Propositional counter-factual definiteness and the EPR paradox

Abstract

In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert subspace that represents P. Determined in such a way, truth or falsity of P can be termed “a factual truth-value” of P. In this present paper, it is proposed to consider “a counter-factual truth-value” of P, i.e., either of the values, true or false, that might have been taken by P if the system had been in a pure state belonging to a Hilbert subspace that does not represent P. The assumption that it is always possible to speak meaningfully of counter-factual truth-values of experimental propositions can be called “the hypothesis of propositional counter-factual definiteness.” As shown in this paper, this hypothesis lies at the basis of the Einstein-Podolsky-Rosen (known as EPR) paradox, a striking and influential thought experiment intended to defy predictions of quantum mechanics, such as the one where measurements of spin along the different axes are incompatible. The purpose of this paper is to show that this hypothesis can be falsified by declining to paste together invariant-subspace lattices of contexts associated with the system (in other words, Boolean algebras or blocks) into one Hilbert lattice. Without such pasting, the EPR paradoxical inference cannot be reached.