Wavefunctions and Minkowski Space-Time: On the Reconciliation of Quantum Theory with Special Relativity

TL;DR

This paper examines how quantum wave-functions can be reconciled with special relativity by analyzing local causality, wave-function reduction, and state evolution in Minkowski space-time, proposing solutions to relativistic quantum theory challenges.

Contribution

It provides a detailed analysis of local causality, local commutativity, and wave-function reduction, proposing solutions for relativistic quantum theory consistency.

Findings

Wave-function collapse challenges relativistic compatibility.

A theory with a preferred foliation predicts correct outcomes.

Relativistic quantum theories must incorporate actual space-time events.

Abstract

The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.