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- Summary:
- Anyone completed the derivation of Einstein's Equation?

In this 1965 paper by Weinberg, https://journals.aps.org/pr/abstract/10.1103/PhysRev.138.B988, he describes a quantum field theory of the graviton in a Coulomb-like fixed gauge, where the free graviton has only space-space components and is traceless. This of course makes the field dynamics non-covariant; he then shows that to get back covariance, you need to add a nonlocal "Newtonian" term to the Hamiltonian and also have the graviton couple to a conserved tensor. After a long calculation he gets back the linear form of Einstein's equations, and argues that the tensor on the right-hand side will include a gravitational energy term that is equivalent to the nonlinear parts of the left-hand side in Einstein's equations. But he does not prove this. He also does not prove that certain noncovariant "gradient terms" in his graviton propagator will not contribute to physical amplitudes; he conjectures that this requirement will in fact fix the form of the gravitational energy term.

Has this approach been taken up by others? Have these conjectures ever been proven?

Has this approach been taken up by others? Have these conjectures ever been proven?