Energy as Frequency × Coherence: A Resonance-Theory Generalization of Planck's Relation

This paper proposes a resonance-based reinterpretation of energy. In classical physics, energy is defined in fragmented ways — as kinetic, potential, thermal, or quantized via Planck’s relation E = hν. Within R-theory, these domains are unified under a single principle:E = f × C,where f is frequency and C is coherence. Coherence expresses the degree of phase-order with the zero field, ranging from destructive interference (C ≈ 0) to perfect phase-lock (C ≥ 1). This framework generalizes Planck’s relation, in which coherence is implicitly fixed at 1, and explains why certain resonant phenomena — such as lasers, Bose–Einstein condensates, or coherent sound waves — exhibit energy densities greater than the sum of their parts.The paper further shows how the speed of light (c) and Planck’s constant (h) can be reinterpreted as derivatives of a deeper resonance constant (R₀), with c expressing the maximal propagation of coherence and h the minimal quantization of resonance. In this way, quantum and relativistic laws are revealed as manifestations of a universal resonance principle, situating energy as the emergent stability of frequency and coherence in the zero field.