Gravity, Gauges and Clocks

TL;DR

This paper explores the definitions of standard clocks in various gravitational theories, contrasting Weyl and Einsteinian clocks, and discusses how atomic clocks could measure proper time in non-Riemannian geometries.

Contribution

It introduces a framework for defining Einsteinian clocks within non-Riemannian gravitation theories using Weyl gauge symmetry.

Findings

Standard Einsteinian clocks can be adapted to non-Riemannian theories.

Atomic clocks may measure proper time in non-metric geometries.

A model of gravitation based on non-Riemannian geometry illustrates these concepts.

Abstract

We discuss the definitions of standard clocks in theories of gravitation. These definitions are motivated by the invariance of actions under different gauge symmetries. We contrast the definition of a standard Weyl clock with that of a clock in general relativity and argue that the historical criticisms of theories based on non-metric compatible connections by Einstein, Pauli and others must be considered in the context of Weyl's original gauge symmetry. We argue that standard Einsteinian clocks can be defined in non-Riemannian theories of gravitation by adopting the Weyl group as a local gauge symmetry that {\it preserves the metric} and discuss the hypothesis that atomic clocks may be adopted to measure proper time in the presence of non-Riemannian gravitational fields. These ideas are illustrated in terms of a recently developed model of gravitation based on a non-Riemannian space-time geometry.