Formal Development of Manifested Mass in Extended Classical Mechanics
MG = MM + |Mapp| ≡ Meff,
Mapp ≡ −ΔPEECM
Mapp ≡ −ΔPEECM
The resulting effective mass governs both gravitational interaction and inertial response.
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In Extended Classical Mechanics (ECM), mass is not treated as an intrinsic, immutable property of matter, but as an emergent manifestation arising from interactional imbalance within a finite spatial domain. This work formalizes the concept of manifested mass as a residual outcome of incomplete vacuum-phase energy manifestation, mediated through Negative Apparent Mass (NAM). The effective observable mass is shown to arise from a frequency disbalance between unmanifested and manifested states, governed by redshift effects and bounded by a maximum interaction radius rmax. Both cosmic-scale and local gravitational redshift, together with inverse-square dilution of manifestation, produce a residual ECM potential deficit −ΔPEECM, which appears observationally as gravitational and inertial mass. This framework provides a unified physical interpretation of mass, gravitation, and inertia without invoking spacetime curvature or relativistic mass constructs.
Extended Classical Mechanics; Manifested Mass; Negative Apparent Mass (NAM); ECM Potential Energy; Frequency Disbalance; Redshift; Finite Interaction Radius; rmax; Gravitation; Inverse-Square Dilution
Classical mechanics traditionally treats mass as a fundamental attribute of matter, while gravitation is described either as a force acting across space or as a geometric property of spacetime. Extended Classical Mechanics (ECM) departs from both views by interpreting mass, gravitation, and inertia as emergent consequences of finite manifestation of vacuum-phase existence.
In ECM, existence is conserved across manifested and unmanifested states. The vacuum phase is characterized by an imperceptible foundational frequency f0, which does not fully manifest across infinite space. Instead, manifestation occurs within bounded spatial regions governed by interactional coupling, frequency redshift, and geometric dilution.
The incomplete realization of vacuum-phase energy leaves a residual ECM potential deficit −ΔPEECM, quantified as Negative Apparent Mass (NAM). Effective observable mass emerges from the combination of intrinsic matter mass and this manifestation residue:
The resulting effective mass governs both gravitational interaction and inertial response.
Manifestation in ECM is spatially finite. No interaction extends indefinitely; instead, manifestation is bounded by a maximum interaction radius rmax. As vacuum-phase frequency transitions into perceptible or interactional states, redshift—cosmic at universal scales and gravitational at local scales—reduces the locally available manifestation energy.
This redshift limits how much of the original vacuum-phase frequency f0 can appear as observable mass-energy. The unmanifested portion remains encoded as −ΔPEECM, directly contributing to NAM and effective mass.
As manifestation propagates through space, the available manifestation per unit area decreases according to inverse-square geometric dilution:
This dilution applies to both the primordial manifestation of the perceptible universe (f0 → fp) and to subsequent local interactional processes (f0 → fmanifested). As the manifestation threshold is crossed, frequency disbalance appears:
The resulting residual potential deficit manifests observationally as NAM, producing effective gravitational and inertial mass.
Extended Classical Mechanics establishes mass, gravitation, and inertia as emergent outcomes of finite manifestation rather than intrinsic primitives. Effective mass arises from frequency disbalance within a bounded spatial domain, quantified by the residual ECM potential deficit −ΔPEECM.
Finite interaction radius, redshift, and inverse-square dilution jointly govern the extent of manifestation, naturally producing NAM and effective observable mass. Gravitation and inertia emerge as unified manifestations of the same conservation-driven mechanism, without invoking spacetime curvature or relativistic mass equivalence.
This formulation provides a classical yet non-Newtonian foundation for understanding mass and gravitation as consequences of conserved existence across manifested and unmanifested states.