Hidden assumptions in the derivation of the Theorem of Bell

TL;DR

This paper revisits Bell's inequalities, showing that their violation in quantum experiments can be explained through Boole's probability theory and algebra, suggesting quantum mechanics may be incomplete rather than implying faster-than-light influences.

Contribution

It demonstrates that violations of Bell's inequalities can be understood via Boole's probability abstractions, challenging common interpretations of nonlocality in quantum mechanics.

Findings

Violations of Bell's inequalities can be explained by Boole's probability theory.

Bell's inequality violations suggest an incompleteness in quantum mechanics.

The algebraic structure underlying Bell's inequalities warrants revision.

Abstract

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.