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
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.
© The Author(s), 2020