Physical Significance of Mathematical Formulas: An Outline of Absolute Kinematics Number-Theoretic Analysis

This paper takes absolute kinematics as the core framework, with the fundamental postulate: observers without intrinsic three-accelerations other than gravitational acceleration have a constant proper four-acceleration magnitude α₀ (approximately \(1.7035 ×10^{-10} ~m / s^{2}\)). Derivations show that \(\alpha_{0}\) is the unique logical intersection of prime distribution, computational complexity, and the geodesic spectrum of hyperbolic geometry, which can be analytically expressed via Dedekind-Rankin type L-functions. The fine-structure constant α is a number-theoretic ratio of background stiffness in hyperbolic space to local knot impedance, with its reciprocal satisfying \(\alpha^{-1}=4 \pi^{3}+\pi^{2}+\pi\). The speed of light c is a logical step constraint for the analytic continuation of number-theoretic series, balancing number-theoretic consistency of dimensions and geometric self-consistency. The only descriptive tool for topological decoherence is the weight-12 Ramanujan discriminant \(\Delta(\tau)\), whose poles correspond to topological phase transition thresholds, one-dimensional rigidity corresponds to vacuum uniqueness, and consistency of analytic continuation meets the computational complexity requirements of the holographic principle. Cross-scale computational verification indicates: microscopic particle decay and neutrino oscillation can be quantitatively described by topological entropy and the Ramanujan τ-function; the shell capacity and 7-period limit of the mesoscopic periodic table originate from the cumulative topological entropy threshold; the macroscopic black hole "no-hair theorem" is a topological-arithmetic phase transition under extreme geometric pressure. The core goal of this paper is to achieve precise descriptions of the physical world relying solely on mathematical tools, thereby deepening the understanding of the significance of physical phenomena.

 

This paper is built on the foundation of three preceding works in the Absolute Kinematics series, with their Zenodo DOIs listed as follows: 10.5281/zenodo.17906793, 10.5281/zenodo.17978262, 10.5281/zenodo.17978597. It further extends the framework by integrating number-theoretic tools to explore the deep connection between mathematical invariants and physical phenomena.