Information and measurement in generally covariant quantum theory

TL;DR

This paper introduces an information-theoretic framework for covariant quantum theory, resolving measurement ambiguities by deriving time ordering from entropy relationships, and proposing a self-contained probability interpretation involving quantum observers.

Contribution

It develops a novel information-theoretic approach to covariant quantum theory, enabling unambiguous multiple measurement predictions without external classical time.

Findings

Time ordering emerges from entropy relationships.

Provides a self-contained probability interpretation.

Enables consistent predictions for multiple measurements.

Abstract

Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the covariant formalism, and use it to interpret the measurement process. We find that the time ordering of measurements emerges as an entropy relationship in the state of the observers, giving unique probabilities for multiple measurements. This approach suggests a new, fully self-contained probability interpretation for generally covariant quantum physics, which makes use of a quantum mechanical description of the observer, in contrast to standard quantum mechanics which assumes an external, classical observer.