Measurement and Probability in Relativistic Quantum Mechanics

TL;DR

This paper develops a relativistic quantum measurement model that extends the Everettian approach, using decoherent histories and envariance to define probabilities consistent with Born's rule, applicable within quantum field theory.

Contribution

It introduces a relativistic, Everettian measurement framework that generalizes envariance for probability assignment in spacetime, addressing the measurement problem in RQM.

Findings

Probabilities over quantum histories are objectively defined using generalized envariance.

Repeated experiments' statistics tend to follow Born's rule as repetitions increase.

Wave function collapse is reinterpreted as an update of knowledge about the universe's eigenstate.

Abstract

Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the traditional "collapse" postulate for quantum measurement is problematic in a relativistic context, at the very least because, as usually formulated, it violates the relativity of simultaneity. The present paper addresses this with a relativistic model of measurement in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The approach is essentially Everettian, in the sense that it uses the unmodified, unitary quantum formalism of RQM. But it addresses the difficulty with typical "many worlds" interpretations on how to even define probabilities over different possible ``worlds''. To do this, Zurek's concept of envariance is generalized to the context of relativistic spacetime, giving an objective definition of the probability of any one of the quantum histories, consistent with Born's rule. It is then shown that the statistics of any repeated experiment within the universe also tend to follow the Born rule as the number of repetitions increases. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates, and their "collapse" can be re-interpreted as simply an update based on additional incremental knowledge gained from a measurement about the "real" eigenstate of our universe.