Extended Classical Mechanics (ECM) satisfies the three decisive scientific yardsticks—internal coherence, dimensional consistency, and empirical adequacy with a falsifiable signature—through the documented content of its published appendices.
1.
Internal coherence
Appendix B
presents a rigorous, line-by-line inspection of every symbol and operator that
appears in the ECM Lagrangian—mass displacement ΔM,
the Planck frequency term hfᴾ, the de Broglie frequency term hfᵈᴮ,
effective gravitational acceleration gᵉᶠᶠ, and all derived quantities. Each
equation is explicitly traced back to the theory’s foundational postulates: Planck’s
energy–frequency relation E = hf,
de Broglie’s momentum–wavelength relation p
= h/λ, and Newtonian force law F = d
p/dt. The derivations are shown to proceed without algebraic
contradiction, establishing a closed, self-consistent mathematical structure
that is free from internal inconsistencies.
2.
Dimensional
consistency
Across the
appendices, every ECM expression is subjected to a comprehensive dimensional
audit. Energy terms are demonstrated to carry the correct dimensions [M L² T⁻²], momentum terms [M L T⁻¹], and frequency terms [T⁻¹]. A worked example in Appendix B §3.2 explicitly confirms that the
composite quantity (ΔMᴾ+ ΔMᵈᴮ)c²
possesses the identical dimensional signature to h f, thereby guaranteeing that
the bridge between ECM’s frequency-governed mass displacement and observed
energy is dimensionally closed and physically meaningful.
3.
Empirical
adequacy and a falsifiable signature
Appendix 40 delivers side-by-side quantitative comparisons between ECM-predicted values and measured anode current densities from CRT thermionic emission experiments. The agreement yields χ² = 1.07 (degrees of freedom = 8), demonstrating statistical consistency with existing high-precision data. Going beyond mere adequacy, Appendix 41 §4 proposes a satellite-borne cavity-QED experiment that predicts a distinctive, falsifiable signature: a fractional deviation of 3.2 × 10⁻⁵ in the photon-recoil frequency shift at β = 0.05. This predicted deviation lies well outside the ±1.1 × 10⁻⁶ error envelope of current optical-lattice clock measurements, providing a clear experimental discriminator between ECM and prevailing relativistic expectations.
Taken together, these appendices demonstrate that ECM meets the three fundamental criteria—internal coherence, dimensional consistency, and empirical adequacy accompanied by a falsifiable prediction—thereby addressing the open questions previously raised.
