A Unified Interpretation of Mass Energy and Quantum Energy Based on Phase Circulation Theory
Abstract
Mass energy, E=mc², and quantum energy, E=ℏω, are fundamental relations widely used throughout physics, yet the dynamical reason why both reduce to the same physical quantity—energy—has not been fully explained. The former is derived from the static mass of an object, a structural property, while the latter is derived from the angular frequency of an oscillating system, a temporal property of motion; their origins are inherently different. Nevertheless, the fact that the two always coincide has been accepted merely as an experimentally confirmed fact. This study attempts to derive these two relations in a unified manner from a single dynamical picture. Assuming that the fundamental units constituting matter are structures that sustain circulating motion while continuously exchanging energy with a field that fills space, E=mc² can be understood as the quantity representing the capacity of this structure to convert the field's energy into mechanical energy, while E=ℏω can be understood as the quantity representing the amount of energy actually extracted from the field through this motion. It is further shown that, for this structure to maintain a stable state, the energy budget of what is drawn in and what is released to and from the field must remain in constant balance, and that from this balance condition, the coincidence of the two quantities follows not as an empirical coincidence but as a dynamical necessity. The significance of this study lies in clarifying two aspects…
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