Stefan Bernhard Rüster

Thanks for your interest in the discussion.

However, let alone any of the main discussion points here, your reference doesn't even reach the environment considered in the main discussion points, plus the main discussion points are purely based on observational findings, not hypothetical assumptions.

regards,

Dear Mr. Stefan Bernhard Rüster

Thank you for your engagement in the discussion. However, I must reiterate that your paper, "Energy Conservation in General Relativity and Flat Rotation Curves of Spiral Galaxies," does not address the core issues under discussion, nor does it align with the classical mechanics interpretations in the context of Extended Classical Mechanics.

The primary discussion points include:

• The equivalence of gravitational mass and matter mass in classical mechanics.

• The influence of dark matter and dark energy on gravitational dynamics.

• The concept of the zero-gravity sphere and its significance.

• The composition of matter mass within gravitationally bound systems.

• The role of gravitating mass in governing gravitational dynamics.

Your work focuses on energy conservation within the framework of General Relativity and its implications for understanding dark matter and dark energy. However, this approach does not reach the environment considered in the current discussion, which is grounded in observational findings, not hypothetical assumptions.

The Extended Classical Mechanics framework, which serves as the foundation of this discussion, adopts Newtonian Classical Mechanics, particularly in the research conducted by Chernin et al. (2013) on "Dark Energy and the Structure of the Coma Cluster of Galaxies." This framework fundamentally contrasts with General Relativity, especially regarding time and space interpretations. In classical mechanics, time is viewed as "abstract," not subject to dilation, unlike the "natural" time in relativity, which is considered dilatable. My research papers, "Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation II" (Thakur et al., 2023) and "Photon Paths Bend Due to Momentum Exchange, Not Intrinsic Spacetime Curvature" (Thakur, 2023), provide evidence that challenges time dilation and spacetime curvature, undermining the validity of General Relativity in these contexts.

Additionally, your reference to a static universe model and Einstein's introduction of the cosmological constant does not address the expansion dynamics driven by dark energy. Our discussion interprets dark energy as arising from gravitational and kinetic interactions within the universe, not as a repulsive force introduced to maintain a static model.

Therefore, your work, based on General Relativity, does not provide a suitable counter to the findings derived from Extended Classical Mechanics. The Newtonian approach used in Chernin et al. and the observational basis of the discussion underscore the limitations of relativistic mechanics in this context.

Citations:

1. Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781

2. Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phase shift in frequencies invalidate time dilation II. TechRxiv. https://doi.org/10.36227/techrxiv.22492066.v2

3. Thakur, S. N. (2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions. https://doi.org/10.32388/81iiae

4. Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.org (MDPI). https://doi.org/10.20944/preprints202409.1190.v2

Best regards,

Soumendra Nath Thakur

Dear Mr. Stefan Bernhard Rüster

Moreover, your paper, based on General Relativity, does not align with the current discussion grounded in Extended Classical Mechanics and the research by Chernin et al. titled "Dark Energy and the Structure of the Coma Cluster of Galaxies," which utilizes Newtonian classical mechanics rather than relativistic mechanics.

In classical mechanics, time is considered "abstract" and not subject to dilation, contrasting with relativity’s concept of "natural" time, which is treated as dilatable. This discussion does not acknowledge "natural" time and, therefore, does not consider time dilation. My research papers, "Relativistic Effects on Phase Shift in Frequencies Invalidate Time Dilation II" and "Photon Paths Bend Due to Momentum Exchange, Not Intrinsic Spacetime Curvature," provide empirical evidence that challenges and invalidates the concepts of time dilation and spacetime curvature, rendering General Relativity unsuitable for discussing the "Dynamics of Gravitationally Bound Systems."

Furthermore, the discussion adopts a model of an expanding universe driven by dark energy, as opposed to the static universe model implied in Einstein’s relativity papers. Both of Einstein's relativity papers, published before 1917, assumed a static universe, which was later invalidated by Lemaître's proposal of an expanding universe and Hubble's observations that galaxies are receding from us.

To preserve the static universe model, Einstein introduced the cosmological constant in his field equations, as detailed in his 1917 paper, "The Cosmological Considerations in the General Theory of Relativity." This constant was initially conceived to counteract gravitational collapse in a non-expanding universe. However, once it became evident that the universe was not static, Einstein retracted the cosmological constant, deeming it unnecessary for an expanding universe.

Even if one considers the cosmological constant as a repulsive force, it was never meant to explain an expanding universe but to maintain a static one. In contrast, the accelerating expansion observed today is attributed to gravitational and kinetic interactions within the universe, collectively termed Dark Energy, and not to any specific force introduced in Einstein's static universe model.

Therefore, given the distinct frameworks and observational bases of Extended Classical Mechanics, your paper, rooted in the relativistic paradigm, does not provide relevant insights or benefits to the current discussion topics.

Best regards,

Soumendra Nath Thakur

Dear Mr. Stefan Bernhard Rüster,

Thank you for engaging in this discussion. It is unfortunate that you have chosen to disengage based on your assessment of my qualifications not as a physicist, rather than addressing the key points of the discussion. Regardless, I would like to clarify a few points and leave the dialogue on a constructive note.

The focus of this discussion is rooted in Extended Classical Mechanics (ECM), which follows a Newtonian framework, particularly as applied in studies like Chernin et al. (2013). This framework contrasts sharply with General Relativity (GR), as it does not assume relativistic effects such as time dilation or spacetime curvature, concepts central to GR but inapplicable in the current context. ECM operates within a classical mechanics interpretation of gravitational dynamics, especially in relation to dark matter and dark energy. These aspects are not adequately addressed by General Relativity’s interpretation, as your own work reflects.

The key elements of the discussion, including the equivalence of gravitational mass and matter mass, the influence of dark matter and dark energy, and the significance of the zero-gravity sphere, remain untouched by the energy conservation model you discuss. While your work provides insight into energy conservation within GR, it doesn’t engage with the Newtonian perspective that informs the gravitational dynamics we are analysing here.

Your comment regarding my standing not as a physicist does not contribute to the scientific merits of the discussion. Science progresses through rigorous debate of ideas, grounded in evidence and clear reasoning, not through personal qualifications. My status as a researcher is based on substantial experience in electronics engineering, physics, and theoretical research, and this discussion is driven by research and observations, as well as scientific methodologies rather than titles.

Ultimately, I was looking forward to a fruitful exchange of ideas on the differences between Newtonian Classical Mechanics and General Relativity in the context of cosmological phenomena. However, I respect your decision to end the dialogue and appreciate the time you took to respond.

Best regards,

Soumendra Nath Thakur