Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom

TL;DR

The paper proves that relativistically invariant Markovian collapse theories require nonstandard degrees of freedom to avoid deterministic evolution, highlighting fundamental constraints in relativistic quantum theories.

Contribution

It demonstrates that standard degrees of freedom cannot support indeterministic evolution in relativistic quantum field theories with stable vacua.

Findings

Standard degrees of freedom lead to deterministic evolution under relativistic invariance.

Relativistically invariant collapse theories must employ nonstandard degrees of freedom.

The stability of the vacuum constrains the nature of possible quantum evolutions.

Abstract

The impossibility of an indeterministic evolution for standard relativistic quantum field theories, that is, theories in which all fields satisfy the condition that the generators of spacetime translation have spectrum in the forward light-cone, is demonstrated. The demonstration proceeds by arguing that a relativistically invariant theory must have a stable vacuum, and then showing that stability of the vacuum, together with the requirements imposed by relativistic causality, entails deterministic evolution, if all degrees of freedom are standard degrees of freedom.