Simplified Extended Classical Mechanics (ECM) expression for the manifestation of Kinetic Energy (KE):

(m−Δm) + Δm ⇒ (m − Δm) + KE

where Δm represents the displaced mass-equivalent of kinetic energy.

Appendix A — Standard Mass Definitions in Extended Classical Mechanics (ECM)

 

Soumendra Nath Thakur

Tagore’s Electronic Lab, India; postmasterenator@gmail.com or postmasterenator@telitnetwork.in

Date May 25, 2025

This appendix establishes a standardized terminology and hierarchy for mass concepts within the Extended Classical Mechanics (ECM) framework. Unlike conventional mechanics, ECM distinguishes between inertial, gravitational, and energetically displaced mass components by contextualizing mass not as a singular scalar but as a dynamic entity shaped by force interactions, field structure, and cosmological embedding. The definitions clarify critical distinctions among inertial mass (m), ordinary baryonic mass (Mᴏʀᴅ), dark matter mass (Mᴅᴍ), total matter mass (Mᴍ = Mᴏʀᴅ + Mᴅᴍ), and derived constructs such as effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ < 0). Also included is the mass-equivalent representation of dark energy (Mᴅᴇ) as an inverse function of total matter.

This taxonomy is essential for ensuring dimensional consistency, physical clarity, and correct application of ECM equations across local, galactic, and cosmological scales. It aims to prevent interpretive and mathematical errors arising from the conflation or misidentification of mass types in both theoretical derivations and empirical applications.

This Standard Mass Definitions Appendix applies universally to all ECM-related works—whether Articles, Reviews, Chapters, Experimental Results, or Data Publications—and is considered a foundational reference across the domain of Extended Classical Mechanics (ECM).

Keywords: Extended Classical Mechanics, ECM, Effective Mass, Apparent Mass, Negative Apparent Mass, Matter Mass, Mᵉᶠᶠ, Mᵃᵖᵖ, -Mᵃᵖᵖ, Mᴍ = Mᴏʀᴅ + Mᴅᴍ,

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Appendix A: Standard Mass Definitions in Extended Classical Mechanics (ECM)

Symbol	Term	Definition	Notes
$m$	Inertial Mass	Local resistance to acceleration; responds to applied forces.	Treated dynamically in Newtonian-like laws; should not be conflated with gravitational or cosmological mass terms.
$M_{\text{ord}}$	Ordinary (Baryonic) Mass	Mass from visible matter: protons, neutrons, electrons.	Measured via luminous content and standard matter density.
$M_{\text{dm}}$	Dark Matter Mass	Non-luminous mass detectable via gravitational effects.	Contributes to galaxy rotation curves, lensing, and cluster dynamics.
$M_{\text{m}}$	Total Matter Mass	$M_{\text{m}} = M_{\text{ord}} + M_{\text{dm}}$	Used in gravitational and cosmological applications; never approximate as $M_{\text{ord}}$ in such contexts.
$M_{\text{app}}$	Apparent Mass	Effective mass loss due to energetic displacement or anti-binding effects (e.g. dark energy influence).	Defined from energy reconfiguration: $M_{\text{app}} = \frac{k}{M_{\text{m}} c^2}$
$M_{\text{eff}}$	Effective Mass	Dynamically retained binding mass: $M_{\text{eff}} = M_{\text{m}} - M_{\text{app}}$	Represents net binding contribution after subtracting displaced/embedded energy.
$M_{\text{DE}}$	Dark Energy Mass Equivalent	Mass equivalent of cosmological displacement energy; derived from inverse total matter mass.	Often approximated via $\frac{1}{M_{\text{m}}} \Rightarrow M_{\text{DE}}$, scaled by constants.
$M_{\text{tot}}$	Total Gravitational Mass	Net gravitational content including matter and energy equivalence.	Sometimes used interchangeably with $M_{\text{m}} + M_{\text{DE}}$ in ECM, depending on context.

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Usage Guidelines in ECM Context

• Never equate $m$ and $M_{\text{m}}$ outside strictly local (solar or terrestrial) regimes.

• When dealing with reciprocal mass terms (e.g., $\frac{1}{M_{\text{m}}}$), always include both ordinary and dark matter components.

• Always contextualize mass terms according to domain:

  • Local: $m \approx M_{\text{ord}}$, if $M_{\text{dm}}$ is negligible.

  • Galactic/Cluster: $M_{\text{m}} \gg M_{\text{ord}}$; use full composite form.

  • Cosmological: Use $M_{\text{m}}$, $M_{\text{DE}}$, and $M_{\text{eff}}$ carefully with proper energetic conversion terms.

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