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

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. Nonlocal entanglement relations provide a means to enforce conservation laws in a probabilistic theory, while the probabilistic nature of nonlocal effects prevents the superluminal transmission of information. In order to explain these measurement-induced changes in terms of fundamental physical processes it is necessary 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 shown that the stochastic modification to the Schroedinger equation is Lorentz invariant. It is further argued that the additional spacetime structure that it 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.