A Scale-relative Approach to Unification: Analogical Equivalence of Fundamental Forces from Atomic to Cosmic Scales

ABSTRACT

This paper proposes a theoretical framework suggesting that the four fundamental forces of nature, gravitational, electromagnetic, strong nuclear, and weak nuclear are interrelated through a principle of scale relativity. Drawing an analogy between the structure of atoms and the solar system, the study examines whether macroscopic gravitational and magnetic interactions are scaled analogues of microscopic nuclear and electromagnetic interactions. By exploring Kepler’s laws of planetary motion as a macro-scale reflection of atomic behavior, a correspondence model is proposed that maps force types across physical scales. The apparent separation of fundamental forces is hypothesized to be an artifact of observational scale rather than a true division in nature. The model is formalized mathematically using scaling functions and dimensional analysis, and illustrated through diagrams. Implications include the prospect for a scale-dependent grand unification, predictions of astrophysical resonances, and tests based on dimensionless invariants.