A Conformally Invariant Unified Theory of Maxwell Fields and Linearized Gravity as Emergent Fields

Abstract

A Lorentz and conformally invariant `Schr\"{o}dinger-like' equation for a massless complex scalar function $\psi$ is derived from an invariant action, and it is shown how the same $\psi$ can be used to calculate both the gravitational field $h_{\mu\nu}$ of linearized Einstein gravity in the TT gauge and the electromagnetic field $F_{\mu\nu}$ in the Lorenz gauge, and that the main difference between classical and quantum aspects of such fields lies in a certain condition that the underlying scalar wave must satisfy to keep it nondispersive. It is also shown how the existence of gravitons can be inferred from the state-dependent quantum noise they create in a model detector.