Simultaneity and the Concept of `Particle'

TL;DR

This paper explores the relationship between the concept of particles and simultaneity in curved spacetimes, proposing an observer-dependent particle interpretation based on radar time that applies universally to different observers.

Contribution

It introduces a new observer-dependent particle concept using radar time, independent of coordinate choices, applicable to various observer motions in curved spacetimes.

Findings

Radar time provides a consistent notion of simultaneity in curved spacetimes.

The observer-dependent particle interpretation aligns with known cases.

The approach is applicable to non-inertial observers and simple cosmologies.

Abstract

The history of the particle concept is briefly reviewed, with particular emphasis on the `foliation dependence' of many particle creation models, and the possible connection between our notion of particle and our notion of simultaneity. It is argued that the concept of `radar time' (originally introduced by Sir Hermann Bondi in his work on k-calculus) provides a satisfactory concept of `simultaneity' for observers in curved spacetimes. This is used to propose an observer-dependent particle interpretation, applicable to an arbitrary observer, depending solely on that observers motion and not on a choice of coordinates or gauge. This definition is illustrated with application to non-inertial observers and simple cosmologies, demonstrating its generality and its consistency with known cases.