Lorentz Group derivable from Polarization Optics

TL;DR

This paper demonstrates that the Lorentz group, fundamental in relativity, can be derived from polarization optics using optical filters, linking space-time symmetries to optical phenomena.

Contribution

It introduces a novel derivation of the Lorentz group from optical filter symmetries, connecting relativistic groups with polarization optics.

Findings

Derivation of Lorentz group from optical filters

Representation of Lorentz group via polarization optics

Connection between space-time symmetries and optical phenomena

Abstract

The Lorentz group is the fundamental language for space-time symmetries of relativistic particles. This group can these days be derived from the symmetries observed in other branches of physics. It is shown that this group can be derived from optical filters. The group O(2,1) is appropriate for attenuation filters, while the O(3) group describes phase-shift filters. The combined operation leads to a two-by-two representation of the six-parameter Lorentz group. It is shown also that the bilinear representation of this group is the natural language for the polarization optics.