"The Question of c" in the Theory of Entropicity (ToE): Implications of the Alemoh-Obidi Correspondence (AOC) for the Speed of Light and Its Generalized Meaning in Modern Theoretical Physics 

In the Theory of Entropicity (ToE), a framework primarily developed by John Onimisi Obidi in 2025, the constant $c$ is reinterpreted from a geometric postulate into a physical consequence of the universe's fundamental "entropic field". [1, 2]

Instead of treating the speed of light ($c$) as an arbitrary constant of spacetime, ToE defines it as the maximum rate at which the entropic field can reorganize energy and information. [3, 4]

The Reinterpretation of $c$

In standard physics, $c$ is a fixed speed limit. In ToE, $c$ is the "speed of causality" determined by the intrinsic properties of the entropic field, much like the speed of sound is determined by the properties of the air it travels through. [2, 5, 6]

• Maximum Refresh Rate: The theory views the universe as an informational system. $c$ represents the universal "refresh rate" or the fastest possible "entropic handshake" between two systems.
• Constitutive Law: ToE proposes that $c$ is derived from the ratio of two field properties: entropic conductivity ($\chi_0$) and entropic capacity ($C_0$).
  • $\chi_0$ measures how readily entropy flows.
  • $C_0$ measures how much entropy the field can store or resist.
  • The ratio of these two dictates the speed at which disturbances (like light) propagate. [2, 7, 8, 9, 10]

Why Light Moves at $c$

According to ToE, light is not the cause of the speed limit; it is simply a massless manifestation that "saturates" the field's maximum reconfiguration rate. The "speed limit" exists because the entropic field itself cannot be rearranged instantaneously. [2, 7, 11, 12]

Consequences of the Entropic $c$

The theory uses this entropic definition to provide physical mechanisms for effects that Einstein described as geometric: [13, 14]

• The No-Rush Theorem: This core principle states that no interaction can be instantaneous. Every event requires a finite time for the entropic field to redistribute and synchronize states.
• Time Dilation: Moving through the entropic field requires a "budget" of entropy. A moving object uses part of its entropic capacity for motion, leaving less for its internal processes (like a clock ticking), which causes time to slow down.
• Relativistic Mass: Mass increase is seen as Entropic Resistance (ERP). As an object approaches $c$, the "entropic gradient" it faces becomes steeper, requiring near-infinite entropy to move faster. [2, 5, 15, 16, 17]

Would you like to explore the mathematical framework (such as the Master Entropic Equation) or how this theory attempts to unify gravity and quantum mechanics?

 

[1] https://medium.com

[2] https://medium.com

[3] https://medium.com

[4] https://encyclopedia.pub

[5] https://encyclopedia.pub

[6] https://www.vaia.com

[7] https://medium.com

[8] https://medium.com

[9] https://encyclopedia.pub

[10] https://medium.com

[11] https://medium.com

[12] https://medium.com

[13] https://encyclopedia.pub

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

[15] https://encyclopedia.pub

[16] https://encyclopedia.pub

[17] https://medium.com

 

In the Theory of Entropicity (ToE), a framework primarily developed by John Onimisi Obidi in 2025, the constant $c$ is reinterpreted from a geometric postulate into a physical consequence of the universe's fundamental "entropic field". [1, 2]

Instead of treating the speed of light ($c$) as an arbitrary constant of spacetime, ToE defines it as the maximum rate at which the entropic field can reorganize energy and information. [3, 4]

The Reinterpretation of $c$

In standard physics, $c$ is a fixed speed limit. In ToE, $c$ is the "speed of causality" determined by the intrinsic properties of the entropic field, much like the speed of sound is determined by the properties of the air it travels through. [2, 5, 6]

• Maximum Refresh Rate: The theory views the universe as an informational system. $c$ represents the universal "refresh rate" or the fastest possible "entropic handshake" between two systems.
• Constitutive Law: ToE proposes that $c$ is derived from the ratio of two field properties: entropic conductivity ($\chi_0$) and entropic capacity ($C_0$).
  • $\chi_0$ measures how readily entropy flows.
  • $C_0$ measures how much entropy the field can store or resist.
  • The ratio of these two dictates the speed at which disturbances (like light) propagate. [2, 7, 8, 9, 10]

Why Light Moves at $c$

According to ToE, light is not the cause of the speed limit; it is simply a massless manifestation that "saturates" the field's maximum reconfiguration rate. The "speed limit" exists because the entropic field itself cannot be rearranged instantaneously. [2, 7, 11, 12]

Consequences of the Entropic $c$

The theory uses this entropic definition to provide physical mechanisms for effects that Einstein described as geometric: [13, 14]

• The No-Rush Theorem: This core principle states that no interaction can be instantaneous. Every event requires a finite time for the entropic field to redistribute and synchronize states.
• Time Dilation: Moving through the entropic field requires a "budget" of entropy. A moving object uses part of its entropic capacity for motion, leaving less for its internal processes (like a clock ticking), which causes time to slow down.
• Relativistic Mass: Mass increase is seen as Entropic Resistance (ERP). As an object approaches $c$, the "entropic gradient" it faces becomes steeper, requiring near-infinite entropy to move faster. [2, 5, 15, 16, 17]

Would you like to explore the mathematical framework (such as the Master Entropic Equation) or how this theory attempts to unify gravity and quantum mechanics?

