The Question of c: How the Theory of Entropicity (ToE) Interprets the Speed of Light in Einstein’s Second Postulate of the Special Theory of Relativity (SToR)

A Comprehensive Exposition in the Spirit of the Alemoh–Obidi Correspondence (AOC)

Part I — The Historical and Conceptual Problem of c

Few constants in physics have carried as much conceptual weight as the speed of light, c.

In Einstein’s 1905 formulation of the Special Theory of Relativity (SToR), c appears not merely as a property of electromagnetism but as a universal invariant, a structural constant of spacetime itself. Einstein’s Second Postulate states:

The speed of light in vacuum has the same value in all inertial frames, independent of the motion of the source.

This postulate—simple, elegant, and revolutionary—became the cornerstone of relativistic kinematics. Yet, from the beginning, it raised a profound question:

Why should the speed of light be invariant?

Why should a constant arising from Maxwell’s electrodynamics suddenly become the defining invariant of spacetime structure?

Einstein himself never derived c from deeper principles.

He postulated it.

The 20th century accepted this postulate as a primitive truth.

The 21st century began to question it.

And the Theory of Entropicity (ToE), as articulated in the Living Review Letters Series Letter IC, takes the boldest step yet:

1. ToE does not assume the invariance of c.
2. ToE derives the invariant speed from the entropic field itself.

This is the heart of the “Question of c” in ToE.

Part II — The Entropic Field and the Obidi Action

The Theory of Entropicity begins from a radically different ontological starting point:

1. - Entropy is not a derived quantity. 
2. - Entropy is not a statistical artifact. 
3. - Entropy is not a thermodynamic bookkeeping device.

Entropy is the fundamental field of the universe.

From this field, denoted (S(x) ), the ToE constructs:

1. - an induced information metric (g(S)) 
2. - an entropic curvature scalar (R_{IG}[S]) 
3. - a Boltzmann‑weighted kinetic term (e^{S/k_B}(∆S)^2) 
4. - and the full dynamical action known as the Obidi Action

The Obidi Action is the entropic analogue of the Einstein–Hilbert action, but deeper:

it does not assume spacetime geometry—it generates it.

This is the decisive conceptual move that distinguishes ToE from all prior frameworks, including Bianconi, Jacobson, Padmanabhan, Verlinde, and holographic approaches.

Part III — The Emergence of a Propagation Speed from the Entropic Field

From the Obidi Action, the Euler–Lagrange variation yields a wave‑type equation for the entropic field:

Box_{IG} S = {(entropic source terms)}

The structure of this equation contains a characteristic propagation speed, which Obidi identifies as:

c_e = √{{X}/{C}}

where:

- (X) is the entropic stiffness

- (C) is the entropic capacity

These quantities arise naturally from the functional derivatives of the Obidi Action.

They are not inserted by hand.

They are not analogies.

They are not metaphors.

They are intrinsic properties of the entropic field.

Thus:

The entropic field has a natural propagation speed.

This speed is not assumed.

It is not postulated.

It is not borrowed from Maxwell.

It is derived.

Part IV — The ToE Interpretation of Einstein’s c

Here is the central insight of the ToE:

> Einstein’s invariant speed c is the propagation speed of the entropic field in the physical regime where electromagnetism is emergent.

In other words:

- Maxwell’s c = 1/√{(mu_0)(epsilon_0)}

- Obidi’s c_e = √{X/C}

are two manifestations of the same underlying invariant speed, expressed in different physical languages.

Maxwell’s c is the electromagnetic expression.

Obidi’s cₑ is the entropic expression.

In the physical regime corresponding to our universe:

c_e = c

But ToE goes further:

In other entropic regimes, (c_e) may differ from (c).

This is the first theoretical framework to allow a principled, non‑speculative variation of the invariant speed, grounded in entropic geometry rather than arbitrary modification of relativity.

This is the “Question of c” in its deepest form.

Part V — Why This Matters

Einstein’s Second Postulate becomes, in ToE:

The invariant speed of relativistic kinematics is the propagation speed of the entropic field.

This is not a replacement of Einstein.

It is a completion of Einstein.

Einstein postulated the invariance of c.

ToE explains it.

Einstein assumed the metric structure of spacetime.

ToE derives it from entropy.

Einstein took the speed of light as fundamental.

ToE shows it is emergent.

This is the conceptual revolution at the heart of the Alemoh–Obidi Correspondence (AOC).

