A note on the problem of proper time in Weyl space-time

TL;DR

This paper examines whether Weyl space-time can serve as a valid model for space-time, focusing on the proper time definition and the implications of the second clock effect within the EPS framework.

Contribution

It provides an analysis showing that rejecting models with the second clock effect leads to Weyl integrable space-time as the most suitable structure for space-time.

Findings

Proper time definition in Weyl space-time predicts the second clock effect.

Rejection of the second clock effect implies Weyl integrable space-time.

Weyl integrable space-time is the most general suitable model for space-time.

Abstract

We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space-time (WIST) as the most general structure that would be suitable to model space-time.