Critical Analysis of Relativistic Transformations and the Abstract Nature of Time:

Abdul Malek

Respected Sir,

I sincerely appreciate your comment and the depth of your perspective on the cosmological constant and Einstein’s theories of relativity. Your insights into the abstract nature of Lorentz Transformations, the gamma factor, and spacetime as purely mathematical constructs resonate with my understanding as well.

Indeed, while Lorentz Transformations were initially introduced as mathematical tools, Einstein applied them as relativistic transformations, incorporating a physical aspect of time that, in principle, should remain abstract and independent of physical existence. The notion that time itself is influenced by relativistic effects is an improper interpretation when considering cosmic time, which ideally progresses unaffected by material conditions.

Furthermore, the major inconsistency within relativistic Lorentz Transformations lies in their failure to account for acceleration between separating frames, as well as their disregard for material stiffness. The gamma factor solely considers velocity as the influencing parameter, neglecting the impact of acceleration and structural rigidity. This omission inevitably leads to inconsistencies in the theoretical framework and its physical predictions.

Your critical approach to these foundational issues is invaluable, and I acknowledge the necessity of re-evaluating these constructs to align scientific principles with objective reality. I appreciate your thought-provoking input and look forward to further meaningful discussions.

Yours sincerely,

Soumendra Nath Thakur

Reasserting the Objective: Historical Accuracy and Conceptual Integrity in the Discussion of Λ.

February 26, 2025

The Discussion Link @RG

Dear Mr. Stefan Bernhard Rüster,

Your response continues to misrepresent the core discussion by shifting the focus away from the historical and conceptual evaluation of the cosmological constant (Λ) and instead imposing a redefined interpretation beyond what Einstein himself introduced and later abandoned.

First, regarding your assertion that "Λ represents a scalar curvature of spacetime when considering matter-free spacetime," this definition applies strictly within the framework of General Relativity (GR).

However, the historical context of Λ, as introduced by Einstein in 1917, was to artificially maintain a static universe, not as an inherent scalar curvature term to explain cosmic expansion. As outlined in my discussion post, Einstein abandoned Λ following Hubble’s discovery of an expanding universe, considering it his "greatest blunder." Therefore, your insistence on redefining Λ in a broader scope beyond its original purpose and subsequent rejection does not engage with the historical and scientific reassessment presented in this discussion.

Second, you reference Chernin’s work and claim that his modified Newtonian gravitational theory aligns with your position. However, as I previously stated, Chernin et al. explicitly utilized a force-based Newtonian framework to analyse dark energy effects in galaxy clusters without relying on curved spacetime. Your selective emphasis on Eqs. (3) and (4) from https://arxiv.org/pdf/1303.3800 does not negate the fact that Newtonian interpretations of cosmic expansion remain valid and are actively explored independently of GR’s curvature-based approach.

Third, your demand that ECM must demonstrate the perihelion shift of Mercury and light deflection at the Sun is an attempt to dismiss its broader relevance by imposing GR’s validation criteria. This rhetorical approach assumes that ECM should be evaluated solely on terms dictated by GR rather than recognizing its independent explanatory power regarding photon dynamics, dark energy, and effective mass principles. While ECM does provide alternative perspectives on gravitational phenomena, its applicability should not be dismissed based on selectively imposed tests that prioritize GR’s assumptions.

The core intent of this discussion post remains the historical and conceptual reassessment of Λ, its original purpose, and the fair attribution of credit regarding cosmic expansion. Instead of addressing these key points, you have shifted the discussion towards promoting a specific viewpoint that extends beyond Einstein’s own interpretation and subsequent rejection of Λ.

Therefore, I encourage you to either engage directly with the discussion’s outlined premises—namely, the historical use and later abandonment of Λ, its force-based implications versus a curvature-based interpretation, and the fair recognition of contributions by Friedmann, Lemaître, and Hubble—or acknowledge that this discussion does not serve as a platform to uncritically impose an interpretation of Λ that Einstein himself discarded.

Best regards, 

Soumendra Nath Thakur