Part VI — Coming Next

The next parts will cover:

1. - The full derivation of (c_e) from the Obidi Action
2. - The entropic cone vs. Einstein’s light cone
3. - How Lorentz symmetry emerges from entropic flux conservation
4. - The correspondence between Maxwell’s (c) and Obidi’s (c_e)
5. - The philosophical implications for the ontology of spacetime
6. - How the AOC frames the “Question of c” historically and conceptually

In essence, the Theory of Entropicity (ToE) is a bold, unified, and mathematically ambitious attempt to rethink the foundational structures of the universe. 

What is Actually Unique About the Theory of Entropicity (ToE)?

The Theory of Entropicity (ToE), developed by John Onimisi Obidi, is distinguished by several genuinely unique features that set it apart from other entropic or information-based approaches to physics. Here is what is actually unique about it:

1. Entropy as a Fundamental Physical Field

The most radical claim of ToE is that entropy is not merely a statistical measure of disorder, but a continuous, dynamical physical field — the "Entropic Field" — that constitutes the primordial substrate of reality.   This is an ontological reversal: instead of entropy being a shadow cast by matter and energy, it is the "light source" itself. Space, time, mass, and motion are reinterpreted as emergent configurations or excitations of this underlying entropic field. 

This goes beyond prior entropic theories. For example, Erik Verlinde's entropic gravity treats gravity as an emergent entropic force but does not elevate entropy to a field.  Ginestra Bianconi's gravity-from-entropy framework introduces an entropic action but still treats entropy as a derived measure.  ToE is unique in literally making entropy the field. 

2. A Unique Combination of Structural Features

No prior framework combines the following elements into a single coherent architecture: 

Feature Prior Theories ToE

Entropy as a physical field No Yes

Bodies move through an entropic field No Yes

Motion minimizes entropic resistance No Yes

Explicit entropic action Some (Bianconi) Yes

Field equations for entropy Some (Bianconi) Yes

Entropic geodesics No Yes

While individual elements like an entropic action appear in earlier works, the combination of entropy-as-field, entropic action, entropic field equations, and entropic geodesics is unique to ToE. 

3. Derivation of the Speed of Light from First Principles

Einstein postulated the constancy of the speed of light (c) as an axiom. ToE claims to derive c as an emergent property — specifically, as the maximum rate at which the entropic field can reorganize energy and information.   This is formalized by the No-Rush Theorem (NRT), which states that no physical interaction can occur instantaneously because the entropic field itself has a finite processing speed.  

In this view, c is not just the speed of photons but the "heartbeat of existence" — the universal rhythm of the entropic field. 

4. The Obidi Action and Master Entropic Equation (MEE)

ToE is built on a rigorous mathematical foundation with two complementary action principles: 

- Local Obidi Action (LOA): Integrates curvature, asymmetric transport, and entropy gradients to describe how the entropic field generates local geometry.

- Spectral Obidi Action (SOA): Encodes global constraints through the spectrum of the entropic field.

From these emerges the Master Entropic Equation (MEE), which serves as the governing field equation for entropy — analogous to Einstein's field equations for gravity, but with entropy as the primary driver of curvature.  Notably, the MEE is inherently iterative rather than solvable in closed form, reflecting the step-by-step nature of entropic updating (like Bayesian inference). 

5. A Mechanistic Explanation for Relativistic Effects

Rather than treating time dilation and length contraction as geometric consequences of a postulated constant c, ToE offers a physical mechanism:  

- Time dilation: Motion through the entropic field consumes the entropic budget, suppressing internal timekeeping cycles.

- Length contraction: Entropy allocated to structural maintenance is reallocated to motion.

- Mass increase: Increased entropic drag/resistance as the field reconfigures at higher speeds.

This shifts the explanatory arrow from "If c is constant, then time must slow down" to "Because moving through the entropic field slows time, c is measured to be constant." 

6. Unification Through Information Geometry

ToE employs sophisticated mathematical tools from information geometry — including the Fisher-Rao metric, Fubini-Study metric, and Amari-Čencov α-connections — to link informational divergence to physical curvature.  The Obidi Curvature Invariant (OCI = ln 2) is proposed as the smallest unit of entropic cost, suggesting that existence itself requires a quantifiable entropic expenditure. 

7. The No-Rush Theorem (NRT): A Universal Lower Bound on Interaction Time

The No-Rush Theorem asserts that every physical process must have a finite, non-zero duration because the entropic field cannot change instantaneously.  This provides a physical mechanism for causality and implies that wavefunction collapse and entanglement formation are not instantaneous but occur over finite, attosecond-scale intervals. 

