ECM Interpretation of the Components in Decomposed Energy

May 23, 2025

In Extended Classical Mechanics (ECM), the total energy of a particle in motion is decomposed into two structurally distinct components: potential energy arising from matter mass (Mᴍ​), and kinetic energy arising from the displacement of apparent mass (−Mᵃᵖᵖ​). This dual-mass framework allows ECM to represent all particle dynamics—including massless and massive states—with classical mass-energy logic.

ECM Total Energy Decomposition Expression:

Eₜₒₜₐₗ = PE + KE = (Mᴍ −Mᵃᵖᵖ) + ½(Mᴍ −Mᵃᵖᵖ)v²

Eₜₒₜₐₗ = Mᵉᶠᶠ + ½Mᵉᶠᶠv²

• Massive Particle: Mᴍ > 0

Motion involves partial transformation of Mᴍ to Mᵃᵖᵖ

• ​For Traditional Massless Particles (e.g., photon): Mᴍ<0 with Mᴍ≠0; v=c

Eₜₒₜₐₗ = ½Mᵉᶠᶠ,ᵧv², where: Mᵉᶠᶠ,ᵧ = (Mᴍ −Mᵃᵖᵖ) = −2Mᵃᵖᵖ

ECM Advantage:

This decomposition allows mechanical and electromagnetic kinetic energy to be represented with the same mass-based structure, unifying classical and quantum particle behaviour under a single extended framework.

Mass-Energy Equivalence Emerging Naturally Within the Extended Classical Mechanics (ECM) Framework

May 22, 2025

1. Mass-energy equivalence emerges naturally and classically from energy transformations via frequency and motion—not as a postulate of relativity, but as a derivation from kinetic energy and apparent mass;

2. Planck's equation E = hf, when interpreted through ECM, logically leads to E = mc² as a classical consequence—not as a relativistic innovation;

3. Einstein’s 1905 formulation, though profound in its relativistic implications, was not the origin of mass-energy equivalence but a reinterpretation from a rest-frame perspective;

4. ECM restores justice to both classical physics and Max Planck, reuniting the concepts of mass, energy, frequency, and motion under a coherent, physical, and classical framework.

This achievement doesn’t just reinterpret an equation—it rewrites a piece of scientific history.

Now ECM is in a strong position to formally challenge the conventional narrative, and more importantly, to show how ECM can extend the legacy of classical physics into domains long thought to be governed solely by relativistic frameworks.

What Extended Classical Mechanics is not:

ECM (Extended Classical Mechanics) is not a return to pre-relativistic classical mechanics. Rather, it extends classical principles by restoring the neglected role of apparent mass (−Mᵃᵖᵖ) as a dynamical and physically consequential component of energy interactions—particularly in dynamical transformations, redshifts, cosmic expansion, and photon behaviour. It is not a placeholder; it is an active participant in the structure of physical reality.

While quantum mechanics provides powerful mathematical formulations for particle-scale interactions, it does not scale naturally to cosmic phenomena without using abstract discrete concepts. On the other hand, ECM works coherently in both the micro and macro domains. It aligns with quantum behaviour at the Planck scale without accepting the metaphysical assumptions of relativistic mechanics, and at the same time provides powerful explanatory power for large-scale structures such as galactic clusters, which is currently being applied collaboratively by international research teams.

The ECM is not an ideological reversion to Newtonianism, nor a speculative leap into idealism - it is a consistent, empirical, and physically grounded framework that aims to reunify momentum, mass, and energy across all levels of nature.

Soumendra Nath Thakur

May 21, 2025

Exploration of Dark Energy and Photon Dynamics through Extended Classical Mechanics (ECM)

May 21, 2025

We are exploring dark energy through ECM, as if we were little kids playing with our dolls! :) …

Just imagine the power of ECM and its negative apparent mass implementation!

That little “doll” of −Mᵃᵖᵖ isn’t just a placeholder anymore—it’s a dynamic actor, shedding light (quite literally!) on redshift, expansion, and energy transformation. The elegance of ECM lies in how simple, classical ideas—mass, energy, force—are re-enchanted when we treat apparent mass as real, transferable, and transformative.

E = mc² naturally and originally from Planck’s own 1900 equation?

May 20, 2025

The discussion revolves around the mass-energy equivalence relation E = mc² which, although famously attributed to Einstein in 1905, emerges more naturally and originally from Planck’s own 1900 equation:

E =h f

Through a detailed reformulation in Extended Classical Mechanics (ECM)—a framework developed to correct overlooked mass-energy dynamics in classical physics—I demonstrate how Planck’s energy-frequency equation can be extended to derive mass-energy equivalence for dynamic particles like photons, entirely without invoking relativity.

In ECM, photon energy is treated as pure kinetic energy derived from an effective (negative apparent) mass:

E = h f = ½ (−2Mᵃᵖᵖ) c² = (−Mᵃᵖᵖ) c²

Here, v=c for photons is used in the classical form ½mv², distinguishing this derivation from relativistic interpretations. The appearance of c² is thus purely kinematics, not relativistic.

This leads directly to the celebrated form E = mc², but grounded classically, and points to Planck—not Einstein—as the rightful conceptual originator. ECM’s presentation further separates itself from relativistic dependence, as its foundational logic was formulated between Newton and Planck’s era. ECM also critically revisits and refines concepts like negative effective mass, showing observational alignment with cosmological phenomena such as redshift and photon momentum.

I have compiled and released several formatted documents for peer engagement:

• Reclaiming Planck’s Legacy: A Classical Derivation of E = mc² via ECM (Academia.edu)
• Re-evaluating the Origin of E = mc²: A Classical Reformulation from ECM (ResearchGate)
• Revisiting the True Origin of E = mc²: Is It Time to Acknowledge Planck Instead of Einstein? (LinkedIn)

A visual timeline and an equational summary are also available to clarify how Planck’s classical formulation leads to ECM’s mass-energy structure without the need for relativistic constructs like time dilation or spacetime curvature.

This post marks the beginning of a deeper public and academic conversation. I welcome your thoughts, critical insights, and historical perspectives on this long-overdue recognition of Max Planck’s role in one of physics’ most celebrated equations.

Warm regards,

Soumendra Nath Thakur
Researcher and Developer,
Extended Classical Mechanics (ECM)