Revisiting factorability and indeterminism

TL;DR

This paper examines the conditions under which factorability and indeterminism are valid in hidden variable theories, highlighting the role of additional variables and their accessibility in quantum measurements.

Contribution

It clarifies the relationship between factorability, determinism, and hidden variables, emphasizing the conceptual and experimental implications of inaccessible variables.

Findings

Factorability depends on the determinism of hidden variables.

Additional hidden variables can restore factorability when initial assumptions fail.

Experimental inaccessibility of certain variables challenges the interpretation of factorability.

Abstract

Perhaps it is not completely superfluous to remind that Clauser-Horne factorability, introduced in [1], is only necessary when \lambda, the hidden variable (HV), is sufficiently deterministic: for {M_i} a set of possible measurements (isolated or not by space-like intervals) on a given system, the most general sufficient condition for factorability on \lambda\ is obtained by finding a set of expressions M_i=M_i(\lambda,\xi_i), with {\xi_i} a set of HV's, all independent from one another and from \lambda. Otherwise, factorability can be recovered on \gamma = \lambda\ \oplus\ \mu, with \mu\ another additional HV, so that a description M_i=M_i(\gamma,\xi_i) is again found: conceptually, this is always possible; experimentally, it may not: \mu\ may be unaccessible or even its existence unknown (and so, too, from the point of view of a phenomenological theory). Results here may help clarify our recent post in [6].