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.

arXiv comment12, 2 figures, updated to match published version

References in corpus (36)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• General relativity as an effective field theory: The leading quantum corrections
• Coincident General Relativity
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• The teleparallel equivalent of general relativity
• A systematic approach to generalisations of General Relativity and their cosmological implications
• Coupling matter in modified $Q$-gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Born-Infeld inspired modifications of gravity
• Teleparallel Palatini theories
• Metric-affine approach to teleparallel gravity
• Hybrid metric-Palatini gravity
• Ghosts in metric-affine higher order curvature gravity
• f(R) Gravity with Torsion: The Metric-Affine Approach
• General Relativity and Weyl Geometry
• Mapping Ricci-based theories of gravity into general relativity
• The Non-Metricity Formulation of General Relativity
• Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics
• A correspondence between modified gravity and General Relativity with scalar fields
• Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models
• Non-Linear Obstructions for Consistent New General Relativity
• Constraints on Nonmetricity from Bounds on Lorentz Violation
• Is Teleparallel Gravity really equivalent to General Relativity?
• Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
• Experimental constraints on the second clock effect
• A note on the problem of proper time in Weyl space-time
• A criterion for compatibility of conformal and projective structures
• Ghost-free Palatini derivative scalar-tensor theory: desingularization and the speed test
• Non-singular and ghost-free infinite derivative gravity with torsion
• Light cone and Weyl compatibility of conformal and projective structures
• Nonminimally coupled Weyl gravity
• A generalized Weyl structure with arbitrary non-metricity
• An Invariant Approach to Weyl's unified field theory

Cited by in corpus (9)

• 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
• A novel approach to autoparallels for the theories of symmetric teleparallel gravity
• 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
• Lost in translation: the Abelian affine connection (in the coincident gauge)
• Interference effects and modified Born rule in the presence of torsion