Unified Resonance Theory: From Δ = 0 to Quantized Matter and Radiation Limits

This work presents an integrated theoretical model that unifies the formation of physical structures, biological stability, and radiative limits under a single resonance principle defined by the product of frequency (ν) and radius (r). The theory begins with the concept of dynamic equilibrium (Δ = 0), in which systems remain stable as long as all internal flows are balanced and synchronized. Disruptions (Δv ≠ 0) result in structural transformations, applicable equally to cosmology and to pathology. Central to this model is the proposition that frequency ν is the only absolute physical quantity, while time, mass, and space emerge as secondary, derived properties from stable ν distributions. Quantized matter arises at specific ν-values where angular dispersion (Δω) reaches a minimum. These resonance solutions correspond to key physical constants: the Bohr radius and the helium nucleus radius. The model further interprets X-rays and gamma rays as the maximum vibrational work outputs of electron-bound and nucleon-bound structures, respectively. The universal constraint ν·r ≈ c / (2π) encapsulates the radiative boundary for all coherent wave-emitting systems. By linking frequency resonance with structural constraints, this framework provides a unified geometrical and vibrational basis for understanding the emergence of matter, the constancy of physical parameters, and the interplay between structure, radiation, and decay. Author: Tetsuo Konno(今野哲夫) https://orcid.org/0009-0002-1842-7865