Gravity of Two Photon Decay and its Quantum Coherence

TL;DR

This paper derives an analytical solution for the gravitational shock wave caused by a decaying particle into null particles, exploring its effects on spacetime and quantum gravitational fluctuations.

Contribution

It provides a novel analytical model for gravitational shock waves from particle decay and applies it to estimate quantum gravitational fluctuations in various systems.

Findings

Discontinuous perturbation on a spherical null shell.

Anisotropic time displacement dominated by quadrupole harmonic.

Quantum fluctuations grow linearly with system duration, exceeding previous models.

Abstract

A linear analytical solution is derived for the gravitational shock wave produced by a particle of mass $M$ that decays into a pair of null particles. The resulting space-time is shown to be unperturbed and isotropic, except for a discontinuous perturbation on a spherical null shell. Formulae are derived for the perturbation as a function of polar angle, as measured by an observer at the origin observing clocks on a sphere at distance $R$. The effect of the shock is interpreted physically as an instantaneous displacement in time and velocity when the shock passes the clocks. The time displacement is shown to be anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay axis, with a magnitude $\delta \tau\sim GM/c^3$, independent of $R$. The velocity displacement is isotropic. The solution is used to derive the gravitational effect of a quantum state with a superposition of a large number of randomly oriented, statistically isotropic particle decays. This approach is shown to provide a well-controlled approximation to estimate the magnitude of gravitational fluctuations in systems composed of null point particles up to the Planck energy in a causal diamond of duration $\tau= 2R/c$, as well as quantum-gravitational fluctuations of black holes and cosmological horizons. Coherent large-angle quantum distortions of macroscopic geometry from fluctuations up to the Planck scale are shown to grow linearly with the duration, with a variance $\langle \delta \tau^2\rangle\sim \tau t_P$ much larger than that produced in models without causal quantum coherence.