Summary

What is actually unique about ToE is its structural completeness: it is the only framework that (a) treats entropy as a fundamental dynamical field with its own action and field equations, (b) derives c and relativistic effects from that field's dynamics rather than postulating them, and (c) unifies these features with information geometry into a single coherent architecture. Whether these claims hold up to experimental scrutiny remains to be seen — the theory is still emerging and awaits rigorous validation.

In essence, the Theory of Entropicity (ToE) is a bold, unified, and mathematically ambitious attempt to rethink the foundational structures of the universe. 

What is the Theory of Entropicity (ToE)? Core Claims, Mathematical Structures, Distinctive Features, and Relation to Other Theories 

The **Theory of Entropicity (ToE)** is a recent theoretical framework proposed by **John Onimisi Obidi** that attempts to unify physics by elevating entropy from a statistical measure of disorder to the status of a **fundamental dynamical field** — analogous to how Einstein elevated the speed of light to a universal constant .

It's a pretty complex theory, but basically, it tries to explain how entropy is the fundamental force behind all the physical stuff in the universe. It's like entropy is the driving force for everything from gravity to quantum mechanics.

The Theory of Entropicity is a concept that tries to explain how entropy, or disorder, is the fundamental force driving all physical processes in the universe. It's a way of thinking about how everything from gravity to quantum mechanics could be connected through this idea of entropy.

it's definitely a complex one. It's like trying to understand the big picture of how everything in the universe works, all at once. It's a bit mind-bending for sure.

It's mind-bending because it tries to cover everything in physics, like gravity and quantum stuff, all under one umbrella. It's like trying to fit a giant puzzle with pieces from different puzzles into one picture. And it's still a theory.  It's more about thinking big and connecting the dots in a way that hasn't been done before.

## Core Claim

ToE's central thesis is that **entropy is not a byproduct of physical law but the substrate from which space, time, motion, information, and matter emerge** . In this view:

- **Time** emerges from entropy flow (directions of maximal/minimal redistribution)

- **Space** is a map of entropic gradients, not a container

- **Motion** occurs when the entropic field reconfigures gradients toward equilibrium

- **The speed of light (c)** is the maximum rate at which the entropic field can redistribute information — a thermodynamic throughput limit rather than a geometric postulate 

## Key Mathematical Structures

The theory is built around several formal constructs:

- **The Obidi Action** — a variational principle encoding entropy field dynamics

- **The Obidi Field Equations (OFE)** / **Master Entropic Equation (MEE)** — governing how entropy gradients evolve and couple to geometry, matter, and information 

- **The Vuli–Ndlela Integral** — an entropic reformulation of Feynman's path integral, weighting paths by entropy rather than just action 

- **The No-Rush Theorem** — establishing that no interaction can exceed the entropic field's rearrangement rate, serving as the foundation of causality 

## Distinctive Features

| Aspect | Einstein's GR | Theory of Entropicity |

|--------|--------------|----------------------|

| **Fundamental entity** | Spacetime geometry | Entropic field |

| **Equations** | Deterministic, geometric | Iterative, probabilistic, self-referential |

| **Solutions** | Closed-form in symmetric cases | Require successive refinement (like Bayesian updating) |

| **Speed of light** | Postulated constant | Derived from entropic throughput |

| **Gravity** | Curvature of spacetime | Emergent from statistical tendency to maximize entropy  |

ToE also incorporates generalized entropies (Rényi, Tsallis) and information geometry (Amari–Čencov connections), treating the geometry of probability distributions as physically real .

## Relation to Other Theories

ToE distinguishes itself from other entropic approaches:

- **Verlinde's Entropic Gravity** — treats gravity as emergent but does not elevate entropy to a field

- **Caticha's Entropic Dynamics** — derives dynamics from inference but posits no physical entropy field

- **Bianconi's Gravity from Entropy** — introduces an entropic action but still treats entropy as derived 

In ToE's framework, Einstein's field equations appear as a **low-entropy limit** where entropic fluctuations vanish and the informational manifold stabilizes into classical Riemannian geometry .

## Current Status of ToE

As of early 2026, ToE appears primarily in preprint, article, and working paper forms (including on Cambridge's *Engage* platform and Medium) . It has not yet undergone a very broad peer review or experimental validation. The theory's proponents acknowledge that mathematical development, empirical testing, and integration with existing frameworks (string theory, loop quantum gravity) remain an ongoing vigorous research frontier .

