The First-Principles Unification of Quantum Mechanics and General Relativity from the Substrate
- 1Institute of Structural Foundations of Physics (ISFP)
Abstract
Quantum mechanics and general relativity describe microscopic quantum phenomena and macroscopic spacetime geometry through different mathematical structures. This article establishes their unification through a common underlying field that generates quantum dynamics and gravitational geometry under different physical conditions.
The starting point is the Master Field Equation, whose explicit realization incorporates propagation, nonlinear density coupling, and stochastic fluctuations. Its amplitude--phase decomposition provides the starting point for formulating quantum dynamics, while the coarse-grained equilibrium density determines an emergent metric from which spacetime curvature is constructed. The transition between fluctuation-dominated and equilibrium-dominated regimes is organized by the fluctuation-to-stiffness parameter ϵ=σ/K and an associated coherence-length relation.
The field-level construction is extended to an operator-valued substrate. The operator formulation supplies a state-space representation, observables, measurement formalism, and the canonical non-commutative algebra. The operator-generated density determines the emergent metric, which in turn governs the subsequent evolution of the same operator field. This mutual dependence establishes a self-consistent quantum–geometric feedback loop represented by a self-coupled substrate equation.
Three quantitative predictions follow from this unified architecture: a finite coherence scale governing the quantum–geometric crossover; a substrate-determined relation between density-fluctuation and metric-fluctuation spectra; and direct quantum–geometric backreaction linking a controlled density change to a geometric response and the subsequent change in quantum evolution. Each prediction has an explicit quantitative relation, an observable signature, and a localized falsifiability criterion derived directly from the substrate parameters.
The article establishes quantum dynamics and spacetime geometry as complementary manifestations of a common substrate through a continuous mathematical structure connecting field dynamics, operator algebra, emergent geometry, self-consistent quantum–geometric feedback, and experimentally testable consequences.
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BibTeX
@misc{vaishnav2026firstprinciples,
title = {{The First-Principles Unification of Quantum Mechanics and General Relativity from the Substrate}},
author = {Mohan Vaishnav},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23496831},
url = {https://zenodo.org/records/23496831},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The First-Principles Unification of Quantum Mechanics and General Relativity from the Substrate
AU - Mohan Vaishnav
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23496831
UR - https://zenodo.org/records/23496831
AB - Quantum mechanics and general relativity describe microscopic quantum phenomena and macroscopic spacetime geometry through different mathematical structures. This article establishes their unification through a common underlying field that generates quantum dynamics and gravitational geometry under different physical conditions. The starting point is the Master Field Equation, whose explicit realization incorporates propagation, nonlinear density coupling, and stochastic fluctuations. Its amplitude--phase decomposition provides the starting point for formulating quantum dynamics, while the coarse-grained equilibrium density determines an emergent metric from which spacetime curvature is constructed. The transition between fluctuation-dominated and equilibrium-dominated regimes is organized by the fluctuation-to-stiffness parameter ϵ=σ/K and an associated coherence-length relation. The field-level construction is extended to an operator-valued substrate. The operator formulation supplies a state-space representation, observables, measurement formalism, and the canonical non-commutative algebra. The operator-generated density determines the emergent metric, which in turn governs the subsequent evolution of the same operator field. This mutual dependence establishes a self-consistent quantum–geometric feedback loop represented by a self-coupled substrate equation. Three quantitative predictions follow from this unified architecture: a finite coherence scale governing the quantum–geometric crossover; a substrate-determined relation between density-fluctuation and metric-fluctuation spectra; and direct quantum–geometric backreaction linking a controlled density change to a geometric response and the subsequent change in quantum evolution. Each prediction has an explicit quantitative relation, an observable signature, and a localized falsifiability criterion derived directly from the substrate parameters. The article establishes quantum dynamics and spacetime geometry as complementary manifestations of a common substrate through a continuous mathematical structure connecting field dynamics, operator algebra, emergent geometry, self-consistent quantum–geometric feedback, and experimentally testable consequences.
ER -