The conditional probabilities and the empirical laws in a free scalar QFT in curved spacetime

TL;DR

This paper introduces a novel approach using prior conditional probabilities to clarify the empirical laws of free scalar quantum field theory in curved spacetime, aiming to address conceptual issues in the interpretation of quantum states.

Contribution

It proposes a new framework employing quantum conditional probabilities to describe empirical laws in QFT in curved spacetime, avoiding vagueness associated with quantum states.

Findings

Empirical laws expressed via prior conditional probabilities.

Reconsideration of the canonical commutation relation in this framework.

Examples illustrating the empirical laws in curved spacetime QFT.

Abstract

Unlike QFT in Minkowski spacetime (QFTM), QFT in curved spacetime (QFTCS) suffers from a conceptual obscurity on the empirical (experimentally verifiable/falsifiable) laws. We propose to employ the notion of prior conditional probabilities to describe a part of the empirical laws of QFTCS. This is interpreted as a quantum conditional probability without no information on the initial state. Hence this notion is expected to be free from the inevitable vagueness of the empirical meaning of quantum states in QFTCS. More generally in quantum physics, this notion seems free from the conceptual problems on state reductions. We confine ourselves to the probabilistic laws of the free scalar fields (Klein-Gordon fields) in curved spacetime, which require some reconsideration on the empirical meaning of the canonical commutation relation (CCR). We give some examples of empirical laws in terms of prior conditional probabilities, concerning the CCR and the free scalar QFTCS.