Special Relativity from Soft Gravitons
  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.
