Phase–Frequency–Time Equivalence and Null Condition: Extended Classical Mechanics Unified Axioms.

Date April 06, 2026

In Extended Classical Mechanics (ECM), all oscillatory phenomena—whether acoustic, piezoelectric, or electromagnetic—follow a universal phase-dependent temporal evolution:

Tx° = x° / (360 f₀) = Δtx°

Here, the effective wave speed is system-dependent:

• Acoustic waves: v = sound speed in the medium

• Electromagnetic waves: v = c (speed of light in vacuum)

This relation links phase, frequency, and effective time consistently, providing a deterministic, bijective indexing of oscillatory states.

The 360° “null condition” serves as a natural completion marker for one full phase cycle, and does not correspond to relativistic time dilation. Instead:

Δf₀ represents the frequency deviation from the primordial Planck frequency fₚ.

Δtx° quantifies cosmic time distortion arising from Δf₀-driven energy/mass transformations.

Observable invariants emerge from the completion of the phase cycle itself; no external geometric constraints or relativistic assumptions are required.

The null condition provides a definitive marker for ECM Phase-Kernel Interference Tests, distinguishing true energetic phase shifts from relativistic-like interpretations.

Thus, ECM provides a self-consistent framework where phase progression, frequency transformation, and temporal emergence are intrinsically linked, and all oscillatory phenomena are governed by these fundamental principles.