Symplectic evolution of an observed light bundle

TL;DR

This paper introduces a symplectic formalism for evolving null geodesic bundles in spacetime, enabling optical analogies and insights into distance reciprocity, with applications to electromagnetic and gravitational waves.

Contribution

It develops a novel symplectic phase space approach to null geodesic evolution, linking spacetime optics with symplectic geometry and revealing new interpretations of distance reciprocity.

Findings

Null bundle evolution is symplectic, analogous to optics.

Spacetime can be modeled as an optical device with lens, magnifier, rotator components.

Distance reciprocity arises from symplectic evolution of null bundles.

Abstract

Each and every observational information we obtain from the sky regarding the brightnesses, distances or image distortions resides on the deviation of a null geodesic bundle. In this talk, we present the symplectic evolution of this bundle on a reduced phase space. The resulting formalism is analogous to the one in paraxial Newtonian optics. It allows one to identify any spacetime as an optical device and distinguish its thin lens, pure magnifier and rotator components. We will discuss the fact that the distance reciprocity in relativity results from the symplectic evolution of this null bundle. Other potential applications like wavization and its importance for both electromagnetic and gravitational waves will also be summarized.