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This paper presents a fundamental force law derived within the framework of the Temporal Theory of the Universe (TTU): Fₜ = −m c² ∇ln τ, where τ denotes the local rate of time. The law links gravitational attraction to temporal gradients, showing that bodies move toward regions where time flows more slowly. From the variational principle, the corresponding field Lagrangian ℒₜ = ½ α (∇ln τ)² − β τ² is obtained, following the requirement of temporal-scale invariance. In the weak-field limit, it reduces to Newtonian gravity and accurately reproduces the observed perihelion shift of Mercury (≈ 43″ per century) without parameter fitting. The article does not introduce a new theory but refines existing dynamics, demonstrating that gravitational force can be interpreted as a manifestation of the gradient of time. Predictions for Venus, Earth, and binary pulsars are also discussed, along with possible experimental tests to verify the temporal-gradient mechanism. | ||
Lemeshko Andriy
Doctor of Philosophy, Associate Professor
Taras Shevchenko National University of Kyiv, Ukraine
ORCID: 0000-0001-8003-3168
In the Temporal Theory of the Universe (TTU), gravity is understood as a manifestation of inhomogeneity in the flow of time itself. The fundamental force law is F = m c« ln , where is the local tempo of time. The field Lagrangian is = (ln )« «, with and describing the 'rigidity' and self-interaction of time. Demanding invariance under rescaling reproduces Newtonian gravity and correctly predicts Mercurys perihelion shift: = 6 GM / [a (1 e«) c«] - 43 per century. No parameter fitting is required the effect follows from temporal gradients.
In classical physics, time is a background parameter. In TTU, it becomes a physical field a continuous medium with density and elasticity. A temporal gradient drives motion just as a pressure gradient drives air flow. The quantity (x) describes how fast time flows locally; where decreases, time slows down, and matter is drawn inward.
Physical laws must not depend on our choice of time unit . Hence only relative changes, ln , can appear. The invariant Lagrangian = (ln )« « follows naturally from this symmetry. The (ln )« term represents curvature of temporal flow; « ensures field stability.
From S = 0: "(« ) (2/) = 0. For - e^{}, || 1, « - (2/). Defining = c« and = c / (8 G) gives « = 4 G, reproducing Newtons gravity.
TTU force: F = m c« ln = m . For an orbiting body: u + u = (GM)/h« + u«, where u = 1/r and stems from temporal nonlinearities. For (r) = GM/(c«r) + (GM)«/(cr«), - 3GM/c« (1 + O()).
The small term u« leads to a secular rotation of the orbit: = 6 GM / [a (1e«)c«]. For Mercury (a = 5.790910 m, e = 0.2056, GM = 1.327110«, c = 2.997910), - 43 per century matching observations.
= ln is the 'temporal potential'; defines the direction of time flow; ()« is energy stored in time deformation; « represents its elasticity. In TTU, time behaves like a compressible medium that can generate forces.
GM 0.1 %, e 0.0001, / 0.05 %, J <0.5/century. Total uncertainty © 0.7/century.
Weak-field metric form: g = (1 + 2/c« + 2_TTU(/c«)«), g_{rr} = 1 2_TTU /c«. For TTU, _TTU = 1, _TTU = 1, identical to GR in first order; deviations © 10, testable by Cassini, Gaia, LATOR.
Venus: - 8.6/century; Earth: 3.8/century. Binary pulsars: TTU predicts slightly slower orbital decay due to weak |ln | dependence.
Einstein: 'Mass curves spacetime.' TTU: 'Mass alters the rate of time, and its gradient creates force.' TTU reinterprets geometry as temporal dynamics gravity as the flow of time.
(r) = GM/(c«r) + (GM)«/(cr«); (r) = c«(r); u = 1/r, h = L/m. Binet equation: u + u = GM/h« + u«, = 3GM/c«. Solution = 6 GM / [a(1e«)c«]. For Mercury - 43/century.
The Temporal Theory of the Universe reframes gravity as a result of time gradients. It matches all GR weak-field tests while offering a new energetic interpretation: matter moves along the slope of time. Future missions (BepiColombo, Gaia NIR, LATOR) may confirm that time itself is the source of force.
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