|
|
Mass Relationships in Extended Classical Mechanics (ECM) versus Classical Inertial Mass
Soumendra
Nath Thakur
ORCiD:
0000-0003-1871-7803
Tagore’s Electronic Lab,
India
postmasternenator@gmail.com
; postmasternenator@telitnetwork.in
February 04, 2025
Abstract
Classical mechanics treats inertial mass as a single positive scalar quantity governing resistance to acceleration and gravitational interaction. Extended Classical Mechanics (ECM) reveals that this apparent simplicity conceals a composite mass structure arising from entropic energy manifestation processes. This work establishes a direct correspondence between classical inertial mass and ECM’s Ordinary mass decomposition, showing that inertia emerges from the balance between positive manifested matter mass and negative apparent mass generated through potential energy release. The formulation provides a unified interpretation of inertial, gravitational, dark matter, and antigravitational phenomena within a single mass–energy manifestation framework.
Keywords
Extended Classical Mechanics (ECM); Inertial Mass; Apparent Mass; Negative Mass; Energy Manifestation; Gravitational Mass; Entropic Dynamics; Dark Matter Interpretation,
1. Classical–ECM Mass Correspondence
In classical mechanics, inertial mass is defined as:
mᵢ
where:
mᵢ - classical inertial mass governing resistance to acceleration and gravitational response.
In Extended Classical Mechanics (ECM), the same observable inertial effect does not arise from a primitive mass quantity, but from the ordered effective gravitational mass resulting from manifestation balance:
mᵢ → Mᴏʀᴅ = Mᴍ - Mᴅᴍ = Mɢ
with:
• Mᴍ - total manifested matter mass content
• Mᴅᴍ - manifested positive effective mass component (dark-matter-equivalent)
• Mᴏʀᴅ - ordered effective gravitational (baryonic) mass governing local dynamics
• Mɢ - effective gravitational mass in ECM
and the manifestation constraint:
Mᵃᵖᵖ ≡ -ΔPEᴇᴄᴍ < 0
Physical meaning
Matter mass Mᴍ forms the total positive manifested reservoir.
Part of it redistributes into the effective enhancement component Mᴅᴍ, leaving the observable inertial/gravitational response as Mᴏʀᴅ.
Thus classical inertia emerges as a net ordered manifestation, not a fundamental substance.
Denotation of Terms
Mᴏʀᴅ - ordinary (baryonic) manifested matter mass of the system
Mᴅᴍ - manifested positive effective mass component corresponding to the gravitationally inferred dark matter contribution, consistent with the effective mass interpretation of dark matter in Chernin et al.
Mᵃᵖᵖ - apparent mass arising from ECM potential energy release
Mᵃᵖᵖ ≡ -ΔPEᴇᴄᴍ
Mᵃᵖᵖ < 0 - intrinsic negative mass character of manifested potential energy
Mɢ - effective gravitational mass governing attraction and repulsion dynamics
Matter Mass in ECM and Its Role
In Extended Classical Mechanics, matter mass represents the total manifested positive mass content arising from energy condensation processes and consists of ordinary (baryonic) matter together with effective dark-matter mass contributions:
Mᴍ = Mᴏʀᴅ + Mᴅᴍ.
Energy–mass exchange proceeds through the ECM manifestation cycle:
ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ KEᴇᴄᴍ
which governs mass redistribution and dynamical behaviour across scales.
Scale-Dependence Warning ⚠️
The manifested effective mass component Mᴅᴍ, while essential for explaining galactic rotation curves and large-scale gravitational enhancement, exhibits negligible influence within gravitationally bound local systems such as planetary, stellar, and compact astrophysical structures. Consequently, in practical ECM applications at small or moderate scales, the contribution of Mᴅᴍ within Mᴍ may be neglected or not explicitly accounted for, becoming significant primarily at galactic and intergalactic regimes.
2. Physical Meaning (ECM Perspective)
In ECM, mass is not an intrinsic substance but a manifestation of energy redistribution governed by entropic dynamics.
Classical inertial mass:
→ appears as a primitive quantity
ECM reveals:
→ it is the net result of manifested matter content modified by energy-driven mass restructuring.
Positive manifested component:
Mᴍ
representing the total accumulated matter mass arising from energy condensation processes.
Effective modifying component:
Mᴅᴍ
representing manifested effective mass that enhances gravitational response through mass redistribution.
Negative manifestation component:
Mᵃᵖᵖ = −ΔPEᴇᴄᴍ
representing released potential energy manifesting as antigravitational influence.
Thus inertia and gravity arise from:
the dynamic balance between manifested matter mass, effective gravitational enhancement, and energy-release-driven negative mass.
