Space-time Symmetry Transformations of Elementary Particles realized in Optics Laboratories

TL;DR

This paper explores how optical systems can simulate space-time symmetry transformations of elementary particles, linking Lorentz group representations with optical filter configurations.

Contribution

It demonstrates the realization of space-time symmetry transformations of particles through optical experiments using Lorentz group subgroups.

Findings

Optical filters can simulate Wigner rotations.

Optical setups can realize Iwasawa decompositions.

Space-time symmetries are accessible in optics laboratories.

Abstract

The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations can generate group representations applicable to different branches of physics. It is pointed out that polarization optics can be formulated in terms of the six-parameter Lorentz group. This allows us to construct optical instruments corresponding to the subgroups of the Lorentz groups. It is shown possible to produce combinations of optical filters that exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions, which are manifestations of the internal space-time symmetries of massive and massless particles.