Observers' measurements in premetric electrodynamics I: Time and radar length

Abstract

The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of the spacetime, like the classical Michelson-Morley, Ives-Stilwell, Kennedy-Thorndike experiments or frequency comparison experiments in general, it is necessary to describe them in theories, which go beyond the Lorentzian metric structure. However, this requires a description of an observer's measurement without relying on a metric. We provide such a description of an observer's measurement of the fundamental quantities time and length derived from a premetric perturbation of Maxwell's electrodynamics and a discussion on how these measurements influence classical relativistic observables like time dilation and length contraction. Most importantly, we find that the modification of electrodynamics influences the measurements at two instances: the propagation of light is altered as well as the observer's proper time normalization. When interpreting the results of a specific experiment, both effects cannot be disentangled, in general, and have to be taken into account.

18 pages, updated to journal version, typos corrected, discussion extended

References in corpus (10)

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• Riemann-Finsler geometry and Lorentz-violating kinematics
• Bipartite Riemann-Finsler geometry and Lorentz violation
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• Classical-physics applications for Finsler $b$ space
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• Quantization of general linear electrodynamics
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• Finsler gravity action from variational completion
• Finsler spacetime geometry in Physics
• Berwald spacetimes and very special relativity
• Mathematical foundations for field theories on Finsler spacetimes
• Randers pp-waves
• Observables from spherically symmetric modified dispersion relations
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• A Cosmological Unicorn Solution to Finsler Gravity
• Revisiting Legendre transformations in Finsler geometry
• A local quantum Mach principle and the metricity of spacetime