 

[1] https://medium.com

[2] https://medium.com

[3] https://medium.com

[4] https://encyclopedia.pub

[5] https://encyclopedia.pub

[6] https://www.vaia.com

[7] https://medium.com

[8] https://medium.com

[9] https://encyclopedia.pub

[10] https://medium.com

[11] https://medium.com

[12] https://medium.com

[13] https://encyclopedia.pub

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

[15] https://encyclopedia.pub

[16] https://encyclopedia.pub

[17] https://medium.com

 

 

In the Theory of Entropicity (ToE), originated by John Onimisi Obidi in 2025, the "question of c" (the speed of light) is reinterpreted from an unexplained postulate into a derived consequence of thermodynamics. 

The ToE moves beyond treating entropy as a passive measure of disorder, defining it instead as a fundamental, dynamic field that permeates the universe. 

The Core Reinterpretation of c

• Maximum Rate of Realignment: ToE proposes that c is the maximum rate at which the universal Entropic Field can reconfigure or redistribute energy and information.
• Light as a Symptom: Light is not deemed to "travel" in the traditional sense, but rather acts as the visible manifestation of this entropic rearrangement speed.
• The "No-Rush Theorem": A foundational principle in ToE stating that "nature cannot be rushed"—no physical interaction or information transfer can exceed the rate at which the entropic field updates. 

ToE vs. Einstein's Relativity

Where Einstein took the constancy of the speed of light (c) as a postulate to build his theory, the Theory of Entropicity (ToE) attempts to derive this constancy as a thermodynamic law. 

Concept	Relativity (ToR)	Theory of Entropicity (ToE)
Speed of Light (c)	A fundamental, postulated universal constant.	The maximum rate of entropic reconfiguration (an emergent property).
Why c is a Limit	Axiom of nature.	"No-Rush Theorem": The entropic field has a maximum processing speed.
Relativistic Effects	Kinematic necessity of space/time geometry.	Entropic resistance to motion; energy is used up to move, leaving less for internal time.

Implications of ToE on 

• Causality Enforcement: The finite rate of entropic redistribution (c) ensures that effects cannot occur before their causes, maintaining consistent causality.
• Entropic Resistance: Moving through the entropic field causes "entropic drag," which explains why objects with mass cannot reach c. As speed nears c, entropic costs become prohibitive.
• Redefining Gravity: Entropic Gravity implies that gravity is not a force but a result of entropic gradients (pressure) in the field that also propagate at c.

In summary, the Theory of Entropicity (ToE) claims that is the "heartbeat of existence"—the universal rhythm of entropic change, rather than just the speed of a photon, as described in this Encyclopedia.pub entry. 

 

 

In the Theory of Entropicity (ToE), developed by John Onimisi Obidi (2025), the question of c is a fundamental reinterpretation of the speed of light. Instead of treating c as an arbitrary, fundamental constant of spacetime geometry (as in Special Relativity), ToE derives c as an emergent, thermodynamic property of the entropic field. 

Here is a breakdown of the question of c within this framework:

1. From Postulate to Entropic Limit

• Einstein's View: c is a postulate—the maximum speed for all massless signals, taken as a foundational axiom of the universe's geometry.
• ToE View: c is the maximum rate at which the "Entropic Field"—the fundamental, physical substrate of the universe—can reorganize itself to redistribute energy and information.
• The "No-Rush Theorem": ToE proposes that nature "cannot be rushed," forbidding superluminal (faster-than-light) processes because entropic realignment takes finite, non-zero time. 

2. Light as a "Tracer" of Entropy

• In ToE, the speed of light is not about photons themselves, but about the speed at which entropic changes propagate.
• Light is merely the visible manifestation of this maximum speed of entropic reconfiguration.
• The "speed of light" is reinterpreted as the "fastest possible entropic handshake". 

3. Relativity as Entropic Inevitability

• Mass Increase/Time Dilation: These are reinterpreted as physical entropic resistances to motion. Moving through the entropic field requires the reconfiguration of the field; as velocity approaches c, this "entropic cost" diverges.
• Constant Speed: The invariance of c
•  is a thermodynamic consequence of the entropic field’s "null cone," rather than a geometric given. 

Summary of the "Question of C" in ToE

Feature	Einsteinian Relativity (ToR)	Theory of Entropicity (ToE)
Status of c	Fundamental Postulate	Emergent Thermodynamic Law
Origin of c	Geometry of Spacetime	Entropic Field Dynamics
Meaning of c	Max speed of light	Max rate of information update
What is c?	A universal constant	"Entropic Cost of Motion" limit

Proponents of this recent theory (as of 2025–2026) suggest that this approach reconciles quantum mechanics and relativity by providing a physical, rather than purely geometric, basis for universal constraints. 

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