Why the Apple Does Not Fall
Year: 2026
Type: article
Abstract: The present work demonstrates that gravitational motion does not arise from a fundamental interaction, but from the structural evolution of admissible configurations within a closed variational framework. Starting from the universal quartic functional, we derive the stationary condition and construct the full admissible configuration space. The associated Hessian operator defines a discrete spectral structure characterized by a universal constant LLL. From the quartic coupling term, an effective kernel emerges with asymptotic behavior K(r)∼1/rK(r) \sim 1/rK(r)∼1/r, leading to radial dynamics r¨∼−1/r2\ddot{r} \sim -1/r^2r¨∼−1/r2 without introducing any force or external law. The motion commonly interpreted as gravitational fall is shown to correspond to a transition toward a globally selected configuration. The same kernel generates orbital motion, Kepler laws, galaxy rotation curves, and the Tully–Fisher relation, all as structural consequences of the variational system. A statistical prediction is derived from the spectral structure, linking the discrete Z3Z_3Z3 closure to the mean eigenvalue of a Markov representation of galaxy data: ⟨∣λ2∣⟩=1−L\langle |\lambda_2| \rangle = 1 - L⟨∣λ2∣⟩=1−L For L=0.25L = 0.25L=0.25, this yields ⟨∣λ2∣⟩=0.75\langle |\lambda_2| \rangle = 0.75⟨∣λ2∣⟩=0.75, in agreement with SPARC data (0.766±0.1070.766 \pm 0.1070.766±0.107) . The results establish that gravitational phenomena, orbital stability, and galactic dynamics are not governed by external forces, but emerge from a closed, generative, and spectrally constrained variational structure.
Author: Edoardo, Livolsi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155000466
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