# Special Relativity from Soft Gravitons

## TL;DR

This paper demonstrates that local, non-Lorentz invariant theories with massless spin 2 particles inherently require special relativity's energy-momentum relation, suggesting relativity's structure can emerge from spin 2 interactions.

## Contribution

It proves that locality and soft gauge invariance in theories with massless spin 2 particles enforce the exact special relativistic energy-momentum relation, even without initial Lorentz invariance.

## Key findings

- Universal graviton couplings are required.
- The energy-momentum relation must be exact.
- Relativity structure can emerge from spin 2 interactions.

## Abstract

We study all translationally and rotationally invariant local theories involving massless spin 2 and spin 1 particles that mediate long range forces, allowing for general energy relations and violation of boost invariance. Although gauge invariance is not a priori required to describe non Lorentz invariant theories, we first establish that locality requires `soft gauge invariance'. Then by taking the soft graviton limit in scattering amplitudes, we prove that in addition to the usual requirement of universal graviton couplings, the special relativistic energy-momentum relation is also required and must be exact. We contrast this to the case of theories with only spin $\leq1$ particles, where, although we can still derive charge conservation from locality, special relativity can be easily violated. We provide indications that the entire structure of relativity can be built up from spin 2 in this fashion.