Wave Function Collapse, Lorentz Invariance, and the Third Postulate of Relativity

TL;DR

This paper demonstrates that a stochastic, nonlinear modification to the Schrödinger equation, modeling wave function collapse, is Lorentz invariant and supports the idea of local commutativity as a third postulate of relativity.

Contribution

It shows that a proposed collapse model maintains Lorentz invariance and introduces local commutativity as a fundamental postulate of relativity.

Findings

The stochastic collapse model is Lorentz invariant.

The model enforces local commutativity of spacelike-separated operators.

The modification preserves conservation laws during measurement.

Abstract

The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic nature of nonlocal effects prevents the superluminal transmission of information, while nonlocal entanglement relations provide a means to enforce conservation laws in a probabilistic theory. In order to explain measurement-induced changes in terms of fundamental physical processes it is important to take these two key characteristics into account. One way to do this is to modify the Schroedinger equation by adding stochastic, nonlinear terms. A number of such proposals have been made over the past few decades. A recently proposed equation based on the assumption that wave function collapse is induced by a sequence of correlating interactions of the kind that constitute measurements has been shown to maintain strict adherence to conservation laws in individual instances, and has also eliminated the need to introduce any new, ad hoc physical constants. In this work it is shone that the proposed stochastic modification to the Schroedinger equation is also Lorentz invariant, even though it is formulated in a preferred reference frame. It is further argued that the additional spacetime structure that the proposed modification requires provides a way to implement the assumption that spacelike-separated operators (and measurements) commute, and that this assumption of local commutativity should be regarded as a third postulate of relativity.