Rescuing the Born Rule for Quantum Cosmology

TL;DR

This paper argues that the Born rule remains sufficient for quantum cosmology when generalized measurements are considered, challenging recent claims that it fails and causes the cosmological measure problem.

Contribution

It demonstrates that the Born rule's perceived failure in quantum cosmology is due to a restrictive definition, and that it remains valid with generalized measurements.

Findings

All probabilities can be derived from the Born rule with generalized measurements.

The perceived insufficiency of the Born rule is not unique to cosmology.

Comments on Hilbert space dimensionality and permutation symmetry are provided.

Abstract

Page has recently argued that the Born rule does not suffice for computing all probabilities in quantum cosmology. He further asserts that the Born rule's failure gives rise to the cosmological measure problem. Here I contend that Page's result stems from his use of an overly restrictive definition of the Born rule. In particular, I demonstrate that all of the probabilities he wishes to compute follow from the Born rule when generalized measurements are permitted. I also register two comments on Page's theoretical setting, relating respectively to Hilbert space dimensionality and permutation symmetry. These considerations lead me to conclude that the claimed insufficiency of the Born rule is by no means specific to the cosmological context.