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Gravity as the Wave Function: Propagation, Acceleration, and Equivalence as the Quantum–Classical Boundary

Ellis Ammons

Published Jun 27, 2026• 1 citation
Publisher

Abstract

Gravity as the Wave Function: Propagation, Acceleration, and Equivalence as the Quantum–Classical Boundary This manuscript presents a unified geometric interpretation of quantum mechanics and gravity, treating the wave function as a realized spacetime phase field. The Intrinsic Spin Momentum (ISM) model is integrated into a continuous field‑operator framework, showing that coordinate‑accelerated detectors interacting with a smooth metric phase geometry naturally saturate Tsirelson’s bound. The upload includes: Full LaTeX manuscript Continuous field‑operator CHSH simulation (Python) ISM contextual model (pedagogical) demonstrating horizon‑restricted phase access Reproducible code verifying Tsirelson saturation (S ≈ 2.8284) Appendices on CHSH algebra and Rindler‑frame decoherence Option A (continuous operator model) is the central mathematical engine of the theory. Option B is included only as an ISM‑specific pedagogical demonstration of contextual phase‑access dynamics and is not used to claim Bell‑valid CHSH violation. This record is part of the ISM series exploring phase geometry, quantum correlations, and gravitational decoherence. email: ellis.ammons1@gmail.com *Todo: create linkable github repo to run CHSH violation python simulation for observers Key Sentences from the Paper “Gravity is not an external classical field acting on a quantum wave function. Gravity is the wave function.” “Propagation creates the wave function by unfurling this phase structure across the metric.” Keywords Gravity; Wave function; Quantum foundations; Intrinsic Spin Momentum; ISM; CHSH; Decoherence; Rindler quantization; Unruh effect; Free‑fall experiments

