On the Probabilistic Compatibility of Special Relativity and Quantum Mechanics

Abstract

In this paper we introduce the three main notions of probability used by physicists and discuss how these are to be used when invoking spacelike separated observers in a relativistic format. We discuss a standard EPRB experiment and concentrate upon problems of the interpretation of probabilities. We promote a particularly conservative interpretation of this experiment (which need not invoke an objective notion of collapse) where probabilities are, tentatively, passively Lorentz invariant. We also argue that the Heisenberg picture is preferable in relativistic situations due to a conflict between the Schrodinger picture and passive Lorentz transformations of probabilities. Throughout most of this paper we discuss the relative frequency interpretation of probability as this is most commonly used. We also introduce the logically necessary notion of `prior-frequency' in discussing whether the choice by an observer can have any causal effect upon the measurement results of another. We also critically examine the foundational use of relative frequency in no-signalling theorems. We argue that SQT and SR are probabilistically compatible, although we do not discuss whether they are compatible on the level of individual events.