Radar orthogonality and radar length in Finsler and metric spacetime geometry

TL;DR

This paper extends the concept of radar orthogonality and length to Finsler spacetimes, providing a framework for measuring spatial lengths in generalized geometries relevant to quantum gravity and electrodynamics.

Contribution

It introduces a general definition of radar orthogonality and length in Finsler spacetimes, expanding the geometric tools for understanding spacetime measurements.

Findings

Defined radar orthogonality and length in Finsler spacetimes.

Applied concepts to a fourth order polynomial Finsler geometry.

Derived deviations from Euclidean length in a generalized Minkowski setting.

Abstract

The radar experiment connects the geometry of spacetime with an observers measurement of spatial length. We investigate the radar experiment on Finsler spacetimes which leads to a general definition of radar orthogonality and radar length. The directions radar orthogonal to an observer form the spatial equal time surface an observer experiences and the radar length is the physical length the observer associates to spatial objects. We demonstrate these concepts on a forth order polynomial Finsler spacetime geometry which may emerge from area metric or pre-metric linear electrodynamics or in quantum gravity phenomenology. In an explicit generalisation of Minkowski spacetime geometry we derive the deviation from the euclidean spatial length measure in an observers rest frame explicitly.