Towards Quantum Field Theory in Curved Spacetime for an Arbitrary Observer

TL;DR

This paper introduces a novel quantum field theory framework tailored for arbitrary observers in curved spacetime, utilizing radar time to define simultaneity surfaces and constructing unitary dynamics under certain conditions.

Contribution

It proposes a new approach to quantum field theory in curved spacetime for arbitrary observers, emphasizing radar time and constructing unitary evolution when surfaces are Cauchy.

Findings

Framework for quantum field theory based on radar time.

Construction of unitary dynamics on Cauchy surfaces.

Discussion of potential information loss in general cases.

Abstract

We propose a new framework of quantum field theory for an arbitrary observer in curved spacetime, defined in the spacetime region in which each point can both receive a signal from and send a signal to the observer. Multiple motivations for this proposal are discussed. We argue that radar time should be applied to slice the observer's spacetime region into his simultaneity surfaces. In the case where each such surface is a Cauchy surface, we construct a unitary dynamics which evolves a given quantum state at a time for the observer to a quantum state at a later time. We speculate on possible loss of information in the more general cases and point out future directions of our work.