićo Đurđević, Milan Vujičić, Fedor Herbut

The three known demonstrations that there exist contextual hidden variables (HV) that reproduce quantum mechanics (the HV theories of Bohm–Bub, Wiener–Siegel, and Gudder) are shown to be special cases of a generalized Gudder’s theory defined in this work. Within this scheme, a symplectic HV theory is introduced for which it is argued that it is physically more useful than Gudder’s theory because it makes possible the definition of a Hamiltonian subquantum dynamical law that reproduces in a natural way the Schrödinger equation. On the other hand, the symplectic HV theory contains as concrete realizations a slightly modified theory of Bohm–Bub and the theory of Wiener and Siegel.

Emilio Santos

F. Pollini

Jeffrey Bub, Vandana Shiva

The conceptually puzzling features of quantum mechanics as a statistical theory all have their source in the impossibility of relating the probability assignments defined by the quantum state to distributions over determinate values of the physical magnitudes. While some interpretations of quantum mechanics, as well as “hidden variable” modifications of the theory, have proposed several constructions for assigning values to magnitudes (beyond the value assignments defined by the quantum state alone), a variety of theorems exist which impose severe restrictions on such theoretical constructions. This note will deal with Bell's proof (in [2]), that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. Bell's result has initiated a series of experiments designed to refute the entire class of local hidden variable theories. We show that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated.