An Open Review of "Physics: Derivation of Speed of Light (c) from the Theory of Entropicity (ToE)": Exploring Potential Merits and Conceptual Framework

It is a foundational principle of scientific progress that new ideas, especially those that challenge established paradigms, should be evaluated on their own merits. History is replete with examples of theories that were initially dismissed but later proven to be revolutionary. In that spirit, this open review sets aside the paper's publication status and focuses on its potential merits, intellectual ambition, and the creativity of its conceptual framework.

This review assesses the work of John Onimisi Obidi on the "Derivation of Speed of Light (c) from the Theory of Entropicity (ToE)^[1][2][3]" by focusing on the positive aspects of its intellectual project, its methodological structure, and the heuristic value of its ideas.

1. Commendable Intellectual Ambition

The most striking positive feature of this paper is its sheer ambition. The author is not attempting to solve a minor, incremental problem. Instead, the work tackles one of the most fundamental questions in physics: Why is the speed of light c what it is, and why is it constant for all observers?

The theory attempts to provide an answer by weaving together concepts from three pillars of modern physics:

• General Relativity (via the gravitational constant, G, and the use of metric tensors)
• Quantum Mechanics (via Planck's constant, ħ)
• Thermodynamics & Information Theory (via Boltzmann's constant, kB, and the central role of entropy, S)

The goal of unifying these domains and deriving a fundamental constant from their interplay is one of the highest aspirations in theoretical physics. This effort, regardless of its ultimate success, demonstrates a laudable commitment to deep, fundamental inquiry.

2. A Structured and Methodical Presentation

The paper follows a logical and recognizable structure that is standard in theoretical physics. This methodical approach is a significant strength, as it allows the reader to follow the author's line of reasoning step-by-step. The key stages include:

• Postulating a Fundamental Action: The theory begins by defining a "Master Entropic Equation" (MEE) or "Obidi Action."^[4][5] This is the standard starting point for modern field theories, from which all dynamics are derived.
• Deriving Field Equations: By applying the principle of least action (varying the action with respect to the entropy field S), the paper derives a non-linear field equation for entropy. This is a standard and powerful technique.
• Linearization and Wave Analysis: The theory then linearizes this equation around a stable background to study small disturbances. This is precisely how one analyzes the propagation of waves (like light or gravitational waves) in other field theories.
• Identifying the Characteristic Speed: From the resulting wave equation, the paper identifies the propagation speed of these "entropic waves" and demonstrates how it relates to the theory's fundamental parameters.
• Discussing Invariance: The paper concludes by constructing an "Entropic Lorentz Group," attempting to show why this derived speed would be measured to be the same by all observers.

This rigorous, step-by-step structure shows a clear command of the mathematical methods of theoretical physics, which makes the proposal, at the very least, coherent and formally articulated.

3. Provocative and Heuristically Valuable Concepts

Even if the theory is speculative, its core concepts have heuristic value—that is, they can be useful for discovery and learning, and they provoke new ways of thinking.

• Entropy as a Dynamical Field: The central idea of promoting entropy from a statistical property of a system to a fundamental, dynamic field is highly provocative. It forces the reader to ask: "What if?" What would be the consequences if entropy itself could have waves and dynamics? This is a creative leap that challenges deep-seated assumptions.
• "Entropic Stiffness" and "Entropic Inertia": The introduction of these terms provides a powerful physical metaphor. It suggests that spacetime has a resistance to changes in entropy (inertia) and a tendency to restore itself (stiffness). The idea that the speed of light emerges from the ratio of these two properties is an intuitive and elegant physical picture.
• A Deeper Origin for c: The theory posits that the value of c is not merely an arbitrary fact of our universe but is instead a necessary consequence of a balance between gravitational (G), quantum (ħ), and thermal (kB) effects. This hypothesis, suggesting a deep connection between the laws of motion, information, and gravity, is profoundly compelling. The paper's conclusion that ToE "derives c as the unique solution keeping 'entropy flux and inertia' in balance" is a powerful and elegant claim.

4. Avenues for Constructive Development

The paper itself points toward future work, which is a sign of a healthy, developing research program. It explicitly mentions the need to:

1. Incorporate irreversibility and Fisher information, suggesting the current model is a simplification that can be made more robust.
2. Explore testable deviations from c under extreme entropy gradients. This is a crucial point, as it opens the door to potential falsifiability—the hallmark of a scientific theory. If the theory could predict a specific, measurable variation in c under specific conditions (e.g., near a black hole's event horizon), it would move from speculative philosophy to testable physics.

Conclusion

While the "Theory of Entropicity(ToE)" exists far outside of mainstream physics, an open-minded review finds several positive attributes in the work. The paper is driven by profound intellectual ambition, is presented in a methodologically sound format, and introduces creative, thought-provoking concepts. It makes a bold attempt to connect disparate fields of physics to explain a fundamental constant of nature.

The value of such a work may not lie in its immediate acceptance, but in its potential to act as a conceptual catalyst. It encourages physicists to re-examine the foundations of their own theories and to ask whether a concept as fundamental as entropy might play a more active, dynamical role in the cosmos than is currently assumed. In the long run, science benefits from such bold, speculative explorations, as they push the boundaries of imagination and can sometimes illuminate the path toward the next true revolution.

This entry is adapted from: https://handwiki.org/wiki/index.php?title=Physics:Derivation_of_Speed_of_Light_(c)_from_the_Theory_of_Entropicity_(ToE)&oldid=3741502