Temporal Theory of Gravitation (TTG) v1.0 — Anchor Core
Year: 2025
Type: article
Abstract: We present the anchor core (v1.0) of the Temporal Theory of Gravitation (TTG), a minimal, falsifiable framework in which a scalar field τ(x) represents physical time and universally couples to matter via a conformal factor A(τ) = 1+βτ. The action consists of the Einstein–Hilbert term plus a canonical kinetic term and potential V(τ). In the Einstein frame this implies a universal non‑conservative coupling ∇_μ T^{μ}{}_ν = −β T ∇_ν τ, yielding a testable fifth‑force phenomenology and energy exchange between matter and the temporal field. We derive the field equations, the Newtonian limit with a Yukawa correction Φ(r) = −GM/r [1+ε e^{−m_τ r}] (ε≃β²), the post‑Newtonian predictions (γ_PPN = β_PPN = 1), and the gravitational‑wave speed c_gw = c. A concise list of falsifiable signatures is provided (MICROSCOPE, spacecraft tracking, LIGO/Virgo/KAGRA). We keep v1.0 strictly minimal: no screening, no nonlinear A(τ) (e.g., cosh), and no TTU extensions. Variants and cosmological specializations lie outside the scope of this anchor document and do not affect the equations and predictions presented here. Keywords temporal field; scalar–tensor gravity; fifth force; post‑Newtonian parameters; gravitational waves; Yukawa potential; MICROSCOPE; spacecraft tracking; falsifiability; energy non‑conservation Table of Contents 1. Postulates 2. Action and Field Equations 3. Newtonian Limit and Yukawa Correction 4. Post‑Newtonian and Gravitational‑Wave Predictions 5. Fifth‑Force Phenomenology 6. Falsifiable Signatures (v1.0) 7. Potential V(τ) and Phenomenology 8. Conclusion 9.References Appendix A. Notation 1. Postulates P1. There exists a fundamental scalar field τ(x) that encodes physical time (not coordinate time). P2. Matter is minimally coupled to the Jordan metric g̃_{μν} = A(τ)^2 g_{μν} with a strictly linear coupling A(τ) = 1 + β τ in v1.0. P3. The dynamics of g_{μν} and τ follow from the action below; all predictions quoted in this document are derived from it without additional mechanisms (no screening in v1.0).
Author: Lemeshko, Andriy
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7082653449
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