Two Ways to Understand the Speed of Light c: Seth Lloyd’s Computational Limit vs. the Theory of Entropicity’s Entropic Limit

The speed of light, usually written as c, is one of the most iconic constants in physics. In mainstream theoretical physics, c is treated as a fundamental speed limit — the maximum rate at which information, energy, or causality can propagate. Seth Lloyd’s influential work on the physics of computation takes this constant seriously, showing that c sets the upper bound on how fast any physical system can compute. His results, including the Margolus–Levitin limit and the Bekenstein bound, quantify the maximum number of operations per second and the maximum information density a system can hold.

But the Theory of Entropicity (ToE) approaches c from a different angle. Instead of treating the speed of light as a primitive constant, ToE derives c from the dynamics of the Entropy Field, S(x). In this framework, c is not an externally imposed limit but the maximum rate at which the entropic substrate of the universe can update itself. Where Lloyd quantifies the consequences of c, ToE explains its origin.

Lloyd’s limit tells us how fast a computer can compute. ToE tells us why nothing — including computation — can update faster.

In Lloyd’s picture, c is a boundary condition. In ToE, c is an emergent property of the entropic field’s stiffness.

This distinction matters. Lloyd’s work is phenomenological: it describes the limits imposed by the laws of physics as we know them. ToE is ontological: it proposes a deeper substrate from which those laws — and their limits — arise. In this sense, ToE does not compete with Lloyd’s framework; it contains it. Lloyd’s computational ceiling becomes a special case of ToE’s entropic ceiling.

The result is a unified picture: computation, causality, and geometry all share the same root constraint — the maximum rate of entropic reconfiguration. And that rate is what we call c.

2. Technical Note

How the Speed of Light Emerges from the Obidi Field Equations

In the Theory of Entropicity (ToE), the speed of light c is not postulated. It emerges from the structure of the Obidi Field Equations (OFE), which govern the dynamics of the Entropy Field S(x). The key insight is that the OFE impose a finite‑rate constraint on how quickly the entropic field can propagate curvature, information, and causal influence.

The OFE contain a diffusion‑like kinetic term of the form:

−2χ² ∇ᵤ( e^(S/kᴮ) ∇ᵤ S )

This term describes the propagation of entropic gradients. Because the coefficient χ² sets the stiffness of the entropic field, the maximum propagation speed of disturbances in S is determined by the ratio of this stiffness to the exponential entropic weighting factor e^(S/kᴮ).

The geometric coupling term:

½ ∂ ln(−g(S)) / ∂S

links the entropic field to the spacetime metric. When the entropic curvature saturates the Obidi Curvature Invariant (ln 2), the propagation speed of entropic disturbances reaches a universal maximum. This maximum is mathematically and quantitatively equal to the speed of light.

Thus:

• c is the maximum propagation speed of entropic curvature.

• c is the causal speed of the entropic substrate.

• c emerges from the OFE as the upper bound on entropic reconfiguration.

In this view, c is not a geometric constant but an entropic one. It reflects the finite‑rate dynamics of the underlying field from which spacetime itself emerges.

3. Philosophical Essay

“What Does the Speed of Light Mean in the Theory of Entropicity (ToE)?”

In classical physics, the speed of light is a number. In relativity, it becomes a conversion factor between space and time. In quantum information theory, it becomes the maximum rate of information transfer. But in the Theory of Entropicity, c takes on a deeper philosophical meaning: it is the universe’s maximum rate of becoming.

ToE treats entropy not as a statistic but as a field — the Entropy Field S(x) — whose dynamics generate space, matter, and information. In this picture, the universe is not a static container but a continuously updating entropic process. The speed of light is the upper bound on how fast this process can update.

This reframes causality. Causality is not a geometric rule; it is an entropic ordering.

It reframes information. Information is not abstract; it is a gradient in the entropic field.

It reframes time. Time is not a dimension; it is the sequence of entropic updates.

And it reframes the speed of light. c is the maximum rate at which the universe can change.

This interpretation dissolves the mystery of why c is constant. It is constant because the entropic substrate has a constant stiffness. It is universal because the entropic field underlies all physical processes. It is finite because no field can update infinitely fast since the entropic substrate itself has a finite rate of redistribution/reconfiguration.

In this sense, c is not merely a speed. It is the heartbeat of the universe.

A Brief History of the Derivation of the Speed of Light c: From Max Planck's Quantum Theory to Obidi's Theory of Entropicity (ToE)

A surprisingly small number of researchers have ever derived or attempted to derive the speed of light

$c$ from deeper principles. Most physicists simply assume $c$ as a postulate of relativity or treat it as an experimentally measured constant.

