Generalized Lorentz invariance with an invariant energy scale

TL;DR

This paper explores a generalized framework for Lorentz invariance that incorporates an invariant energy scale, modifies transformation laws at high energies, and explains phenomena like the ultra high energy cosmic ray anomaly.

Contribution

It introduces a non-linear Lorentz transformation formalism preserving relativity with an invariant energy scale and applies it to cosmic ray anomalies.

Findings

Proposes a formalism with energy-dependent speed of light.

Explains the ultra high energy cosmic ray anomaly.

Suggests a maximum momentum and diverging speed of light at high energies.

Abstract

The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultra high energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.