Matter‑Wave Gravity Response Spectrum (MWGRS)

Jincheng Zhang

Published Aug 17, 2026• 0 citations

Abstract

The interaction between quantum matter waves and gravitational fields is a central theme in the quest to reconcile quantum mechanics with general relativity. This paper introduces the concept of a matter‑wave gravity response spectrum (MWGRS), defined as the frequency‑dependent response function χ_g(ω) that quantifies how a matter‑wave state ψ(t) reacts to temporal variations in the gravitational potential. Beginning with the Schrödinger equation in a weakly curved spacetime, we derive the linear response of the wavefunction to small metric perturbations. The response function is obtained by Fourier transforming the time‑dependent phase shift induced by the perturbation. Explicit expressions for a free particle and for a two‑path interferometer are presented, revealing how the MWGRS encodes information about both the intrinsic dynamics of the particle and the geometry of the interferometric paths. We discuss the implications of the MWGRS for upcoming precision gravimetry experiments, including its sensitivity to hypothetical spacetime foam and holographic noise. The paper concludes with a perspective on how measuring χ_g(ω) could provide a new window into the quantum structure of spacetime, potentially guiding the design of future quantum‑gravity experiments.

DOI: 10.5281/zenodo.21973222

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