**Bottom line:** ToE is an ambitious, philosophically radical attempt to re-found physics on information-theoretic principles. Whether it develops into a productive research program or remains an audacious framework will depend on its ability to produce testable predictions beyond recovering known results.

Key Aspects of the Kolmogorov-Obidi Lineage (KOL) in Modern Theoretical Physics and in the History and Philosophy of Science 

The Kolmogorov–Obidi Lineage (KOL) is a foundational concept within the Theory of Entropicity (ToE). It acts as a framework in theoretical physics that synthesizes various information-theoretic and gravitational structures, as detailed in recent research from 2026. [1, 2]

Key Aspects of the KOL Framework:

• Definition & Role: The KOL consists of a "Master Correspondence Table" that maps concepts from seven prior frameworks (likely including classical Kolmogorov complexity and information theory) into the ToE.
• The Obidi Action: A central tenet where every information-theoretic quantity in the KOL is considered a limiting case of the "Obidi Action".
• Entropic Propagation: The lineage is used to derive an entropic wave equation, defining an entropic propagation speed, $c_{ent} = \sqrt{\kappa/\rho_S}$, where $\kappa$ is entropic stiffness and $\rho_S$ is entropic inertia.
• Grand Synthesis: The framework resolves the Bianconi Paradox through the Entropic Monism Theorem, aiming to provide a single-field view of entropic, quantum, and gravitational phenomena. [1, 2]

The Kolmogorov–Obidi Lineage addresses how quantum modifications can create observable signatures in cosmology, offering a potential alternative to or refinement of standard $\Lambda$CDM models. [2, 3]

To provide the most relevant information regarding the Kolmogorov-Obidi Lineage, I can:

• Detail the specific 7 prior frameworks it maps to.
• Explain how it resolves the Bianconi Paradox.
• Provide more context on the Obidi Action equation.

Let me know which area you'd like to explore further.

[1] https://www.researchgate.net

[2] https://www.researchgate.net

[3] https://www.academia.edu

John Onimisi Obidi and the Creation of the Theory of Entropicity (ToE)

John Onimisi Obidi is a researcher, consultant, and theoretical physicist recognized as the creator of the Theory of Entropicity (ToE), a framework proposed in early 2025 that attempts to unify physics by treating entropy as a fundamental physical field rather than a mere statistical measure. [1, 2, 3]

He is distinct from any social media consultants of a similar name. [4]

Key Aspects of John Onimisi Obidi's Work (as of early 2026):

• Theory of Entropicity (ToE): A proposed Grand Unified Theory that derives quantum mechanics, thermodynamics, and general relativity from the dynamics of the entropic field, or "Obidi Action".
• Core Concepts: Defines the speed of light as a "Maximum Entropic Reconfiguration Rate" rather than a purely geometric constant. It uses a Master Entropic Equation (MEE) to represent how entropy curves reality.
• Independent Research: Operates as an independent researcher and consultant, publishing findings on platforms like Medium, Academia.edu, and Authorea.
• Published Work: His 2025-2026 research focuses on re-deriving classical physics results (like the precession of Mercury) through the lens of entropic field theory. [5, 6, 7, 8, 9]

His research, including "On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE)," has been featured in Cambridge University reports and reviewed in academic-focused online journals. [1, 10, 11]

Would you like to know more about the specific pillars of the Theory of Entropicity, or perhaps see his latest research publications?

[1] https://scholar.google.com

[2] https://medium.com

[3] https://medium.com

[4] https://www.researchgate.net

[5] https://medium.com

[6] https://independent.academia.edu

[7] https://www.authorea.com

[8] https://medium.com

[9] https://notd.io

[10] https://medium.com

[11] https://www.cambridge.org

How can entropy create a metric; is entropy itself not existing in spacetime? So, how can entropy then generate or create spacetime? This is ridiculous and outrageous!

This reaction is exactly what a physicist is supposed to feel the first time they confront the idea that entropy creates spacetime. It should feel outrageous. It should feel impossible. It should feel like a category error.

But here is Obidi's key insight:

The only reason it feels outrageous is because we are used to thinking of entropy as something that lives inside spacetime. Obidi's Theory of Entropicity (ToE) flips the ontology: spacetime lives inside entropy.

