Reevaluating the Andromeda Paradox and Terrell-Penrose Effect in Light of Post-Relativistic Cosmology and Emergent Time:

Soumendra Nath Thakur 

April 07, 2025

The so-called Andromeda Paradox arises from a relativistic interpretation grounded in Einstein’s static universe—a pre-Hubble cosmological model. Hubble’s discovery of the expanding universe, however, invalidated the static model and, with it, undermined the consistency of certain relativistic propositions—especially those tying time dilation directly to velocity near the speed of light.

In this context, time is not a natural physical entity subject to contraction or dilation, but rather an emergent abstraction—arising from the progression of existential events. The Big Bang model clearly supports this: it is the existential event that gave rise to space and time, not the other way around. This understanding renders the relativistic idea of "frozen time" at light speed conceptually untenable.

The reference to the Terrell-Penrose effect, which replaces the older notion of Lorentz contraction with a rotated visual frame due to the differential arrival times of light rays from different parts of the object, is indeed a refined interpretation. However, this does not correct the foundational flaws. It remains embedded in the same relativistic structure that assumes a fixed speed of light governs both visual perception and temporal behavior. While visually more accurate, the Terrell-Penrose rotation does not resolve the deeper inconsistency of time as a physical entity, nor does it accommodate an expanding universe where spacetime itself evolves.

Furthermore, modern observations of distant galaxies receding faster than light due to space expansion show no such visual distortions or rotated frames as relativistic logic would suggest. These galaxies are seen clearly—not as thin 1D lines or rotated frames—which contradicts the visual and temporal predictions made by both Lorentz contraction and its Terrell-Penrose modification.

Thus, even this so-called “enriching logic” is still confined within a flawed framework that presupposes a static background and natural time. The relativistic structure, whether in its original or modified form, does not align with the empirical reality of an expanding universe where time is emergent and galaxy-scale observations defy relativistic visual expectations.

Max Planck’s Legacy: The True Foundations of Energy-Mass Equivalence:

Soumendra Nath Thakur 

April 04, 2025

In 1899—well before the advent of relativity—Max Planck introduced Planck units, deriving fundamental quantities such as Planck length, Planck mass, Planck time, and Planck temperature. He achieved this through dimensional analysis, using the speed of light (c) from Maxwell's equations, the Planck constant (h) which he himself discovered, and Newton's gravitational constant (G).  

His groundbreaking work on black body radiation, evident in his rugged appearance during those years, led to the formulation of the Planck Equation (E = hf) in 1900—a fundamental energy-frequency relationship of the universe. This equation later influenced Einstein’s derivation of the famous energy-mass relation (E = mc^2). However, the frequency-mass relationship and the broader energy-mass equivalence principle were already recognized by classical scientists well before Special Relativity was formulated in 1905.

Infinity: An Abstraction Beyond Comparison in Reality:

April 03, 2025

Dear Enrico P. G. Cadeddu,

Your comment presents an inconsistent proposition because it appears to contradict the fundamental nature of infinity as defined in mathematics.

Infinity is Unreachable in a Finite Sense:

Infinity, by definition, is not something that can be "reached" or "constructed" in a stepwise manner from finite elements. It exists as a concept beyond any finite bounds, whether represented through numbers, sets, or sequences.

Proper Subsets of an Infinite Set Do Not Dictate Its Infinite Character:

An infinite set remains infinite regardless of the nature of its proper subsets.

Some proper subsets can be finite e.g., {1,2,3} ⊂ N, while others can be infinite e.g., the set of even numbers within N.

The union of infinite subsets can still be infinite, so claiming that a union of proper subsets results in something "not infinite" suggests a misunderstanding of set theory.

Infinity as a Defined Mathematical Concept is Self-Consistent:

The Peano axioms and the axiom of infinity in set theory define an internally consistent framework for handling infinite sets like N.

Any argument that rejects infinity yet still relies on the structure of N (which is inherently infinite) creates a paradox.

Conclusion:

The claim in your text only holds if one assumes an inconsistent mathematical principle, which contradicts established definitions.

The very nature of an infinite set remains infinite, and its proper subsets (whether finite or infinite) do not alter its infinite character.

Infinity is not something "dictated" by subsets but an inherent property of the set itself.

This perspective aligns with rigorous mathematical reasoning: Infinity, though an abstract and unreachable concept in a constructive sense, remains well-defined and self-consistent within proper mathematical frameworks.

Best regards,

Soumendra Nath Thakur

With Deep Respect:

April 03, 2024

Dear Dr. Jean-Claude Dutailly,

I would like to extend my sincere gratitude and deepest respect for your insightful comment from 2015. Your words, written nearly a decade ago, continue to resonate with those of us who seek a more profound and scientifically grounded understanding of the universe.

Your perspective on the philosophical and empirical challenges of cosmology, the necessity of mathematical progress in gravitational theories, and the critical need to comprehend gravitation and inertia beyond their conventional interpretations is both enlightening and inspiring. It is rare to find such a balanced view—one that acknowledges the limitations of existing models while also recognizing the need for deeper exploration rather than complacency with established paradigms.

Reading your statement today reaffirms my belief that scientific inquiry must not stagnate but rather evolve through rigorous examination, conceptual innovation, and mathematical refinement. While I will not delve into my own work (Extended Classical Mechanics) in this message, I must acknowledge that your words profoundly align with its foundational motivations. Your novel approach to questioning the status quo continues to encourage me in my efforts to bridge gaps in our understanding of mass, gravity, and inertia.

It is always an honor to encounter thoughts that withstand the test of time, and yours undoubtedly do. I extend my utmost respect and appreciation for your valuable contribution to scientific discourse.

Thanking you,
Yours faithfully,
Soumendra Nath Thakur

Abstraction vs. Physicality: The Nature of Space and Dimensions:

April 02, 2025

Space is an abstract concept; it lacks intrinsic physical properties. For instance, length itself has no inherent attributes—it is merely a one-dimensional extension that defines the direction in which the length of a physical object is measured. It does not exist as a measurable entity on its own but serves as a reference for measurement.

Similarly, height, depth, and time function as conceptual tools rather than physical entities. Time, for example, is not a tangible substance but a mental framework that allows us to perceive and understand change. The combination of spatial dimensions—length, height, and depth—provides meaning to physical transformations, yet these dimensions do not possess physical properties in and of themselves. Unlike tangible objects, they do not have independent existence; rather, they serve as abstract references that facilitate the measurement and comprehension of physical reality.