Gravity of Two Photon Decay and its Quantum Coherence

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 δτ ∼ GM/c 3 , independent of R. The velocity displacement is isotropic. The solution is used to estimate the angular distribution of gravitational perturbations from 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 coherent, nonlocal, spacelike correlations of weak-field gravity from systems composed of null point particles up to the Planck energy, including macroscopic quantum coherence of causal quantum-gravitational fluctuations. The solution is extrapolated to estimate gravitational fluctuations from a gas of relativistic particles, and from quantum distortions of a black hole or cosmological horizon.

Angular correlations of causally-coherent primordial quantum perturbations

“…A simple example discussed in the Appendix is the decay of a particle into two null particles. In the linear, weakfield limit, it can be proven that the gravitational wave function, a superposition of metric distortions measured by clocks on the spherical boundary of a causal diamond, has a universal angular power spectrum [41].…”

“…In the causally-coherent scenario, gravitational effects on spacetime in all directions remain entangled as part of a single coherent, quantum system until the state of a causal diamond collapses. The physical effect of this directional quantum-geometrical coherence can be calculated in a simple system [41]: a point particle of mass M at rest decays into two null particles, and their gravitational effect far from the decay axis is measured by clocks, observed from the world line of the body where the decay happens (see Fig. 22).…”

“…The linear solution for the classical metric of this system is described in ref. [41]. The classical geometry a time t after the decay is a discontinuous spherical null shock wave that separates an exterior Schwarzchild met- 22.…”

“…The space-time structure of the gravitational shock wave from decay of a massive particle into two null point particles, and its effects on measurements of anisotropic time distortions, adapted from ref. [41]. The effect of the particle's gravity is to "drag" the space-time along with it on the null trajectory, causing an instantaneous displacement in time and velocity, with a decay axis shown by the solid trajectory in space-time (left) and in space (right).…”

Symmetries of the Primordial Sky

“…As an example of the gravitational effect of coherent causal entanglement on an angular pattern, consider the classical distortion of causal structure from the gravity of an idealized EPR-type system [5], consisting of a pointlike particle that decays into a pair of oppositelypropagating photons (Fig. 1).…”