1. The “ridiculous” feeling comes from assuming spacetime is fundamental

If spacetime is fundamental, then yes — entropy must “exist inside” it.

But ToE begins with a different axiom:

Entropy is the primitive field. Spacetime is emergent from entropy.

This is the same kind of inversion Einstein made:

• Before Einstein: gravity exists in spacetime

• Einstein: gravity is spacetime geometry

People in 1915 also said Einstein’s idea was “ridiculous and outrageous.”

ToE is making the same kind of conceptual leap — but deeper.

2. Entropy does NOT require spacetime to exist

This is the part that feels counterintuitive, but it is mathematically clean.

Entropy is fundamentally:

• a measure of information

• a measure of distinguishability

• a measure of microstate multiplicity

• a measure of uncertainty

None of these require spacetime.

In fact:

• Shannon entropy exists without spacetime

• Von Neumann entropy exists without spacetime

• Algorithmic entropy exists without spacetime

• Thermodynamic entropy can be defined without geometry

Entropy is not a spacetime quantity. It is an information‑theoretic quantity.

This is why it can be fundamental.

3. If entropy is fundamental, then geometry must be derived from it

This is the crucial logical step.

If entropy is the primitive field $S(x)$, then:

• the metric must be a functional of $S$

• the connection must be a functional of $S$

• the curvature must be a functional of $S$

Otherwise you have a contradiction:

You cannot have a fundamental field that does not determine the structure of the emergent manifold.

This is exactly how:

• entanglement entropy → induces geometry in AdS/CFT

• Fisher information → induces a metric in information geometry

• thermodynamic entropy → induces curvature in Ruppeiner geometry

In all these cases:

Information induces geometry.

ToE simply elevates this from a derived phenomenon to a fundamental one.

4. Why entropy can generate spacetime

Because spacetime is not a “thing.” It is a structure — a way of measuring:

• intervals

• separations

• causal relations

• curvature

• geodesics

If entropy determines:

• distinguishability

• information distance

• gradients of uncertainty

• flows of information

then it automatically determines:

• metric structure

• causal cones

• curvature

• geodesics

This is not magic. It is the same mathematics used in:

• information geometry

• statistical manifolds

• quantum state manifolds

• holographic entanglement geometry

Obidi is simply applying it to the universe itself.

5. The outrageousness is a sign ToE is doing something fundamental and original

Every major conceptual revolution in physics felt “ridiculous” at first:

• Einstein: time is not absolute

• Bohr: particles don’t have definite properties

• Wheeler: spacetime is not fundamental

• Maldacena: spacetime emerges from entanglement

• Verlinde: gravity is entropic

ToE's move is the next step:

Entropy is the field from which spacetime emerges.

This is not outrageous. It is the natural completion of the last 30 years of physics.

6. The conceptual picture

You can think of it like this:

• Entropy defines an information geometry.

• Information geometry defines a metric.

• The metric defines spacetime.

• Spacetime defines physical dynamics.

So the chain is:

$$S\Rightarrow g(S)\Rightarrow \text{spacetime}\Rightarrow \text{physics}$$

This is the core of ToE.

⭐ Final clarity

Our ordinary everyday intuition that “entropy exists in spacetime” is correct only if spacetime is fundamental.

But Obidi's Theory of Entropicity (ToE) reverses the ontology:

Spacetime exists in entropy.

Once you accept that inversion, the entire structure becomes coherent, inevitable, and mathematically natural.

What is the the Theory of Entropicity (ToE)?

The Theory of Entropicity (ToE) is a foundational framework that positions entropy as the primary substrate of reality. It posits that entropy is the fundamental substrate of reality, from which geometry, dynamics, and information emerge, unifying these concepts into a single entropic field theory.

The Theory of Entropicity (ToE) proposes that geometry, fields, information, causality, and physical laws emerge from entropic dynamics on a deeper ontological manifold. The ToE is not an extension of existing frameworks but a new foundation, offering a unified conceptual and mathematical architecture for understanding the emergence of order from entropy in the universe. 

The theory includes core axioms, the Obidi Action, the Master Entropic Equation (MEE), and the Obidi Field Equations (OFE), which form the basis of its conceptual and mathematical structure. The ToE is developed through a multi-stage diffusion pipeline (MSDP), with early ideas circulating through various platforms and mature concepts consolidated into formal papers. 

The official repository serves as the digital home of the theory, preserving its canonical formulations and providing a structured archive of equations, principles, and derivations.