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
We revisit the concept of phase time, which has been previously proposed as a solution to the problem of time in quantum gravity. Concretely, we show how the geometry of configuration space together with the phase of the wave function of the Universe can, under certain conditions, lead to the definition of a positive-definite squared norm from which probabilities can be defined. The norm is conserved under time evolution, and we obtain a version of Ehrenfest's theorem that is analogous to the one in ordinary quantum mechanics. We address how the present approach avoids some difficulties that were encountered in previous attempts at defining an Ehrenfest theorem relative to phase time in the context of relativistic quantum mechanics and canonical quantum gravity, and how it is connected to a notion of gauge fixing the inner product. We conclude with a brief outlook.
Quantum spatial uncertainty is usually introduced as a fundamental property of microscopic systems through the Heisenberg uncertainty relation between position and momentum. In this work, we investigate whether a Heisenberg scale uncertainty bound can emerge from classical higher dimensional geometry without initially assuming wave functions or noncommuting quantum operators. We consider ordinary three dimensional space as a projection of a higher dimensional configuration space containing one compact fourth spatial dimension q 4 with characteristic length L. The compact sector is described by a hidden phase space distribution ρ(q 4 ,p 4 ), where curvature and warping of the compact geometry generate a position- dependent compact momentum p 4 (q 4 ) and therefore a nonzero compact phase space covariance. To connect the hidden compact sector with observable variables, we introduce an explicit compact to three dimensional projection rule. Applying the classical Cauchy-Schwarz inequality to the projected observable variables yields a conditional lower bound on the measurable position-momentum product without any using wave function. The resulting uncertainty scale is determined by the parameter such as compact covariance, the phase overlap between the curvature-induced momentum modulation and the projection coordinate and a geometric compact action scale derived from the higher-dimensional gravitational sector. The compact gravitational action leads to an effective uncertainty scale of the form [Formula: see text] (c is light velocity, L is size of compact dimension and G 4 is gravity constant). The proposed framework provides a compact-geometric mechanism capable of generating a Heisenberg-scale projected uncertainty bound from higher dimensional classical geometry.