Essence of Extended Classical Mechanics (ECM)

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Date: October 09, 2025

Abstract

Extended Classical Mechanics (ECM) provides a unified framework integrating Newtonian, Einsteinian, and Quantum Mechanics through a mass-differential formalism that includes Mᵉᶠᶠ (effective mass), Mᵃᵖᵖ (apparent mass), and ΔMᴍ (mass differentials). ECM naturally incorporates gravitational and antigravitational effects as complementary energy redistribution phenomena. Relativistic behaviors emerge from frequency-dependent phase distortions rather than spacetime geometry, and quantum energy quantization is seamlessly integrated, establishing ECM as a frequency–mass–energy bridge across scales.

Extended Classical Mechanics (ECM) serves as the unifying foundation for three prevailing branches of physics:

Newtonian Classical Mechanics — governed by F = Ma, where mass (M) and time (t) are constants.
Einsteinian Relativistic Mechanics — governed by γ = 1/√(1 − v²/c²), introducing velocity-dependent mass, time, and length changes, giving relativity its mechanical character ^[1].
Quantum Mechanics — governed by E = hf and probabilistic microstates.

ECM extends these frameworks using mass-differential formalism — Mᵉᶠᶠ, Mᵃᵖᵖ, and ΔMᴍ — linking macroscopic, relativistic, and quantum regimes under one principle, while integrating gravitational and antigravitational effects ^[2].

KEᴇᴄᴍ = (ΔMᴍ⁽ᵈᵉᴮʳᵒᵍˡᶦᵉ⁾ + ΔMᴍ⁽ᴾˡᵃⁿᶜᵏ⁾)c² = ΔMᴍc² = hf

ECM forms a frequency–mass–energy bridge unifying mechanical, relativistic, quantum, gravitational, and antigravitational domains.

Footnotes (Back to Top)

[1] In Extended Classical Mechanics (ECM), the Lorentz factor (γ) is not treated as a fundamental constant of nature or an external relativistic correction. It is instead regarded as a derived mathematical construct, used only to illustrate how the Mᵉᶠᶠ varies with motion-induced frequency distortion. Expressed comparatively:
γ = 1/√(1 − v²/c²) ⇒ Mᵉᶠᶠ ≈ γMᴍ
Within ECM, γ signifies mass–frequency coupling, not geometric curvature of spacetime.
Cautionary Note: This relation is presented only as an illustrative mathematical form. ECM does not claim that physical transformations of mass, time, or length occur as in relativity. The Lorentz factor (γ) fails to account for acceleration-based transitions, material stiffness, and variable gravitational or antigravitational conditions that influence frequency and energy redistribution. Therefore, expressions like γMᴍ or t/γ remain comparative, not physical. ECM replaces such interpretations with frequency-based relations like Δtₑ꜀ₘ ∝ 1/f, where f ∝ ΔMᴍc²/h, describing true energy–mass coupling without invoking spacetime geometry.
[2] Antigravitational effects in ECM correspond to transitions involving −Mᵃᵖᵖ, representing outward energy release complementary to gravitational attraction (positive Mᵃᵖᵖ), forming a mass–energy duality ^[IV].

References (Back to Top)

[I] Einstein, A. Zur Elektrodynamik bewegter Körper, Annalen der Physik, 1905.
[II] Planck, M. Über die Begründung des Gesetzes der Energieverteilung im Normalspektrum, Annalen der Physik, 1900.
[III] Appendix 21: Effective and Apparent Mass Dynamics in ECM. DOI: 10.13140/RG.2.2.25261.38882
[IV] Appendix 32: Energy Density Structures in ECM. DOI: 10.13140/RG.2.2.22849.88168