Graviton Fluctuations in Gravitational Wave Patterns: Analysis via Iterations

Abstract: Detections of gravitational waves since GW150914 has gained renewed interest in potential quantum-classical correspondences between GWs and gravitons. While a complete quantum theory of gravity remains elusive, graviton fluctuations have been hypothesized as sources of stochastic noise in gravitational interactions. Utilizing the Einstein-Langevin equation that describes graviton fluctuations, in attempt to form a correlation with GW generation, we treat the coalescing binary heuristically as a rotating, contracting Gaussian volume. This stochatic picture of GW formation implies the treatment of the contained gravitons as a Brownian bath. From the Einstein-Langevin equation, we establish a scaling relation where quanta dissipation depends inversely with the contracting volume (i.e., coalescence). Using an Euler iteration scheme, we simulate the graviton fluctuations from inspiral to merger as a Wiener process, revealing a signal that qualitatively resembles macroscopic GW waveforms. While inherently heuristic, this approach provides a computational framework for exploring graviton-scale perturbations in GW formation, with reproducible implementations in Wolfram Mathematica and equivalent Python code in the appendix.