The Born Rule Dies

TL;DR

The paper argues that the Born rule, fundamental to quantum probabilities, fails in cosmological contexts with many universe copies, necessitating a new rule to define observational probabilities, exemplified by a volume-averaged measure.

Contribution

It introduces a new volume-averaged measure as a replacement for the Born rule in cosmology where multiple universe copies prevent standard probability assignment.

Findings

Born rule does not apply in large universe scenarios

Proposes a volume-averaged measure for probabilities

Highlights the measure problem in cosmology

Abstract

The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer can distinguish all the different possible outcomes corresponding to the projection operators. However, theories of inflation suggest that the universe may be so large that any laboratory, no matter how precisely it is defined by its internal state, may exist in a large number of very distantly separated copies throughout the vast universe. In this case, no observer within the universe can distinguish all possible outcomes for all copies of the laboratory. Then normalized probabilities for the local outcomes that can be locally distinguished cannot be given by the expectation values of any projection operators. Thus the Born rule dies and must be replaced by another rule for observational probabilities in cosmology. The freedom of what this new rule is to be is the measure problem in cosmology. A particular volume-averaged form is proposed.