Conformally invariant proper time with general non-metricity

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...

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Bibliographic Details
Published inThe European physical journal. C, Particles and fields Vol. 80; no. 5; pp. 1 - 11
Main Authors Delhom, Adrià, Lobo, Iarley P., Olmo, Gonzalo J., Romero, Carlos
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020
Springer
Springer Nature B.V
SpringerOpen
Subjects
Astronomy
Astrophysics and Cosmology
Earth surface
Elementary Particles
Hadrons
Heavy Ions
Invariants
Measurement Science and Instrumentation
Muons
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
String Theory
Tensors
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Summary: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.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-020-7974-y