Temporal Theory of Gravitation (TTG v1.1) - Horizon Extension
Year: 2025
Type: article
Abstract: TTG v1.1 extends the minimal anchor core (v1.0) by introducing nonlinear, even-parity coupling functions A(τ), such as: Series at τ≈0: α(τ) = β tanh(βτ) = β² τ − (β⁴/3) τ³ + O(τ⁵); A(τ) = cosh(βτ) = 1 + (β²/2) τ² + (β⁴/24) τ⁴ + O(τ⁶). (A.1) A(τ) = cosh(β·τ) or A(τ) = exp(γ·τ²⁄2M²) The scalar-matter coupling is governed by the derivative: (A.2) α(τ) ≡ d(ln A)/dτ In the small-field limit, α(τ) admits an even-parity expansion: (A.3) α(τ) = α₁·τ + α₃·τ³ + ... where α₁ = β², α₃ = −β⁴⁄3 (for A(τ) = cosh(β·τ)) This structure enables environmental screening: in high-density regions (e.g., Solar System), τ → 0 implies: (A.4) α(τ⊙) ≈ 0 ⇒ suppressed fifth forces The core formalism remains unchanged; the extension lies solely in the functional form of A(τ), ensuring full backward compatibility: (A.5) α(τ) → β = const ⇒ TTG v1.1 → TTG v1.0 To characterize the spatial range of scalar-mediated interactions, we define the Yukawa interaction range: (A.6) λ_τ ≡ 1⁄m_τ (Yukawa interaction range) We also provide explicit parameter ranges, compare TTG with other screening mechanisms, and discuss quantum stability. Keywords Time; time density; time flow; time pressure; time vortex; temporal theory; TTG; TTE; electrostatics; gravity; quantum nonlocality; CP violation; muonic hydrogen; alpha decay; regularization; substance; causality; ontology; quantum gravity; experimental verification Units & Conventions We work in natural units ħ = c = 1 throughout the theoretical formulation (Sections 2--3, 5, 7--9). In phenomenological, post‑Newtonian, and gravitational‑wave expressions (Sections 4, 6, 10), constants c and ħ are reinstated explicitly to maintain SI units. The Newtonian potential Φ has dimensions [Φ] = m²·s⁻², and its dimensionless post‑Newtonian counterpart is defined as U ≡ Φ/c². The scalar mass m_τ sets a Yukawa interaction range λ_τ ≡ ħ/(m_τ c) in SI units, which reduces to λ_τ = 1/m_τ in natural units. Table of Contents 1. Introduction: From Anchor to Adaptation 2. Screening Mechanism: Coupling Functions and α(τ)2.1 Comparison with Other Screening Mechanisms 3. Field Equations and Dynamics 4. Newtonian and Post-Newtonian Limits 5. Cosmology and Large-Scale Dynamics 6. Gravitational Waves and Dipole Radiation6.1 Screening Behavior 7. Falsifiable Predictions and Signal Table 8. Parameter Space and Priors8.1 Core Parameters8.2 Scalar Coupling Behavior8.3 Priors for Screening Consistency8.4 Explicit Parameter Bounds8.5 Environmental Regimes8.6 Scalar-Mediated Force8.7 Constraints and Estimation 9. Quantum Corrections and Theoretical Stability9.1 Symmetry Protection9.2 Radiative Stability9.3 UV Completion9.4 Summary of Stability Features 10. Comparison with Dark Matter and MOND10.1 Galactic Rotation Curves10.2 Effective Mass Interpretation10.3 Comparison with MOND10.4 Applicability and Limitations10.5 Hybrid Interpretation Table 11. Conclusion: TTG as a Living Framework References Appendix A. Comparison with TTG v1.0
Author: Lemeshko, Andriy
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083020980
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