Spectral Suppression of Center-of-Mass Coupling to Gravitational Tidal Fluctuations

If gravity is quantized, geodesic separations experience stochastic tidal fluctuations (Parikh, Wilczek, and Zahariade, 2021). These fluctuations couple through spacetime curvature to the mass quadrupole moment. Nearly every current experiment searching for such fluctuations monitors center-of-mass translation, which generates a lab-frame quadrupole oscillating at twice the trap frequency ($\sim 10^{5}$~rad/s). Internal quadrupolar elastic modes of the same particles oscillate at $\sim 10^{11}$~rad/s. For any tidal noise spectrum rising as $\omega^n$ with $n \geq 1$ --- a condition required by the correspondence principle --- the spectral density at internal mode frequencies exceeds that at center-of-mass frequencies by a factor of $10^{6n}$. All known calculations of the tidal noise spectral index --- graviton emission (Toro\v{s}, Mazumdar, and Bose, 2024), vacuum fluctuation-dissipation, and dimensional analysis --- independently yield $n = 5$, giving a suppression of $10^{30}$. The internal $\ell = 2$ modes of mesoscopic solids, with GHz frequencies fixed by the Lamb spectrum, occupy the frequency range where tidal coupling peaks. No existing or proposed experiment monitors them for gravitational signatures. This paper identifies and quantifies the gap.