Determinism and Relativity

Eftichios Bitsakis

Four forms of physical determination are presently known in physics: classical or mechanical determination, related to classical mechanics; dynamical determination, related to the relativistic theories of electromagnetism and gravitation; classical statistical determination, related to classical statistical theories; and quantum statistical determination, related to modern microphysics. The concept of interaction is a fundamental on-tological category, a moment of which is the causal relation; interaction is also local, taking place at finite velocities. Following the evolution of physical theories, it is possible to attest to the historicity of the concept of interaction and, accordingly, of the categories of interaction and determination. According to the Copenhagen School, causality and locality are incompatible with quantum mechanics. On the contrary, according to the point of view developed here, realism, causality and locality are simultaneously compatible in the domain of microphysics.

Patrick H. Byrne

Stephen G. Brush

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.

Hoshang Heydari

In this paper we will establish a relation between geometric uncertainty relation and the determinant of the quantum covariance matrix for mixed quantum states. We will show that determinant of the covariance matrix represents the squared metric area of a parallelogram. In this setting the geometric uncertainty relation compares a metric area to a symplectic area. Moreover, we will in details investigate relation between J-holomorphic maps and geometric uncertainty relation for mixed quantum states. We will argue that determinant of the quantum covariance matrix is equal to the harmonic energy of a holomorphic map that minimize the areas.

Thomas A. Brody