Eur. Phys. J. C (2020) 80: 415
https://doi.org/10.1140/epjc/s10052-020-7974-y

Regular Article - Theoretical Physics

Conformally invariant proper time with general non-metricity

¹ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot, 46100, Valencia, Spain
² Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, Lavras, MG, 37200-000, Brazil
³ Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba, 58051-970, Brazil

^* e-mail: iarley_lobo@fisica.ufpb.br

Received: 7 February 2020
Accepted: 24 April 2020
Published online: 12 May 2020

Abstract

We show that the definition of proper time for Weyl-invariant space-times given by Perlick naturally extends to spaces with arbitrary non-metricity. We then discuss the relation between this generalized proper time and the Ehlers–Pirani–Schild definition of time when there is arbitrary non-metricity. Then we show how this generalized proper time suffers from a second clock effect. Assuming that muons are a device to measure this proper time, we constrain the non-metricity tensor on Earth’s surface and then elaborate on the feasibility of such assumption.