Revisiting factorability and indeterminism

Abstract

Perhaps it is not completely superfluous to remind that Clauser-Horne factorability, introduced in [1], is only necessary when λ, 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 λ is obtained by finding a set of expressions M_i=M_i(λ,ξ_i), with {ξ_i} a set of HV's, all independent from one another and from λ. Otherwise, factorability can be recovered on γ= λ \oplus\ μ, with μ another additional HV, so that a description M_i=M_i(γ,ξ_i) is again found: conceptually, this is always possible; experimentally, it may not: μ 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].