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 $delta tausim GM/c^3$, 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.
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