Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Date: October 09, 2025
Extended Classical Mechanics (ECM) is the unifying foundation capable of guiding the three prevailing branches of physics:
1. Newtonian Classical Mechanics — governed by macroscopic mass–motion relations (F = Ma), where mass (M) and time (t) are treated as constants.
2. Einsteinian Relativistic Mechanics — governed by the Lorentz factor (γ = 1/√(1 − v²/c²)), which introduces velocity-dependent variations in mass, time, and length, giving relativity its mechanical character beyond mere geometric representation [1].
3. Quantum Mechanics — governed by frequency-dependent energy quantization (E = hf) and probabilistic microstates.
ECM not only extends these frameworks through mass-differential formalism — employing effective mass (Mᵉᶠᶠ), apparent mass (Mᵃᵖᵖ), and mass differentials (ΔMᴍ) — to link the macroscopic, relativistic, and quantum regimes under a single principle, but also integrates gravitational and antigravitational effects within the same formalism [2].
In ECM, these dual aspects are interpreted as complementary manifestations of energy redistribution through mass differentials:
KEᴇᴄᴍ = (ΔMᴍᵈᵉᴮʳᵒᵍˡᶦᵉ + ΔMᴍᴾˡᵃⁿᶜᵏ)c² = ΔMᴍc² = hf
— establishing ECM as the frequency–mass–energy bridge unifying mechanical, relativistic, quantum, gravitational, and antigravitational domains.
In short, 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.
Footnotes:
[1] In Extended Classical Mechanics, the Lorentz factor (γ) is not treated as an external relativistic correction but as an emergent consequence of the variation of effective mass (Mᵉᶠᶠ) with motion-induced frequency distortion. Thus, γ represents mass–frequency coupling, not spacetime geometry:
γ = 1/√(1 - v²/c²) ⇒ Mᵉᶠᶠ = γMᴍ
Accordingly, phenomena such as relativistic mass increase, time dilation, and length contraction emerge as frequency-dependent phase distortions within the mass-energy continuum, rather than as geometric curvature of spacetime [3].
[2] In ECM, antigravitational effects correspond to transitions involving negative apparent mass (−Mᵃᵖᵖ). These transitions represent the outward or energy-release phase of the mass-differential field, complementing the inward (gravitational) phase associated with positive Mᵃᵖᵖ. Together, these form a balanced mass–energy duality driving both attraction and expansion phenomena across physical scales [4].
References:
1. Einstein, A. Zur Elektrodynamik bewegter Körper, Annalen der Physik, 1905.
2. Planck, M. Über die Begründung des Gesetzes der Energieverteilung im Normalspektrum, Annalen der Physik, 1900.
3. Appendix 21: Effective and Apparent Mass Dynamics in Extended Classical Mechanics (ECM). DOI: https://doi.org/10.13140/RG.2.2.25261.38882
4. Appendix 32: Energy Density Structures in Extended Classical Mechanics (ECM). DOI: https://doi.org/10.13140/RG.2.2.22849.88168
