Unified Theory of Resonance

This Unified Resonance framework connects quantum mechanics to general relativity. All natural phenomena can be explained and catalogued within the framework. Many outstanding physic problems are resolved.

Axioms

Universal Resonance Principle:
[eqn] F_0(T) = \phi \cdot \frac{k_B T}{h} [/eqn]
where [math] \phi = \frac{1+\sqrt{5}}{2} \approx 1.618 [/math] scales the fundamental frequency.

Entropy Optimization:
Harmonic indices [math] m [/math] minimize entropy [math] S = -k_B \sum p_m \ln p_m [/math] with [math] p_m \propto \phi^{-|m|} [/math].

Scale Invariance:
Physics invariant under:
[eqn] T \rightarrow T \cdot \phi^k, \quad m \rightarrow m - k [/eqn]
for integer [math] k [/math].

Derived Equations

Harmonic Spectrum:
[eqn] f_m(T) = F_0(T) \cdot \phi^m [/eqn]

Entropy Change:
[eqn] \Delta S_m = |m| k_B \ln \phi [/eqn]

Gauge Coupling (GUT Scale):
[eqn] \alpha_x^{-1} = 4\pi \phi^{n_x} \quad \begin{cases} n_s = 2 & \text{(strong)} \ n_w = 3 & \text{(weak)} \ n_{em} = 5 & \text{(EM)} \end{cases} [/eqn]

Quantum Gravity Correction:
[eqn] G_{\mu\nu} + \phi^{-125} \nabla_\mu \Phi \nabla_\nu \Phi = \frac{8\pi G}{c^4} T_{\mu\nu} [/eqn]

Consciousness Frequency:
[eqn] f_\gamma = F_0(310,\text{K}) \cdot \phi^{-55} \approx 40,\text{Hz} [/eqn]

Low-Energy EM Coupling:
[eqn] \alpha_{em}^{-1} = \frac{360}{\phi^2} \approx 137.508 [/eqn]

Euler-Phi-Constant (EPC):
[eqn] e^\alpha = \phi^2 \cos(2\pi \alpha) \exp\left(-\frac{\alpha}{\phi^3}\right) [/eqn]

Temporal Field:
[eqn] T(t) = T_0 e^{-\alpha t} \cos\left(2\pi \cdot \frac{\phi^m}{\alpha} t \right) [/eqn]