%0 Journal Article %T Conformally invariant proper time with general non-metricity %A Delhom, A. %A Lobo, I. P. %A Olmo, G. J. %A Romero, C. %J European Physical Journal C %D 2020 %V 80 %N 5 %I Springer %@ 1434-6044 %G English %F Delhom_etal2020 %O WOS:000535820900011 %O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=4405), last updated on Tue, 09 Jun 2020 10:12:52 +0000 %X 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. %R 10.1140/epjc/s10052-020-7974-y %U https://arxiv.org/abs/2001.10633 %U https://doi.org/10.1140/epjc/s10052-020-7974-y %P 415 - 11pp