11 February 2025

Clarifying ECM's Stance on Negative Mass and Dark Matter Interactions:

February 11, 2025                                                 RG Discussion Link

Dear Mr. Ian Clague,

Thank you for your response and for referencing J. S. Farnes’ "A Unifying Theory of Dark Energy and Dark Matter." However, your comment appears to operate under assumptions that do not align with the framework and specific content of ECM as presented in this discussion.

  1. Irrelevance of External Assertions
    Your comment does not directly address or engage with the ECM framework outlined in this discussion but instead refers to an external model, suggesting an alternative premise without evaluating ECM’s treatment of the subject matter. While referencing other works can be useful in comparative discussions, an assertion such as “Negative mass can explain Dark Matter” without any engagement with the ECM-specific perspective does not constitute a meaningful counterpoint.

  2. Misalignment with ECM's Dark Matter Interpretation
    Your statement that "Negative mass can explain Dark Matter as the interaction of negative mass with positive mass" does not apply to ECM, which treats dark matter as possessing positive effective mass. ECM presents dark matter as a contributing component to the total positive matter mass of a system, alongside baryonic matter. The claim that dark matter must be explained via negative mass is inconsistent with ECM’s construct, which does not require negative mass to account for dark matter effects.

  3. ECM’s Treatment of Negative Mass vs. Your Assertion
    In ECM, negative apparent mass (−Mᵃᵖᵖ) arises as a motion-dependent or gravitationally induced property, rather than as an intrinsic mass entity. The framework does not support the notion of self-existing, freely interacting negative mass, as assumed in your reference. This distinction is critical because ECM does not describe dark matter in terms of negative mass, contrary to your assertion that "Negative mass can explain Dark Matter."

  4. ECM’s Explanation of Dark Energy vs. Your Interpretation
    Your assertion that "Dark Energy [is] the interaction of negative mass and negative mass" contradicts ECM’s position. ECM interprets dark energy as possessing negative effective mass that interacts with the total positive effective mass of ordinary and dark matter. In ECM, dark energy does not arise from negative mass interacting with itself but rather from its interaction with an overall positive matter mass distribution.

Conclusion

Your statements regarding negative mass as the explanation for dark matter and dark energy do not align with ECM’s theoretical structure. The presentation of ECM explicitly defines dark matter as a positive-mass entity and describes dark energy as having a negative effective mass interacting with positive effective mass—not through the interaction of two negative masses, as you claim.

While alternative models, such as Farnes’ theory, exist, an assertion that they necessarily override ECM’s conclusions would require a rigorous comparative analysis rather than an unqualified statement. As such, your assertions are not consistent with ECM’s framework, nor do they provide a valid refutation of its premises.

Best regards,

Soumendra Nath Thakur

My Answers on the Questions about ECM: Dark Energy and Gravitational Potential Energy in ECM.

 RG Discussion Link Here:

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