  In this essay we review the central difficulty in formulating a viable
quantum field theory in which gravity is emergent at low energies, rather than
mediated by a fundamental gauge field. The Weinberg-Witten theorem forbids spin
2 massless modes from carrying Lorentz covariant stress-energy. In General
Relativity the stress-energy is not covariant because it violates a gauge
symmetry, but a gravitational theory without fundamental spin 2 gauge
invariance must either lack a stress-energy operator or have a non-relativistic
graviton. The latter option is incompatible with the principle of equivalence,
though such theories are not necessarily ruled out at low energies.
