Temporal Quantum Gravity: A Complete Theory of Temporal Field Coupling
Year: 2025
Type: article
Abstract: Quantum Time Gravity (QTG) is a covariant quantum field theory in which time is represented by a fundamental operator field τ̂(x), interacting with matter and inducing spacetime geometry. The metric is defined via an operator ansatz: (1) ĝμν(x) = ημν + ξ · ∂μ τ̂(x) · ∂ν τ̂(x) This formulation renders geometry a derivative structure, emergent from quantum configurations of τ̂(x). The theory achieves background independence through Wheeler–DeWitt-type constraints, and introduces natural screening via environment-dependent coupling functions α(τ), derived from correlation profiles A(τ). QTG yields falsifiable predictions across multiple observational regimes: dipole gravitational wave dephasing in asymmetric binaries (ΔΨ(f) ∼ 10⁻³–10⁻²), tensor anomalies in cosmic microwave background polarization (ΔB/B ∼ 10⁻³), and medium-dependent corrections to Newtonian gravity (m_τ > 10⁻¹⁴ eV, ξ < 10⁻² AU²). These effects are encoded in the spectral and statistical structure of the temporal field and are testable via current and upcoming missions (LISA, CMB-S4, Euclid). In appropriate limits, QTG recovers General Relativity and Quantum Mechanics, while offering novel mechanisms for dark matter phenomenology, CMB anomalies, and quantum nonlocality. The theory presents a conceptually complete and falsifiable framework in which geometry, causality, and dynamics emerge from the quantum structure of time. Keywords: quantum time; operator metric; background independence; Wheeler–DeWitt constraint; temporal field; falsifiability; gravitational waves; CMB polarization; scalar–tensor comparison; spectral geometry; causality; canonical quantization; dark matter phenomenology; quantum nonlocality; environment-dependent screening 📑 Table of Contents (Revised for Submission) Abstract 1. Introduction 2. Ontological Foundations 2.1. Postulate I: Time as a Quantum Operator 2.2. Postulate II: Temporal Density 2.3. Postulate III: Geometry as a Derived Structure 3. Theoretical Framework 3.1. Central Equations and Interaction Lagrangian 3.2. Background Independence and Operator Metric 3.3. Action Principle and Derivation of Field Equations ← 🆕 3.4. Canonical Quantization and Hilbert Space Structure ← 🆕 4. Canonical Screening Mechanisms 4.1. Hyperbolic Model: Saturated Coupling 4.2. Gaussian Model: Linear Sensitivity 4.3. Spectral Damping and UV Regularization ← 🆕 5. Observational Predictions 5.1. Modified Newtonian Potential and Static Solutions 5.2. Dipole Gravitational Wave Emission in Asymmetric Binaries 5.3. Cosmological Corrections to Expansion 5.4. CMB Polarization Shifts and Tensor Anomalies 5.5. Large-Scale Structure Correlations and BAO Deviations ← 🆕 6. Falsifiability and Experimental Tests 6.1. MICROSCOPE: Null Violation of the Equivalence Principle 6.2. LISA / Einstein Telescope: Dipole Dephasing in NS–WD Systems 6.3. CMB-S4 / LiteBIRD: E/B-Mode Shifts 6.4. Euclid / LSST / DESI: Statistical Signatures in Galaxy Distributions 6.5. Parameter Constraints from Existing Data ← 🆕 6.6. Forecasts for Future Missions ← 🆕 7. Discussion and Conclusions References Appendix A. Derivation of τ_env in Spherical Media Appendix B. Mathematical Rigor of the Metric Ansatz B.1. Signature Preservation B.2. Singularities and Smoothness B.3. Renormalization and Spectral Expansion B.4. Covariance and Operator Geometry B.5. Comparison with Scalar–Tensor Theories Appendix C. Recovery of GR and QM in Classical Limits C.1. Weak-Field Limit and Flat Spacetime C.2. Classical Action and Einstein Equations C.3. Wheeler–DeWitt Constraint and Timeless Quantum Gravity Appendix D. Numerical Estimates and Parameter Bounds ← 🆕 D.1. Constraints from MICROSCOPE and Lunar Laser Ranging D.2. Bounds on ξ, m_τ, β from Solar System Tests D.3. Forecasts for ΔΨ(f), ΔB/B, and ξ(r) Deviations Appendix E: Archival Index and Technical Summary
Author: Lemeshko, Andriy
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083419080
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