Universality and Falsifiability of Quantum Spacetime Decoherence: A Gauge-Invariant Framework for Gravitational-Wave Phase Diffusion (2512.02782v1)

Abstract: We develop a fully gauge-invariant and rigorously derived framework for computing the cumulative decoherence of gravitational waves (GWs) propagating through a stochastic quantum spacetime. Working directly with the Riemann-tensor two-point function and exploiting the extreme adiabaticity of cosmological GW propagation, we show that phase diffusion, rather than amplitude attenuation or mode mixing, is the unique leading-order imprint of microscopic curvature fluctuations. Our main theoretical result is a universality theorem: for any quantum-gravity model whose curvature fluctuations possess a finite correlation length, the accumulated phase variance grows linearly with distance, independent of the underlying microphysics. This diffusive scaling contrasts sharply with coherent astrophysical effects and with nonlocal models. The frequency exponent therefore becomes a clean spectral discriminator, separating string-foam recoil, holographic or scale-invariant noise, and causal-set discreteness. We obtain these results from first principles by evaluating the projected Riemann correlator along null geodesics and determining the exact conditions under which deviations from universality can arise. Finally, we outline a hierarchical Bayesian strategy for measuring this effect with LIGO, LISA, and Pulsar Timing Arrays. Although standard Planck-scale fluctuations remain far below current sensitivity, this framework provides a sharp and falsifiable test of exotic quantum-spacetime scenarios, particularly those with macroscopic correlation lengths or strong energy dependence.