Inertial Geometry from Information Rate Conservation: Microscopic Unification of Mass, Time Dilation, and Energy--Frequency Relations

In traditional formulations, time dilation and ``relativistic mass'' increase in special relativity are usually viewed as two independent kinematic effects, while quantum mechanics directly relates energy to frequency through the Planck relation E=\hbar \omega. For a massive particle, when its velocity approaches the speed of light, total energy grows rapidly, corresponding to growth of plane wave phase frequency \omega; yet proper time flow of the same particle exhibits Lorentz dilation, with i