A Single-Ratio Origin of Physical Constants and the Four Fundamental Interactions

This paper presents a unified geometric reinterpretation of physical constants and the four fundamental interactions—gravity, electromagnetism, the strong force, and the weak force—based on a single primitive physical ratio U ≡ E / r The energy–distance ratio.Rather than treating time, mass, force, or coupling constants as independent fundamental entities, the framework reconstructs them as emergent, regime-dependent quantities arising from a self-regulated geometric structure. Within this formulation, the four fundamental interactions are not distinct force laws, but correspond to different elastic regimes of a single underlying geometric response defined on the u-space. In this picture, conventional physical constants (such as c, ℏ, and G) do not play the role of primitive inputs. Instead, they function as reconstruction gauges, encoding how different physical regimes are realized within the same geometric foundation. The apparent hierarchy and diversity of interactions emerge from saturation, phase alignment, and elastic transitions in the underlying structure, rather than from independent coupling parameters. This work provides a concrete realization of force unification that avoids additional assumptions, hidden dimensions, or ad hoc scale matching. The resulting framework offers a minimal and computationally efficient description of interactions across microscopic and macroscopic scales, while remaining compatible with known physical behavior. The present manuscript is a focused and self-contained study on the unification of physical constants and the four interactions. It is conceptually connected to a broader, extended theoretical development by the author (spanning multiple scales and applications), but can be read independently without reference to that larger body of work. Modern physics provides highly successful mathematical answers to the question of how physical phenomena operate.Yet, the deeper structural question of why these interactions take their observed forms remains open. This work does not aim to replace existing computational frameworks, but instead proposes a geometric ratio–phase structure (SRCD–GPT) that addresses why the four fundamental interactions emerge as distinct regimes of a single self-regulated elastic system. ================================================================================== “This work isolates and presents a focused, independently readable subset of a broader SRCD framework, concentrating on the geometric unification of fundamental constants and the four fundamental interactions.” ================================================================================== The author welcomes inquiries for collaboration involving the application of the SRCD framework to empirical datasets. To ensure consistency with the theoretical foundations established in this Zenodo-archived work, the author serves as the primary point of contact for the integration of SRCD’s predictive structure with new experimental results. ================================================================================== Update Notice This version includes an explicit interpretation of the fine-structure constant within the SRCD–GPT framework, clarifying its role as an elastic ratio parameter rather than an independent input constant.In addition, the unified master equation table has been updated to reflect the finalized SRCD–GPT formulation, providing a consolidated view of interaction regimes and their correspondence within the single elastic ratio coordinate. --------------------------------------------------------------------------------- Update Notice(ver.4.0) Empirical Four-Force Validation Update (Empirical Data Expansion):This version includes a comprehensive empirical validation of the SRCD framework across all four fundamental interactions, using experimentally established datasets without fitting, tuning, or data manipulation. The following real-world datasets were analyzed: Strong interaction:IAEA ENSDF nuclear level data for Xe-135(N = 38 nuclear excitation levels) Weak interaction:PDG decay widths and lifetimes(N ≈ 30 representative decay channels) Electromagnetic interaction:Hydrogen atomic spectral lines (Rydberg series)(N = 74 measured transitions) Gravitational interaction:Planetary and satellite orbital data (NASA/JPL)(N = 21 orbital systems) All datasets were mapped using the same SRCD transformation and evaluated via circular variance, revealing a consistent geometric phase organization across vastly different physical regimes. =====================================================================================