Soumendra Nath Thakur
February 05, 2025
Mᴏʀᴅ (Ordinary/Baryonic Matter): This is the mass of protons, neutrons, and electrons. It's the "normal" matter we're familiar with.
Mᴅᴍ (Dark Matter): This is non-luminous matter that interacts gravitationally but not through electromagnetic forces. It's included in the total matter mass.
Mᴍ (Total Matter Mass): Mᴍ = Mᴏʀᴅ + Mᴅᴍ. This is the total mass of ordinary and dark matter within a system.
Mᴅᴇ (Dark Energy Effective Mass): This represents the effective mass contribution from dark energy. It's important to note that this is not dark energy itself, but its effect on mass.
Mᵃᵖᵖ (Apparent Mass): This is a dynamic, non-physical quantity that reflects observed mass variations due to external forces. It can be negative.
Mᵉᶠᶠ (Effective Mass): Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ = Mᴍ + Mᴅᴇ. This is the mass that governs gravitational interactions in ECM.
Mɢ (Gravitating Mass): Mɢ = Mᵉᶠᶠ. This is the mass that appears in the gravitational force equation in ECM.
Key Points and Clarifications:
Mᴅᴇ vs. Dark Energy: Mᴅᴇ is the effective mass contribution from dark energy, not dark energy itself. This distinction is crucial.
Apparent Mass as a Dynamic Term: Mᵃᵖᵖ is a dynamic and non-physical term. It reflects the observed mass variations, not a change in the actual physical mass.
Kinetic Energy in ECM: The equation (1/2) Mᴏʀᴅ⋅v² + (1/2)Mᴅᴍ⋅v² = −Mᵃᵖᵖ shows how the kinetic energy of ordinary and dark matter is related to the apparent mass.
I do not see any question but I acknowledge the importance of the concept of mass. The best I have read about it is the book:
https://books.google.com/books/about/Concepts_of_Mass_in_Classical_and_Modern.html?id=lYvz0_8aGsMC
February 19, 2025
Dear Mr. Jose Gaite,
In reponse to your question:
Mass Concepts in Classical, Relativistic, and Extended Classical Mechanics (ECM):
The book you referred, Concepts of Mass in Classical and Modern Physics by Max Jammer presents traditional mass concepts, primarily defining mass as either inertial mass or rest mass. However, these descriptions do not account for dynamic effective mass or apparent mass.
Extended Classical Mechanics (ECM) expands upon these conventional definitions by introducing negative apparent mass and negative effective mass, extending the concept of mass beyond ordinary matter to include the effects of dark matter. This distinction is crucial in understanding mass interactions at different cosmic scales.
Mass Equivalence in Different Frameworks
In classical mechanics, inertial mass is equivalent to gravitational mass:
m = m𝑔
In relativistic mechanics, rest mass (invariant mass) is also equated to gravitational mass:
m = m𝑔
In Extended Classical Mechanics (ECM), gravitating mass (Mɢ) is equivalent to effective mass (Mᵉᶠᶠ), which includes both matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ):
Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)
where matter mass (Mᴍ) is the combined mass of ordinary matter (Mᴏʀᴅ) and dark matter mass (Mᴅᴍ):
Mᴍ = Mᴏʀᴅ + Mᴅᴍ
Effective Mass at Celestial and Galactic Scales
At celestial or planetary scales within a galaxy, effective mass (Mᵉᶠᶠ) can be either positive or negative, depending on the balance between matter mass and negative apparent mass:
If matter mass dominates (Mᴍ > Mᵃᵖᵖ), then effective mass is positive:
Mᵉᶠᶠ > 0
If negative apparent mass dominates (Mᵃᵖᵖ > Mᴍ ), then effective mass becomes negative:
Mᵉᶠᶠ < 0
The ECM expression for gravitating mass can also be rewritten as:
Mɢ = Mᴍ + (−Mᵃᵖᵖ)
This formulation aligns conceptually with the expression discussed by A. D. Chernin et al. in Dark Energy and the Structure of the Coma Cluster of Galaxies:
Mɢ = Mᴍ + Mᴅᴇ,
where Mᴅᴇ represents the effective mass of dark energy, which is always negative:
Mᴅᴇ < 0
While ECM extends this concept by incorporating negative apparent mass alongside dark energy effects, both frameworks recognize the role of negative mass contributions in gravitational dynamics.
This framework provides a more comprehensive approach to understanding mass interactions in the universe, bridging the gap between classical mechanics and modern astrophysical observations.
Author:
Soumendra Nath Thakur
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