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Matter-Wave Gravity Response Spectrum (MWGRS)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

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.21973223

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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.
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.
This work proposes a phenomenological framework linking quantum localization to weak-field gravitational response through informational load functionals. The central idea is that the degree of spatial localization of a quantum state may be associated with an effective participation factor governing how strongly that state contributes to inertial and gravitational phenomena. Localization is quantified using standard measures such as the inverse participation ratio (IPR), combined with reference scales that render localization dimensionless. A monotonic substrate response function is introduced to map localization load to observable effects. In the weak-field regime, a linear response approximation recovers familiar gravitational scaling relations. The framework does not modify Schrödinger dynamics, introduce new particles, or attempt a full theory of quantum gravity. Instead, it explores whether aspects of gravity normally described geometrically can be reinterpreted as state-dependent informational load. Illustrative empirical connections are discussed using known atomic ionization data to show how varying localization regimes may correspond to different participation factors. These examples are intended as phenomenological consistency checks rather than precision derivations. Scope and Status: This work is exploratory and interpretational. It is intended as a conceptual bridge between quantum and gravitational descriptions, not as a completed fundamental theory. Predictions are restricted to weak-field regimes, and strong-field behavior is left open. Key Points: Treats mass-like behavior as state-dependent participation Uses established localization measures (IPR) Introduces substrate response only phenomenologically Does not invoke gravitons or modify QM equations Suggests testable scaling relations in principle Purpose: The goal is to stimulate discussion on whether gravitational response might be expressible in informational or localization terms, providing an alternative viewpoint on the QM–GR interface.Update in this version: Reference of Effective Mass Theory. Noticed there exist the effe
Description This work develops a phenomenological framework that relates quantum localization to weak-field inertial and gravitational response using scalar “informational load” functionals. The central proposal is that mass-like behavior can be treated as a state-dependent property: more spatially localized quantum states couple more strongly to inertial and gravitational effects than delocalized states. Localization is quantified using standard concentration measures, primarily the inverse participation ratio (IPR). A dimensionless load variable is constructed and mapped to observable effects through a monotonic response function. In the linear (weak-load) regime, this construction reproduces familiar post-Newtonian scaling for time dilation and light propagation, providing consistency with weak-field general relativity. The framework is strictly diagnostic and interpretational. It does not modify Schrödinger or Dirac dynamics, does not introduce new particles or forces, and does not propose a microscopic theory of quantum gravity. Instead, it provides an effective scalar language for organizing how localization may influence inertial and gravitational response. As a simple phenomenological check, atomic ionization energies are used to estimate relative participation factors across different localization regimes. These examples illustrate consistency of the scaling picture rather than serving as precision tests. Scope and status • Valid only in weak-field / post-Newtonian regimes • Coarse-grained and phenomenological • No claims regarding strong gravity or full quantum gravity • Intended as an organizational and interpretive framework Key features • Mass-like response treated as a state-dependent participation factor • Uses established localization diagnostics (IPR) • Introduces only effective response functions • Compatible with standard quantum mechanics and general relativity • Suggests qualitative scaling relations that may be testable in principle Purpose The goal is to provide a compact conceptual bridge between quantum localization and gravitational response, and to encourage discussion of whether weak-field gravitational behavior can be expressed in terms of state-dependent informational or localization measures.
This work proposes a phenomenological framework linking quantum localization to weak-field gravitational response through informational load functionals. The central idea is that the degree of spatial localization of a quantum state may be associated with an effective participation factor governing how strongly that state contributes to inertial and gravitational phenomena. Localization is quantified using standard measures such as the inverse participation ratio (IPR), combined with reference scales that render localization dimensionless. A monotonic substrate response function is introduced to map localization load to observable effects. In the weak-field regime, a linear response approximation recovers familiar gravitational scaling relations. The framework does not modify Schrödinger dynamics, introduce new particles, or attempt a full theory of quantum gravity. Instead, it explores whether aspects of gravity normally described geometrically can be reinterpreted as state-dependent informational load. Illustrative empirical connections are discussed using known atomic ionization data to show how varying localization regimes may correspond to different participation factors. These examples are intended as phenomenological consistency checks rather than precision derivations. Scope and Status: This work is exploratory and interpretational. It is intended as a conceptual bridge between quantum and gravitational descriptions, not as a completed fundamental theory. Predictions are restricted to weak-field regimes, and strong-field behavior is left open. Key Points: Treats mass-like behavior as state-dependent participation Uses established localization measures (IPR) Introduces substrate response only phenomenologically Does not invoke gravitons or modify QM equations Suggests testable scaling relations in principle Purpose: The goal is to stimulate discussion on whether gravitational response might be expressible in informational or localization terms, providing an alternative viewpoint on the QM–GR interface.Update in this version: Reference to the Effective Mass Theory.Reference to the Objective Collapse Theory
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show that the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future. Physics on the large scale is based on Einstein’s theory of general relativity (GR), which interprets gravity as the curvature of spacetime. Despite its tremendous success as an isolated
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by the recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations, and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future.