Radar orthogonality and radar length in Finsler and metric spacetime geometry

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.