Conformally invariant proper time with general non-metricity
Adrià Delhom, Iarley P. Lobo, Gonzalo J. Olmo, Carlos Romero
Abstract
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.
Topics & Concepts
MathematicsMeasure (data warehouse)Invariant (physics)Proper timeLTI system theoryTensor (intrinsic definition)Relation (database)Pure mathematicsMathematical analysisClass (philosophy)Space timeSurface (topology)Term (time)Characterization (materials science)Discrete time and continuous timeTime domainDiscrete mathematicsCalculus (dental)Noncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesAdvanced Mathematical Theories and Applications