Extended Classical Mechanics (ECM)

Extended Classical Mechanics: The Phase Kernel Formalism — Rethinking Gravity Beyond GR’s Spacetime Curvature

In this detailed presentation, two narrators, A and B, explore how Extended Classical Mechanics (ECM) redefines gravitational phenomena through the Phase Kernel Formalism — a framework that replaces geometric curvature with phase accumulation and effective refractive index variations.

Rather than interpreting gravity as the warping of spacetime, ECM treats it as a wave-based modulation of phase velocity, yielding the same measurable predictions as General Relativity (GR) in the weak-field regime — but derived from fundamentally different physical reasoning.

Highlights

• Shapiro Delay (Phase–Algebra Derivation):
  ECM expresses gravitational time delay as cumulative phase retardation — Δtᴇᴄᴍ ≡ Δtᴳᴿ — arising from an effective refractive index linked directly to potential energy variations.
• Gravitational Lensing Time Delay:
  The phase-integral approach that naturally reproduces Fermat’s principle, combining geometric and Shapiro components without invoking spacetime curvature.
• Perihelion Precession (Phase Perturbation):
  A reinterpretation of orbital precession as a cumulative phase–angular shift, preserving GR’s predictive accuracy via an explicit perturbation framework.
• Testing Predictive Power:
  ECM’s parameterised phase kernels allow direct comparison with precision datasets — Cassini, Viking, VLBI, and pulsar timing — by fitting phase-shift coefficients for deviations from GR.

Key Takeaway

If every gravitational observation we make is phase- and time-based, should phase itself be regarded as the true fabric of physical reality?

ECM invites you to look beyond geometry — toward a unified wave–mass–energy picture where gravity emerges as a phase phenomenon.