Determinism and locality in quantum mechanics

W. Michael Dickson

Gerard ’t Hooft

A. Berthelot

W. Michael Dickson

Yemima Ben‐Menahem

This chapter discusses the conceptual relationship between determinism and locality, particularly in the context of quantum mechanics (QM). It first examines the connection between determinism and locality in abstract terms, and then in the context of QM. It then considers four possible combinations of locality and determinism: locality and determinism, nonlocality and determinism, locality and indeterminism, and nonlocality and indeterminism. It also explains how determinism and locality are linked to a central tenet of QM—the Heisenberg uncertainty relations. Three approaches that link uncertainty and nonlocality are explored: the first two, attributed to Erwin Schrödinger and I. Pitowsky, argue from the uncertainty relations to entanglement; the second, following S. Popescu and D. Rohrlich, from entanglement to the uncertainty relations. The chapter argues that determinism and locality are independent concepts but can offset each other under certain conditions, so that violation of the one permits satisfaction of the other.

Jiří Souček

Abstract. In this note we shall show that the proof of the nonlocality of Quantum Mechanics given in [1] contains a gap. We also show that Bell inequalities cannot be derived in the modified QM. In the paper [1] there is a proof of the nonlocality of Quantum Mechanics (QM). In the proof of this statement the main step is the following implication: “from EPR correlations to the predetermination”. This means the following: “A deterministic hidden variable theory was one’s only hope, if one wanted to explain the predicted quantum correlations in a local way. ” ([1]. Page 2) – i.e. the nonlocality or the pre-determination. “The important thing was instead that the only way to explain the perfect correlations locally is to attribute outcome-determining properties to the individual particles. These properties, evidently, would vary randomly from one particle pair to the next, but would be fixed (in an appropriately correlated way) once and for all at the source for a given particle pair. ” ([1], page 2). This may be called the pre-determination. “ … such deterministic hidden variables are the only way to account locally for the