Unifying Gravity and EM: A Riddle You Can Solve

Apply three rules to this riddle:\\ 1. Start from standard theory\\ 2. Work with quantum mechanics\\ 3. No new math\\ Start from the vacuum Hilbert-Maxwell action: \[S_{H-M}=\int\sqrt{-g}d^4x(R-\frac{1}{4c^2}(\nabla^{\mu} A^{\nu}-\nabla^{\nu}A^{\mu})(\nabla_{\mu}A_{\nu}-\nabla_{\nu}A_{\mu}))\] The Hilbert action cannot be quantized, so drop the Ricci scalar. To do more than EM, use an asymmetric tensor: \[S_{GEM}=\int\sqrt{-g}d^4x\frac{1}{4c^2}\nabla^{\mu}A^{\nu}\nabla_{\mu}A_{\nu} \] The metric is fixed up to a diffeomorphism. With a constant potential, the Rosen metric solves the field equations, is consistent with current tests, but predicts 0.7 $\mu$arcseconds more bending around the Sun than GR. Gauge symmetry is broken by the mass charge of particles.