February 11, 2025
Dear Mohammad Shafiq Khan,
Thank you for your engagement in the discussion on Extended Classical Mechanics (ECM). I appreciate your thought-provoking questions, and I fully agree that questioning everything is the essence of scientific progress. However, as I am actively engaged in multiple aspects of my research, some responses may take time, as I prefer to provide well-founded answers rather than instant ones.
1. Gravitational Potential Energy in ECM
Within ECM, the gravitational potential energy for a test matter mass mₘ is expressed as:
Uᴇᴄᴍ = − GMᵉᶠᶠmₘ/r
where:
• Uᴇᴄᴍ: is the gravitational potential energy of the test mass mₘ
• G: is the gravitational constant
• Mᵉᶠᶠ: is the effective mass of the source
• mₘ: is a test matter mass of the source
• r: is the radial distance
The effective mass Mᵉᶠᶠ accounts for both baryonic matter and the apparent mass contribution, which extends the classical framework to accommodate additional effects such as dark matter and dark energy.
2. Dark Energy in ECM
Dark energy is treated in ECM through the concept of apparent mass (Mᵃᵖᵖ), leading to an effective mass representation:
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ
where:
• Mɢ: Gravitating Mass
• Mᴍ: Matter Mass
• −Mᵃᵖᵖ: represents the influence of dark energy (with a negative contribution).
This formulation aligns with the work of A.D. Chernin et al., where the dark energy effective mass (Mᴅᴇ) is included as a component influencing the dynamics of large-scale structures. When the apparent mass dominates, the effective mass can become negative, corresponding to the repulsive effect of dark energy.
3. The Nature of Dark Energy Before the Big Bang
Before the Big Bang, the concept of gravitational potential and dark energy as we understand them today may not have existed in the same manner. In ECM, potential energy requires the presence of mass-energy interactions, space, and time—all of which were non-existent before the Big Bang event. Thus, dark energy, in its present form, would not have existed as an independent entity.
For further insights into the conceptual foundations of existence, space, time, and energy, I recommend reviewing the following resources:
A Clear Understanding of Existence, Event, Time, and Space in Relation to Matter and Energy https://www.researchgate.net/post/A_Clear_Understanding_of_Existence_Event_Time_and_Space_in_Relation_to_Matter_and_Energy
The Nexus of Existence and Events https://www.researchgate.net/post/The_Nexus_of_Existence_and_Events
Big Bang Nucleosynthesis (Wikipedia) https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis
I appreciate your thought-provoking contributions and look forward to further discussions that challenge and refine our understanding of fundamental physics.
Best regards,
Soumendra Nath Thakur
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