Dimensional Consistency and Physical Units
In any extended theoretical framework, preserving dimensional homogeneity of physical quantities is essential to ensure compatibility with empirical measurement standards. Extended Classical Mechanics (ECM) rigorously aligns its composite mass and energy relations with classical dimensional analysis, as detailed in Appendix B: Alignment with Physical Dimensions and Interpretations of Standard Categorization of Energy Types in Extended Classical Mechanics (ECM). [ResearchGate][1]
The total energy expression in ECM, analogous to classical formulations, maintains consistent physical units:
Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ,
where each term carries the standard dimension of energy [M L² T⁻²]. In ECM, potential energy evaluated for a resting mass and kinetic energy arising from negative apparent mass both resolve to this unit, ensuring dimensional fidelity with classical benchmarks. [ResearchGate][1]
The dimensional validation in Appendix B demonstrates:
• The potential energy term [Mᵉᶠᶠgᵉᶠᶠh] has consistent energy dimensions even when interpreted within a manifestation framework.
• The kinetic energy term derived from apparent mass contributions likewise yields [M]·[LT⁻²]·[L] = [M L² T⁻²], confirming that ECM’s kinetic interpretation (energy arising from displaced matter mass) respects classical dimensionality.
• Inverse mass expressions and dynamic displacement terms are regularized using dimension-consistent scaling parameters to preserve homogeneity throughout the extended relations. [ResearchGate][1]
Thus, ECM’s mass–energy relations are not only theoretically motivated but also dimensionally consistent with standard physical units, bolstering the framework’s empirical credibility.
3. Conceptual Punch line
Classical mechanics compresses a two-component ECM mass system into the single symbol mᵢ.
Or equivalently:
Inertia is not fundamental - it is an emergent balance between positive manifested matter and negative apparent mass.
4. Discussion
This ECM formulation naturally accounts for a broad range of gravitational and inertial phenomena through manifestation-driven mass redistribution:
• Gravitational attraction emerges from the dominance of manifested effective mass Mᴅᴍ, which enhances the net gravitational response of matter systems.
• Large-scale antigravitational behaviour arises from the influence of negative apparent mass Mᵃᵖᵖ = -ΔPEᴇᴄᴍ, producing repulsive dynamical effects without invoking additional fields or constants.
• The observational roles attributed to dark matter and dark energy are unified as complementary manifestations of the same energy redistribution process governing ECM mass dynamics.
• No exotic particles or new substances are required; all effects follow directly from classical energy transformation extended through manifestation physics.
Instead, all observable mass and energy phenomena proceed through the fundamental ECM manifestation cycle:
ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ KEᴇᴄᴍ,
which governs the continuous conversion between potential energy, manifested matter mass, and kinetic energy.
The intrinsic negative character of Mᵃᵖᵖ thus provides a physically grounded origin for cosmological repulsion and large-scale acceleration while remaining fully consistent with classical dimensional structure.
5. Conclusion
Extended Classical Mechanics replaces the classical notion of inertial mass as a primitive scalar with a physically grounded composite mass relationship:
mᵢ = Mᴍ - Mᴅᴍ
where the observed inertial response emerges from the net balance between total manifested matter mass and the manifested effective mass component associated with gravitational enhancement.
Through the underlying manifestation process,
ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ KEᴇᴄᴍ,
inertia and gravity arise as emergent consequences of entropic energy redistribution rather than intrinsic properties of matter.
This reinterpretation:
• unifies inertia, gravitation, dark matter, and antigravity within a single manifestation framework
• preserves classical dimensional structure while extending physical meaning
• provides a coherent mass–energy ontology grounded in dynamical processes
ECM thus reframes mass not as a fundamental substance, but as a dynamic manifestation of energy flow and structural redistribution.
References (ECM Core Works)
Thakur, S. N., Appendix B - Alignment with Physical Dimensions and Interpretations of Standard Categorization of Energy Types in Extended Classical Mechanics (ECM), Thakur S. N. May 30, 2025. DOI: 10.13140/RG.2.2.34193.75365 [ResearchGate][1]
Thakur, S. N., Frequency-Governed Mass, Apparent Mass Gradients, and the Emergence of Gravitation in Extended Classical Mechanics, ResearchGate Preprint, DOI: 10.13140/RG.2.2.12275.18721
Thakur, S. N., Phase Kernel Framework in Extended Classical Mechanics, ECM White Paper, 2025
Thakur, S. N., Energy Manifestation and Negative Apparent Mass in ECM, ECM Series Notes, 2024–2025
Chernin et al., Dark Energy and Zero-Gravity Radius in Cosmic Structures, Astronomy Reports, 2013