Soumendra Nath Thakur | ORCID: 0000-0003-1871-7803
Abstract
Extended Classical Mechanics (ECM) establishes a mass–energy framework fundamentally distinct from relativistic rest-energy formulations. ECM derives mass–energy behaviour entirely from classical kinetic-energy principles, where dynamical transformations occur through mass displacement rather than through relativistic mass–energy equivalence. Specifically, kinetic energy emerges from the transition of potential energy into apparent mass (−Mᵃᵖᵖ), not from intrinsic rest-mass energy. This yields a unified, scale-consistent description of baryonic matter, dark-matter effective mass, and matter–dark-energy interactions using purely classical mechanics, extending the framework naturally from galactic to cosmological scales.
1. ECM’s Foundational Distinction: Classical Mass–Energy vs. Relativistic Rest Energy
A defining feature of ECM is its rejection of the relativistic assumption that mass and energy are universally interchangeable via E = mc². Instead, ECM treats mass and energy as classically bound quantities whose transformations arise solely from interaction-driven displacement. In relativity, rest mass is intrinsic and carries its own invariant rest-energy. ECM, by contrast, does not assign inherent energy to rest mass. Mass does not convert into energy except through classical work, interaction, or gravitational displacement.
ECM therefore bases its entire mass–energy structure on the classical idea that:
Energy manifests through changes in mass-distribution within the potential field.
Kinetic energy (KEᴇᴄᴍ) is not a relativistic mass increase; it is a re-expression of displaced potential energy represented through effective mass changes. This makes ECM a distinct classical system, not a reinterpretation or modification of relativistic mechanics.
2. Kinetic Energy as Displaced Potential Energy — Apparent Mass (−Mᵃᵖᵖ)
In ECM, classical kinetic energy is written as:
KEᴇᴄᴍ = −ΔPEᴇᴄᴍ = ΔMᴍc²
Here:
- ΔMᴍ represents displaced mass arising from potential-energy conversion,
- apparent mass (−Mᵃᵖᵖ) captures the negative mass component of this displacement,
- Mᵉᶠᶠ defines the dynamical effective mass response of the system.
Thus, kinetic energy is entirely classical in ECM and does not rely on relativistic rest-energy principles. Energy is stored, released, and transformed through mass-distribution changes, preserving classical mechanical causality.
3. Observable/Measurable Matter Mass (Mᴍ) — Behaviour Across Scales
ECM uses the term observable/measurable mass to denote physically detectable mass independent of the system’s internal mass-exchange structure. Mᴍ behaves differently depending on scale.
3.1 Local (Galactic) Scale
Within galaxies and gravitationally bound systems, Mᴍ behaves like ordinary baryonic mass. Dark-matter effects appear as classical stabilizing fields that merge smoothly with baryonic dynamics, requiring no exotic particles.
3.2 Intergalactic and Cosmological Scales
At large scales, ECM treats matter mass Mᴍ as a combination of:
- baryonic mass, and
- dark-matter effective mass.
These interact with dark-energy effective mass, which produces classical repulsive acceleration. This unified interaction explains cosmic expansion without invoking spacetime curvature or relativistic dark-energy formulations.
4. Classical Origin of ECM’s Mass–Energy Relations
ECM’s mass–energy structure emerges directly from classical mechanics:
- Kinetic energy arises from mechanical displacement.
- Potential energy stores classical mass-equivalent structure.
- Energy transfer corresponds to a change in mass distribution (ΔMᴍ).
- No intrinsic rest-energy is assumed.
- No relativistic curvature or spacetime geometry is invoked.
Thus, the expression ΔMᴍc² is purely classical, capturing mass displacement, not rest-energy conversion.
5. The Resulting Conceptual Picture
ECM provides a unified picture in which:
- mass–energy is classical and interaction-based;
- kinetic energy originates from potential-energy displacement;
- apparent mass (−Mᵃᵖᵖ) and effective mass (Mᵉᶠᶠ) define dynamical behaviour;
- baryonic and dark-matter contributions combine naturally as Mᴍ;
- matter–dark-energy interactions produce classical cosmic acceleration;
- no relativistic rest-mass identity is required.
ECM therefore stands as a distinct classical alternative to relativistic cosmology, offering a unified mass–energy interpretation across local, galactic, and cosmological scales.
