Deriving the Einstein Equivalence Principle from the Fibonacci Cascade: Temporal Depth and Local Gravity in Fractal Mechanics
Year: 2026
Type: preprint
Abstract: The Einstein Equivalence Principle (EEP) β the equality of gravitational time dilation and gravitational acceleration β is a foundational postulate of General Relativity (GR), not derived from a deeper principle. We show that within Fractal Mechanics (FM), the EEP is a mathematical consequence of a single cascade parameter Im(π), where π = (1+β5)/2 is the golden ratio. In FM, the local flow of time and the local gravitational coupling both depend on Im(π) with the same coefficient π½ = π, derived analytically from the FM Lagrangian inter-level coupling term. The resulting formula, πΊ_πππππ β πΊβ (1 + π Β· πΏπΌπ(π)/πΌπ(π)β ) = π_πππππ/πβ , directly encodes the EEP without postulating it. We derive two testable predictions: (i) residual correlations between the measured value of Newtonβs constant G and local crustal geological density, unaccounted for by existing Cavendish experiments; and (ii) a small but specific correction πΏπΉπ to the gravitational redshift near compact objects, testable with future pulsar timing and atomic clock experiments.
Author: Leroy, RΓ©mi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204155021
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