A note on the problem of proper time in Weyl 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.

19 pages and 3 figures

References in corpus (2)

• Inducing the cosmological constant from five-dimensional Weyl space
• Cosmological models in Weyl geometrical scalar-tensor theory

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• Experimental constraints on the second clock effect
• Conformally invariant proper time with general non-metricity
• Note on the absence of the second clock effect in Weyl gauge theories of gravity
• Weyl geometric effects on the propagation of light in gravitational fields
• Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity
• An Invariant Approach to Weyl's unified field theory
• On the Cauchy Problem for Weyl-Geometric Scalar-Tensor Theories of Gravity
• Inhomogeneous spacetimes in Weyl integrable geometry with matter source
• Double layers in Weyl geometry and some physical implications