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

Author: Soumendra Nath Thakur
Affiliation: Tagore s Electronic Lab, India
Email: postmasterenator@gmail.com | postmasterenator@telitnetwork.in
Date: May 25, 2025
DOI: 10.13140/RG.2.2.31762.36800

Revision Note: This version incorporates contextual enhancements based on insights and definitions formalized in Appendix 29 and Appendix 30, including energetic identities, updated symbols, and ECM constants.

📥 Download PDF Version: Click here to download from ResearchGate

Abstract

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 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 are the mass-equivalent of dark energy (Mᴅᴇ) and kinetic matter mass (Mᴍ,ᴋᴇ).

This taxonomy supports dimensional consistency, physical clarity, and proper application of ECM equations across local, galactic, and cosmological scales.

Usage Guidelines in ECM Context

Never equate m and Mᴍ outside strictly local (solar or terrestrial) regimes.
When using reciprocal mass terms (e.g., 1/Mᴍ), always include both ordinary and dark matter components.
Contextualize mass terms according to domain:
- Local: m ≈ Mᴏʀᴅ, if Mᴅᴍ is negligible.
- Galactic/Cluster: Mᴍ ≫ Mᴏʀᴅ; use full composite form.
- Cosmological: Use Mᴍ, Mᴅᴇ, and Mᵉᶠᶠ with appropriate energy transformations.

Standard ECM Mass Definitions

Symbol	Term	Definition	Notes
m	Inertial Mass	Local resistance to acceleration; responds to applied forces.	Treated dynamically in Newtonian-like laws; distinct from gravitational or cosmological mass.
Mᴏʀᴅ	Ordinary (Baryonic) Mass	Visible matter: protons, neutrons, electrons.	Measured via luminous content and matter density.
Mᴅᴍ	Dark Matter Mass	Non-luminous mass inferred via gravitational effects.	Relevant to galaxy rotation, lensing, and structure formation.
Mᴍ = Mᴏʀᴅ + Mᴅᴍ	Total Matter Mass	Composite mass used in gravitational and cosmological calculations.	Should never be approximated by inertial mass m.
Mᵃᵖᵖ	Apparent Mass	Effective mass loss due to displacement or anti-binding.	Defined by Mᵃᵖᵖ < 0; conservation implies ΔMᴍ ≡ −Mᵃᵖᵖ.
Mᵉᶠᶠ	Effective Mass	Net retained binding mass after displacement.	Computed as Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mᴍ + \|Mᵃᵖᵖ\|.
Mᴍ,ᴋᴇ	Kinetic Matter Mass	Derived via kinetic energy: KE = (1/2)Mᴍ,ᴋᴇ v^2	Useful in interpreting redshift and frequency-induced dynamics.
Mᴅᴇ	Dark Energy Mass Equivalent	Mass equivalent of displacement energy.	Approx. by Mᴅᴇ ≈ k / (c^2 Mᴍ), where k = 5.558 x 10^-34 Js.
Mₜₒₜ	Total Gravitational Mass	Combined gravitational effect of matter and energy.	Contextually equivalent to Mᴍ under ECM.

Energetic Conservation Notes

Mass transitions in ECM uphold energy conservation through identities such as:

ΔMᴍ ≡ −Mᵃᵖᵖ
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

Total energy is maintained as:

Eₜₒₜ = Mᵉᶠᶠc^2 + KEᴇᴄᴍ

Relevant Appendices

Appendix B : Dimensional Consistency in ECM Energetics
Appendix 6 : Angular-Time and Phase Displacement
Appendix 29 : Cosmological Frequency Cycle and Energetic Reversion
Appendix 30 : Post-Latent Dynamics and Dual-State Evolution