Special Relativity from Soft Gravitons

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 $\le 1$ 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.

6 pages in double column format, 1 figure. V2: Added appendix on more details of locality in spin 2; expanded discussion with comments on implications for Lorentz violating models; added references

References in corpus (4)

• Quantum Gravity at a Lifshitz Point
• Strong coupling in Horava gravity
• Quantization of Horava Gravity in 2+1 Dimensions
• General Relativity from Causality

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• Symmetries from Locality. II. Gravitation and Lorentz Boosts
• Acausality in Superfluid Dark Matter and MOND-like Theories
• Causal Modifications of Gravity and Their Observational Bounds
• Symmetries from Locality. I. Electromagnetism and Charge Conservation
• Symmetries from Locality. III. Massless Spin 2 Gravitons and Time Translations