DSR, Optics and Electrodynamics

TL;DR

This paper explores solutions in DSR theories revealing their implications in optics and electrodynamics, including a frequency-dependent vacuum refractive index and modified Lorentz transformations near the Planck energy.

Contribution

It introduces a modified refractive index in DSR, leading to new electrodynamics features and a first-order approximation of Lorentz transformations near the Planck scale.

Findings

Vacuum acts as a frequency-dependent refractive medium.

Electric fields can be stronger or weaker near Planck energy.

Derived modified Lorentz transformations consistent with DSR.

Abstract

We investigate some interesting solutions in the DSR theories. These solutions have important features in optics and mechanics. We use these similarities for a better understanding of these theories. We know that, the vacuum in the DSR has an effective refractive index which depends on the frequency of the light. We find this modified refractive index which leads us to a modified Electrodynamics with some new interesting aspects, for example near the Planck energy the electric field can be stronger or weaker than the usual case. Also, we will find a new modified Lorentz transformations in the first order of the Planck length which are very similar to the usual Lorentz transformations.