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DOI: 10.13140/RG.2.2.20565.49122
Negative gravitational potential energy is conventionally treated as a reference-dependent quantity without independent physical agency. In this work, Extended Classical Mechanics (ECM) reinterprets negative potential energy as a real manifestation deficit associated with the formation of structured existence. This deficit is shown to possess mechanical relevance: its gradients generate gravitational attraction, its conservation yields inverse-square scaling, its dilution produces dark-energy–like behavior, and its monotonic decay governs cosmic time distortion and the arrow of time. By replacing geometric curvature and ad hoc cosmological constants with a single physically meaningful quantity—manifestation imbalance—ECM provides a unified classical framework for gravity, expansion, dark energy, temporal asymmetry, and cyclic cosmology.
Keywords: Extended Classical Mechanics, Negative Potential Energy, Manifestation Imbalance, Dark Energy, Arrow of Time, Conformal Cyclic Cosmology,
In classical mechanics, gravitational potential energy is expressed as
This formulation reflects the attractive nature of gravity: as masses approach one another, the potential energy decreases relative to infinite separation.
Standard explanations often attribute the negative sign to reference choice. While mathematically valid, this view fails to explain why attraction universally corresponds to an energy deficit, or why bound configurations possess fundamentally different energetic properties from unbound ones.
A gravitationally bound system:
The negative sign therefore encodes a real energetic deficit. Kinetic energy gained during infall is balanced by a reduction in configuration energy, preserving conservation.
Extended Classical Mechanics (ECM) formalizes this deficit via manifestation imbalance:
Here, \( \Delta PE_{\text{ECM}} \) represents the change in manifestation potential associated with structure formation.
The negative sign indicates that manifested structure corresponds to an energetic shortfall relative to an unmanifested reference state.
The gravitational (NAM) field is defined as
Because the source quantity is intrinsically negative, its gradient produces inward-directed attraction without additional postulates.
Flux conservation requires
Under isotropy, this yields the inverse-square law:
Let \( N(t) \equiv |\mathbf{g}_{\text{NAM}}| \) denote the monopolar NAM amplitude. A general decay law is
The residual manifestation deficit accumulates as a smooth background identified with ECM dark energy:
Time distortion is defined as
with rate
As manifestation imbalance decays, time distortion weakens and the arrow of time fades.
In the asymptotic future:
The time-reset operator
provides a natural ECM realization of conformal cyclic cosmology (CCC).
This is not a convention. Infinite separation corresponds to absence of manifestation coupling and absence of deficit.
Negative gravitational potential energy represents a real manifestation deficit. Its gradients generate attraction, its dilution produces dark energy behavior, and its monotonic decay defines the arrow of time.
Within Extended Classical Mechanics, negative gravitational potential energy is no longer a coordinate artifact or bookkeeping convention. It represents a real manifestation deficit in the energetic configuration of existence. This deficit acts as the source of gravitational attraction through its spatial gradients, enforces inverse-square behavior via flux conservation, and evolves dynamically as structures form and dissolve.
As manifestation imbalance is progressively diluted, its residual component emerges as ECM dark energy, while its decay rate governs cosmic time distortion and defines the arrow of time. When fully exhausted, both gravitational influence and temporal asymmetry vanish, naturally enabling conformal cyclic renewal without invoking geometric singularities or fine-tuned constants.
By replacing spacetime curvature, relativistic mass postulates, and a fundamental cosmological constant with a single physically interpretable quantity, ECM offers a parsimonious and conceptually unified description of gravity, cosmic expansion, dark energy, time, and cosmological evolution. Negative gravitational potential energy thus emerges not as a secondary effect, but as the primary physical driver of cosmic dynamics.
| Aspect | ECM | General Relativity | ΛCDM |
|---|---|---|---|
| Nature of Gravity | Gradient of manifestation deficit | Spacetime curvature | Derived from GR |
| Negative PE | Real physical deficit | Coordinate-dependent | Inherited Newtonian |
| Dark Energy | Residual diluted deficit | Not intrinsic | Λ constant |
| Time | Emergent, distorted by NAM | Fundamental coordinate | Inherited |
In ECM, negative gravitational potential energy is not a modeling convenience, but the primary physical driver of cosmic evolution.