DOI
10.5281/zenodo.20971593

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Gravity as the Wave Function: Propagation, Acceleration, and Equivalence as the Quantum–Classical Boundary This manuscript presents a unified geometric interpretation of quantum mechanics and gravity, treating the wave function as a realized spacetime phase field. The Intrinsic Spin Momentum (ISM) model is integrated into a continuous field‑operator framework, showing that coordinate‑accelerated detectors interacting with a smooth metric phase geometry naturally saturate Tsirelson’s bound. The upload includes: Full LaTeX manuscript Continuous field‑operator CHSH simulation (Python) ISM contextual model (pedagogical) demonstrating horizon‑restricted phase access Reproducible code verifying Tsirelson saturation (S ≈ 2.8284) Appendices on CHSH algebra and Rindler‑frame decoherence Option A (continuous operator model) is the central mathematical engine of the theory. Option B is included only as an ISM‑specific pedagogical demonstration of contextual phase‑access dynamics and is not used to claim Bell‑valid CHSH violation. This record is part of the ISM series exploring phase geometry, quantum correlations, and gravitational decoherence. email: ellis.ammons1@gmail.com *Todo: create linkable github repo to run CHSH violation python simulation for observers Key Sentences from the Paper “Gravity is not an external classical field acting on a quantum wave function. Gravity is the wave function.” “Propagation creates the wave function by unfurling this phase structure across the metric.” Keywords Gravity; Wave function; Quantum foundations; Intrinsic Spin Momentum; ISM; CHSH; Decoherence; Rindler quantization; Unruh effect; Free‑fall experiments
This work demystifies quantum paradoxes by showing that the phenomena often labeled as “spooky action” arise from unfactorizable classical local processes that lie outside the scope of Bell’s tests, indicating that the universe remains locally real and that physical states exist independently of measurement. It presents a deterministic hidden‑variable framework, relativistically compatible with quantum entanglement, based on Intrinsic Spin Momentum (ISM). In this model, spin is treated as a real internal momentum circulation with definable vector structure, phase, curvature, and acceleration. Phase‑created correlations between intrinsic spin momenta reproduce CHSH‑type values without superluminal signaling or Einstein’s so‑called “spooky action at a distance.” The Bloch sphere emerges as the geometric representation of internal spin structure, and phase alignment on this sphere provides the mechanism for entanglement correlations, demonstrating that classical unfactorizable processes can reproduce Bell‑inequality violations without breaking any known laws of physics. This stands in stark contrast to the widely publicized interpretation of the 2022 Nobel Prize in Physics, which claimed that Bell‑test violations imply that the universe is “not locally real.” The model generalizes naturally to higher‑spin systems, linking intrinsic spin geometry to gravitational curvature. Gravitational waves dynamically modulate intrinsic spin acceleration, offering a physical mechanism for quantum gravity that diverges worldlines through localized curvature rather than as a purely coordinate effect of spacetime geometry. This unified picture replaces “spooky action” with correlated spin geometry embedded in a dynamic relativistic spacetime. Contact: ellis.ammons1@gmail.com Keywords: Intrinsic Spin Momentum, quantum gravity, entanglement, Bloch sphere, CHSH correlations, relativity, hidden variables, gravitational waves, phase geometry, spin structure.
Intrinsic Spin Momentum (ISM Model) presents a classical hidden‑variable framework capable of reproducing CHSH violations without invoking nonlocality or quantum indeterminism. The model assigns each entangled pair an intrinsic spin‑momentum phase, or a set of phases, established at emission. Measurement outcomes depend on local detector settings and this shared phase structure, producing non‑factorizable correlations while preserving physical locality. The ISM Model serves as a minimal, geometry‑based abstraction of more detailed physical approaches. In particular, it complements the author’s earlier work Quantum Mechanics as Deterministic Electromagnetic Logic, where intrinsic spin and phase relationships arise from confined electromagnetic excitations. The ISM Model isolates the essential correlation‑producing mechanism—shared phase geometry—without committing to a specific physical ontology. This paper clarifies the distinction between physical locality and Bell‑locality, demonstrates how classical non‑factorizable models can exceed CHSH = 2, and provides a simple Monte‑Carlo simulation illustrating the resulting correlations. The ISM Model offers a unified, classical perspective on quantum‑like correlations and their geometric origin.
We propose a novel operator-based formulation of quantum gravity grounded in two foundational principles: a discrete causal lattice and algebraic microcausality. Departing from traditional continuum approaches and wavefunction-based quantum mechanics, this framework models spacetime and matter as emergent phenomena arising from the algebraic structure of displacement operators. In this first part of a two-part series, we construct the foundational framework and demonstrate how key features of quantum mechanics—such as the uncertainty principle, de Broglie relations, and entanglement—emerge naturally without invoking wavefunctions, path integrals, or metric-based geometry. Operator non-commutativity on the causal lattice gives rise to a self-consistent quantum structure with natural ultraviolet finiteness, intrinsic time directionality, and a microcausal interpretation of measurement. This foundational part lays the groundwork for gravitational dynamics, cosmology, and the grand unification principles of gravity and the Standard Model to be explored in the sequel to quantum gravity part II.
Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.
This paper develops a hydrodynamic derivation of nonrelativistic quantum mechanics within the Hydrodynamic Quantum Gravity (HQG) programme. Using the Madelung transformation, the Schrödinger equation is written in amplitude–phase form and shown to be exactly equivalent to (i) a continuity equation for a conserved density and (ii) an Euler-type momentum equation augmented by the “quantum potential” term. In this interpretation, the quantum potential is treated as an effective dispersive stress associated with structured vacuum dynamics, rather than as a purely formal mathematical artefact. The paper reviews how standard quantum features appear naturally in the hydrodynamic variables: interference and diffraction as phase-driven flow, stationary states as time-harmonic solutions, and quantisation as a consequence of single-valued phase (circulation) constraints. It also discusses how pilot-wave style dynamics can be expressed in this language, and surveys laboratory analogues (including walking-droplet experiments) as phenomenological motivation and intuition-building, without claiming identity between the analogue systems and the quantum vacuum. Interpretation note: “Superfluid/condensate” language is used here as an effective mathematical/analogue description of vacuum behaviour; the paper does not assert a material substrate or an operationally accessible preferred rest frame. This paper is part of a series. Companion preprints develop the gravitational and electromagnetic components of the HQG framework and discuss additional open problems and testable predictions. Discussion and feedback: https://github.com/Gptham123456/Hydrodynamic-Quantum-Gravity/discussions
We propose a theoretical framework in which time is described as a physical field charac- terized by a time-density field ν. In this formulation, the local flow of time is determined by ν, and gravitational acceleration arises from its spatial gradient. The theory reproduces New- tonian gravity in the weak-field limit and provides a consistent relativistic formulation through a ν-dependent metric.. By extending ν to a complex scalar field, key structures of quantum mechanics emerge naturally, including probability density, momentum, and uncertainty. Fur- thermore, the path integral formulation is interpreted as arising from the phase structure of the time-density field. The quantum potential is derived from the amplitude of ν, providing a direct mechanism for quantum phenomena such as wave packet spreading, quantization, and tunneling. These results suggest that gravity and quantum behavior may originate from a com- mon underlying structure associated with time itself. While the present formulation is not yet a complete quantum theory, it offers a unified perspective that connects classical gravity and quantum mechanics within a single framework. This version includes a minor typographical correction in the mathematical expressions. In the previous version, the exponential function was mistakenly written as "exp!" in several equations. I have corrected this to the proper notation "exp(...)". This correction does not affect the theoretical results or conclusions of the work.