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DOI: RG.2.2.28413.01764
Author: Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Affiliation: Tagore's Electronic Lab, India
Correspondence: postmasterenator@gmail.com ; postmasterenator@telitnetwork.in
Date: January 31, 2026
Extended Classical Mechanics (ECM) presents a structurally distinct framework for gravitation, kinetic energy manifestation, and cosmic-scale dynamics by explicitly separating mass-dominated gravitational balance from traditionally-massless kinetic evolution. In contrast to the conventional assumption that kinetic and radiative processes carry no gravitational mass contribution (m = 0), ECM introduces the concept of negative apparent mass (Mapp < 0) as a physically manifested outcome of potential energy depletion and frequency-governed dynamics.
Within this framework, matter mass is redefined as MM = Meff − (−Mapp), where the apparent deficit is not discarded but re-indexed into the gravitational sector. Consequently, the total gravitational mass satisfies the closure relation MG = MM + MDE = Meff, establishing direct conceptual and mathematical alignment with the observational formulation reported by Chernin et al. (2013).
ECM further decomposes matter mass as MM = MORD + MDM, providing a unified interpretation of ordinary matter, dark matter, and dark energy as manifestations of a single mass–energy redistribution process governed by frequency dynamics. This abstract formalism enables a consistent description of gravitation, antigravitation, and cosmic expansion without invoking relativistic curvature or exotic energy creation.
In conventional physical frameworks, entities such as photons are classified as massless by construction, with rest-matter mass strictly defined as zero. Under this assumption, the gravitational mass is likewise null, resulting in a hard conceptual boundary:
Extended Classical Mechanics (ECM) removes this hard stop by reinterpreting what vanishes in the traditional limit. Within ECM, it is not mass manifestation itself that disappears, but only the traditional rest-matter component. This distinction permits a consistent extension of mass participation without violating experimental constraints on rest mass.
In ECM, the traditionally massless condition is re-expressed as a negative change in manifested matter mass, identified with negative apparent mass arising from potential–energy transformation:
The matter mass participating in gravitational interactions is therefore written as:
This expression makes explicit that effective mass in ECM includes contributions beyond traditional rest mass, even for entities conventionally treated as massless.
Retaining the classical equivalence between inertial and gravitational mass but extending its content, ECM defines gravitational mass as:
With dark energy identified as negative apparent mass,
the gravitational mass becomes:
This identity establishes a central result of ECM: gravitational mass and effective mass are equivalent when the full kinetic–potential mass budget is accounted for.
This mass-closure structure is not merely theoretical; it is already implicit in successful observational treatments of gravitational systems.
Extended Classical Mechanics (ECM) explicitly acknowledges and aligns with the gravitational mass decomposition employed by Chernin et al. (2013) in their observational analysis of the Coma cluster of galaxies. In that work, the gravitational mass governing large-scale dynamics is expressed as the sum of a positive matter contribution and a negative dark-energy contribution,
where Mm represents the total matter mass and MDE is an effective negative mass associated with dark energy, responsible for antigravitational behavior beyond the zero-gravity radius RZG. This formulation is not introduced as a theoretical hypothesis in that study, but rather as an empirically motivated construct required to correctly reproduce the observed structure and dynamics of the Coma cluster.
ECM adopts this same gravitational mass decomposition as an observationally validated identity, while providing a distinct physical interpretation for the origin of the negative contribution. Within ECM, dark energy is identified with negative apparent mass arising from kinetic–potential energy transformation,
Under this identification, the Chernin et al. gravitational mass relation becomes a special case of the general ECM mass-closure condition,
Importantly, ECM does not reinterpret the observational results of Chernin et al. as evidence for a photon-defined or universally applicable zero-gravity radius. Instead, it restricts the validity of RZG to gravitationally interacting systems in which a balance between positive matter mass and negative effective mass is physically meaningful. The observational success of the Chernin formulation is thus preserved, while its scope is embedded within a broader kinetic–mass framework.
This explicit alignment demonstrates that ECM is not in conflict with established observational cosmology. Rather, it provides a deeper physical foundation for empirically successful mass decompositions by identifying the kinetic origin of the negative mass term and clarifying the scale-dependent conditions under which gravitational balance can exist.
Reference:
Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., &
Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies.
Astronomy and Astrophysics, 553, A101.
This formulation preserves the traditional constraint of zero rest-matter mass for photons and other radiative entities while allowing them to participate dynamically through negative apparent mass. As a result, ECM provides a closed, internally consistent framework capable of describing photon antigravitation, kinetic termination, and global antigravitational dominance without contradiction.
Accordingly, the term traditionally massless is not semantic decoration but a necessary conceptual bridge, signaling that what vanishes in conventional physics is rest mass alone—not mass manifestation itself.