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

TL;DR

This paper introduces a conformally invariant scalar wave framework that unifies Maxwell fields and linearized gravity, revealing their classical and quantum distinctions and suggesting a way to infer gravitons through quantum noise analysis.

Contribution

It presents a novel conformally invariant Schrödinger-like equation that unifies electromagnetic and gravitational fields and explores their quantum properties and detection methods.

Findings

Derived a Lorentz and conformally invariant scalar wave equation.

Unified description of electromagnetic and gravitational fields using a single scalar function.

Proposed a method to infer gravitons from quantum noise in detectors.

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.