
Abstract We develop a dimensionally consistent, variationally grounded model of gravity as the inertial response to spatial gradients of the normalized proper-time rate: Θ = dτ⁄dt The canonical test-body law is: F_g = −m · c² · ∇ln Θ · [1 + χ(Ξ)] where Ξ = ρ · e^{iC} is a complex order parameter, and χ(Ξ) is a dimensionless susceptibility encoding vacuum⁄medium response via: · amplitude perturbations: δρ⁄ρ₀ · thermal dependence: U_eff(φ, T) · gradient contributions In the weak-field limit: χ → 0, ∇ln Θ = ∇φ_N⁄c² which recovers Newtonian gravity without ad-hoc coefficients. The dynamics follow from a scalar-field Lagrangian with curvature coupling and matter interaction, ensuring conservation laws (Noether) and placing the 4π factor in the field equation (Poisson), not in the force law. The framework yields quantitative, falsifiable predictions for: · altitude-dependent clock⁄accelerometer correlations · thermal⁄plasma-driven sources · coherence-sensitive anomalies Order-of-magnitude estimates are consistent with reported Kozyrev-type weight variations. This formulation resolves earlier issues with dimensionality, parameter tuning, and additive force composition, unifying gravitational and thermo-material effects within a single field equation for Θ (or φ = ln Θ), and provides a testable baseline for TTG as a time-structured theory of gravity. Keywords: time-rate field; temporal gradient; scalar Lagrangian; gravitational redshift; susceptibility; coherence; Poisson equation. Table of Contents Abstract Keywords 1. Introduction 2. Not Just Curvature 3. The Arrow of Time 4. Time as a Source of Energy 5. The Cause of Gravity 6. On the Creation of Gravity 7. On Controlling Time 8. Mathematics of Time 9. Mathematical Model — Lagrangian Core 10. Experimental Program (operational) References Appendix A. Phase Representation of the Time Field Introduction It is misleading to treat the “gravitational field” as a substance in its own right. One may of course speak of spacetime curvature, yet curvature by itself is a geometric description of admissible trajectories, not an independent agent that “pushes.” (Descartes already cautioned that “weight” should not be reified as a thing but understood via underlying causes.) Einstein’s theory brilliantly unifies gravity with geometry: massive bodies curve spacetime, and free bodies follow geodesics that resemble motion into a “gravitational funnel.” Elegant as this picture is, it leaves open the question of what, in force language, drives motion. 1. Not Just Curvature Our perspective separates guidance from drive. Curvature guides motion by shaping geometry; the drive seen by an accelerometer is the inertial response to spatial gradients of the local time-rate. Define: Θ ≡ dτ⁄dt, φ ≡ ln Θ Then the test-body law is: F_g = −m · c² · ∇φ = −m · c² · ∇ln Θ (see Eq. (1.4)) Spacetime curvature R influences motion indirectly by reshaping φ through the field equation (Poisson in the weak-field limit), rather than by entering as an additive term in the force; cf. Eqs. (1.8)–(1.9). This is a complement to GR, not a denial. In the weak, static regime one has: ∇ln Θ = ∇φ_N⁄c², hence F_g = −m · ∇φ_N Beyond that regime, the same framework naturally accommodates vacuum⁄coherence and thermo-material responses via a dimensionless susceptibility χ encoded in the Lagrangian sector—yielding testable departures without ad-hoc force summations. Reference 1. Ziguneko, Stanislav. 1991. “How Is the Time Machine Constructed?” Znak voprosa [Question Mark], no. 5. Online resource: https://www.klex.ru/qa3 (accessed 5 Oct 2025). [in Russian] 2. Miroshnikov, R. M. 1988. “Restless Rest Mass.” Tekhnika – molodezhi [Technology for the Youth] 1 (Jan): 57–60. 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Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511535093. 19. Faraoni, V. 2004. Cosmology in Scalar–Tensor Gravity. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-1-4020-1989-0. 20. Birrell, N. D., and P. C. W. Davies. 1982. Quantum Fields in Curved Space. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511622632. 21. Wald, R. M. 1984. General Relativity. Chicago: University of Chicago Press. 22. Noether, E. 1918. “Invariante Variationsprobleme.” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 235–257. [Engl. transl.: “Invariant Variation Problems,” Transport Theory and Statistical Physics 1(3) (1971): 186–207.]
A completely new approach to explaining gravity has been proposed. Gravity is connected to the interaction of the "arrow of time" with curved space-time, with temporal gradients added as a key element. Essentially, it has been deduced that gravity is the manifestation of the inertia of matter, driven by the arrow of time as it passes through zones of local time deceleration. This is not merely a refreshing perspective on the nature of gravity but a complete reevaluation of how energy and time are linked to the fundamental forces of the universe. The proposed approach could serve as a foundation for future experiments and models.
Experimental validation of time effects, Space-time curvature, Temporal energy dynamics, General relativity, Energy conservation in gravity, Time gradient effects, Gravitational fields, Mass-energy relationship, Gravity, Thermodynamic influence on gravity, Time anomalies, Inertia and gravitational interaction
Experimental validation of time effects, Space-time curvature, Temporal energy dynamics, General relativity, Energy conservation in gravity, Time gradient effects, Gravitational fields, Mass-energy relationship, Gravity, Thermodynamic influence on gravity, Time anomalies, Inertia and gravitational interaction
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