Observer dependent geometries

TL;DR

This paper reviews two frameworks—Finsler spacetimes and Cartan geometry on observer space—that explore observer-dependent geometries, potentially offering insights into quantum gravity and phenomena beyond classical general relativity.

Contribution

It compares and discusses the properties of Finsler spacetimes and Cartan geometry on observer space as models for observer-dependent geometries in quantum gravity contexts.

Findings

Finsler spacetimes generalize Lorentzian geometry with observer-dependent metrics.

Cartan geometry on observer space provides a framework for non-tensorial transformation laws.

Both frameworks could explain phenomena not accounted for by classical general relativity.

Abstract

From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.