Conformally invariant proper time with general non-metricity

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.

12, 2 figures, updated to match published version

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Cited by in corpus (8)

• New models and Big Bang Nucleosynthesis constraints in $f(Q)$ gravity
• Late-time cosmology with phantom dark-energy in $f(Q)$ gravity
• Nonmetricity theories and aspects of gauge symmetry
• Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Kinematics in Metric-Affine Geometry
• Interference effects and modified Born rule in the presence of torsion
• Lost in translation: the Abelian affine connection (in the coincident gauge)