Observers’ measurements in premetric electrodynamics: 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. * norman.guerlebeck@zarm.uni-bremen.de † christian.pfeifer@ut.ee 1 We will highlight in Sec. II that the photon sector of the SME is included in the premetric approach to electrodynamics. 2 The "metric" of that theory does not solely depend on the manifold's coordinates but also on the frame it is measured in, in particular, its motion with respect to a preferred frame. arXiv:1801.07724v2 [gr-qc]

Randerspp-waves

“…These studies suggest that time dilations between observers moving relatively to each other would yield different results for Randers and Lorentzian pp wave spacetimes due to the different normalization of timelike geodesics. Similarly, speed light measurements may not coincide for different observers due to the modified null condition for light rays [54], although this strongly depends on the observer model employed [52]. These important questions will be addressed in future work.…”

“…In particular, is there any kind of physical observable that could distinguish Randers pp-waves from Finsler pp-waves and/or Lorentzian pp-waves? Such questions cannot be answered without a consistent observer framework; see, for example, [52,53]. These studies suggest that time dilations between observers moving relatively to each other would yield different results for Randers and Lorentzian pp wave spacetimes due to the different normalization of timelike geodesics.…”

Berwald spacetimes and very special relativity

“…Finsler geometry immediately emerges in the context of modified dispersion relations. These may for example arise from an effective description of Planck scale quantum gravity effects [14,58,59], or from field theories with field equations not (solely) defined by a Lorentzian metric [33,34,40,[60][61][62]. Part of the motivation for this work lies in a particular instance of the latter, the very special relativity (VSR) framework by Cohen and Glashow [5].…”

“…This definition of Finsler spacetimes is constructed so as to cover interesting examples from physics, such as light propagation in area metric geometry and local and linear pre-metric electrodynamics [32][33][34], which include the bi-metric light-cone structure of birefringent crystals. The most important ingredient in our definition is the use of a r-homogeneous function L instead of the 1-homogeneous function F .…”

Finsler spacetime geometry in physics

“…ǫ = 0, F ǫ is a 1-homogeneous Finsler function, for massless particles F 0 must not necessarily be 1-homogeneous. The transition from a dispersion relation to a Finslerian geometry has been worked out explicitly for Planck scale modified dispersion relations [2,38] and for weakly premetric electrodynamics [25]. Depending on the Hamiltonian from which one starts a huge variety of Finsler functions can be obtained.…”