Potential Energy Depletion and the Kinetic Termination
in Extended Classical Mechanics (ECM)

Abstract

This report provides a focused physical and mathematical clarification of the mechanism termed kinetic termination within the Extended Classical Mechanics (ECM) framework, with particular emphasis on the role of potential energy depletion in traditionally massless dynamics.

The report systematically establishes how quantized energy emission—such as photon generation during electronic transitions—corresponds to a depletion of potential energy (−ΔPEᴇᴄᴍ) rather than a loss of mass or energy continuity. ECM identifies this depletion as a physically manifested quantity, giving rise to negative apparent mass, which governs the subsequent dynamical and gravitational behaviour of the emitted entity.

Through explicit mass–energy relations and Planck-scale considerations, the report demonstrates how photons, while retaining zero rest-mass, remain dynamically and gravitationally active via re-indexed kinetic–potential contributions. This process leads to kinetic termination, a regime in which motion is dominated by kinetic redistribution rather than matter-mass inertia, naturally producing antigravitational effects at larger scales.

The supplementary material reinforces the ECM mass-closure condition,

and shows how this identity preserves energy conservation while extending classical mechanics to cosmological and radiative regimes without invoking relativistic curvature or exotic energy creation.

Potential Energy Depletion and the Kinetic Termination in Extended Classical Mechanics (ECM)

In Extended Classical Mechanics (ECM), photon emission and traditionally massless dynamics are not treated as purely radiative or kinematic processes. Instead, they represent a structured redistribution of the total energy–mass budget, where potential energy depletion manifests dynamically as kinetic behaviour and gravitational participation.

1. Quantized Energy Transition

Photon emission originates from discrete electron transitions between quantized energy levels. In ECM, this process represents a redistribution of the system’s total energy budget rather than a simple radiation event.

Energy Conservation: The energy released during a transition is

ECM Potential Energy Identity: This released energy corresponds directly to a depletion of the system’s potential energy,

Kinetic Manifestation: ECM establishes that this potential energy depletion dynamically translates into kinetic effects,

This constitutes the first bridge between potential and kinetic behaviour, and it applies even to entities conventionally treated as massless.

2. Mass–Energy Conversion to Negative Apparent Mass

ECM identifies a physical mass manifestation associated with this energy redistribution. The depletion of potential energy is interpreted as a change in manifested matter mass.

Mass Link:

Planck-Scale Quantization: At the quantum level, this negative apparent mass can be expressed through mass–energy equivalence,

This formalism shows how traditionally “massless” photons acquire an ECM-effective negative mass, allowing their energy budget to participate in gravitational and dynamical processes.

3. Kinetic Termination and Antigravitation

The photon’s dynamical behaviour in ECM is governed by its negative apparent mass rather than by rest-matter mass.

Definition:

Mass Closure: This negative apparent mass is re-indexed into the gravitational sector, ensuring total mass consistency,

Termination Mechanism: Because Mᵃᵖᵖ < 0, the dynamics shift from matter-dominated motion to kinetic redistribution. This transition leads to kinetic termination and contributes to antigravitational behaviour at cosmological scales.

Summary of ECM Mathematical Links

Key ECM Insight

In ECM, the term “massless” refers strictly to zero rest-matter mass. The associated potential energy depletion (−ΔPEᴇᴄᴍ) remains dynamically active as negative apparent mass. This allows photons to participate in gravitation and cosmic-scale dynamics without violating conventional rest-mass constraints.