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Classical mechanics accounts for force and motion using invariant matter mass. However, gravitational phenomena reveal that interaction energy alters inertia and gravitational coupling without creating new matter.
Extended Classical Mechanics (ECM) resolves this by introducing Negative Apparent Mass (NAM), a dynamical mass-equivalent associated with manifested interaction energy.
ECM is built on an explicit energy redistribution principle:
No independent gravitational field-energy entity is introduced. All gravitationally relevant energy is internalized within mass terms.
When potential energy is released during gravitational interaction, the system exhibits increased dynamical response without an increase in matter content.
ECM identifies this manifested interaction energy as a negative apparent mass:
NAM is not exotic matter. It is an energetic mass-equivalent representing manifested interaction.
The net mass governing acceleration and gravitational coupling in ECM is the effective mass:
This relation is derived directly from mechanical energy redistribution, not from cosmological observation.
In cosmology, observations are often summarized as:
where Mᴅᴇ < 0 represents a repulsive contribution inferred from large-scale dynamics.
This relation is empirical and scale-specific. It does not derive the underlying mechanism.
The ECM relation:
is a mechanical derivation valid at all scales.
By contrast:
is an observational summary. Its agreement with ECM is supportive evidence, not a defining assumption.
In Extended Classical Mechanics (ECM), gravitational interaction energy is accounted for through explicit energetic redistribution:
Energy conservation is therefore maintained without introducing a separate gravitational field-energy density.
Within ECM, the classical quantities are not identified through the Newtonian equivalence assumption mᵢ = m𝑔. Instead, ECM distinguishes their physical roles:
Accordingly, ECM does not require endorsement of the Newtonian gravitational field-energy density expression for internal consistency.
The assumption that consistency with mᵢ = m𝑔 mandates adoption of that field-energy expression constitutes the hybrid inconsistency analyzed in the referenced paper.
Extended Classical Mechanics establishes effective mass through explicit energy redistribution, introducing Negative Apparent Mass as a universal dynamical entity.
Dark Energy relations emerge as empirical confirmations of ECM behavior at cosmic scales, not as foundational inputs.
Thus, ECM provides a unified mechanical framework from laboratory dynamics to cosmology, without invoking hybrid field-energy constructs.