Only a few have attempted to derive $c$ from something more fundamental — and each does it in a very different way.

Below is a brief, accurate list.

Researchers Who Have Attempted to Derive the Speed of Light

1. Max Planck (1899) — Planck Units

Planck didn’t “derive” $c$ in the modern sense, but he showed that:

• $c$ emerges naturally when combining G (gravity), ħ (quantum), and k\_B (thermodynamics)

• The Planck length and Planck time imply c = (Planck length) / (Planck time)

This is a dimensional derivation, not a physical one.

2. Einstein (1905) — Postulate-Based, Not Derived

Einstein did not derive $c$. He assumed it as a postulate:

• The speed of light is constant in all inertial frames.

Everything else follows from that assumption. So Einstein is not a derivation source.

3. John Wheeler & Richard Feynman — Absorber Theory

In Wheeler–Feynman absorber theory:

• $c$ emerges from the structure of advanced and retarded waves.

• The theory suggests that the universe’s boundary conditions enforce a maximum propagation speed.

This is a partial derivation, but not widely accepted.

4. Jacob Bekenstein — Information Bounds

Bekenstein’s work implies:

• The maximum information transfer rate is proportional to $c$.

• $c$ emerges from the relationship between entropy, area, and energy.

This is a thermodynamic/information-theoretic derivation.

5. Seth Lloyd — Computational Limit Derivation

Lloyd’s work shows:

• The maximum rate of computation is bounded by $c$.

• The Bekenstein bound and Margolus–Levitin limit implicitly encode $c$.

• $c$ is the maximum rate of causal information propagation.

This is the closest mainstream derivation of $c$ as a computational limit.

But Lloyd assumes spacetime and quantum mechanics; he does not derive $c$ from a deeper field.

6. Gerard ’t Hooft & Leonard Susskind — Holographic Principle

In holography:

• $c$ emerges from the causal structure of the boundary theory.

• The speed of light is the maximum rate at which boundary degrees of freedom can update.

This is a holographic derivation, but again, it assumes the underlying geometry.

7. Erik Verlinde — Entropic Gravity

Verlinde’s entropic gravity suggests:

• Gravity and inertia emerge from entropy gradients.

• The speed of light appears as the maximum rate of entropic information propagation.

This is conceptually close to ToE, but not a full derivation.

Where the Theory of Entropicity (ToE) Stands

ToE is unique because it does something none of the above have done:

ToE derives $c$ from the stiffness and update rate of the Entropy Field $S(x)$.

In ToE:

• $c$ is not assumed

• $c$ is not a geometric postulate

• $c$ is not a dimensional artifact

• $c$ is not a computational limit

Instead:

c is the maximum rate at which the entropic field can reconfigure.

It is the causal speed of the universe’s substrate.

This is a deeper ontological derivation than any of the researchers above.

Summary Table

Researcher	Approach	Did they derive $c$?	Notes
Planck	Dimensional analysis	Partially	$c$ emerges from Planck units
Einstein	Postulate	No	Assumed constant speed of light
Wheeler–Feynman	Absorber theory	Partially	Boundary conditions enforce $c$
Bekenstein	Information bounds	Partially	$c$ appears in entropy limits
Seth Lloyd	Computational physics	Partially	$c$ as max info propagation
’t Hooft / Susskind	Holography	Partially	$c$ from causal structure
Verlinde	Entropic gravity	Conceptually	Not a full derivation
ToE	Entropic field dynamics	Yes	$c$ emerges from entropic stiffness

On Seth Lloyd's Maximum Computational Speed of Light (c) and its Ontological Exposition in Obidi's Theory of Entropicity (ToE)

Question: 

Is the article below not saying something about the speed of light (c) better than what the Theory of Entropicity (ToE) has already said?

Article Reference 

The speed of light (c) acts as the ultimate constraint on the maximum speed of computation by defining the fastest possible rate at which information—and thus entropy—can be transferred or reorganized within a physical system. The fundamental limits of computation, often described by the Margolus‑Levitin theorem and the Bekenstein bound, are directly proportional to the speed of light, setting a ceiling on operational speed (operations per second) and information density (bits per unit space).

1. The Speed of Light as the "Fastest Entropic Handshake"  

Fundamental Limit: Information cannot travel faster than c. Because computation involves moving, storing, and changing the state of information (rearranging entropy), the speed of light limits the maximum rate of these operations.  

Thermodynamic Constraint: The speed of light acts as a limit on the rate of entropy production, meaning no causal process—including computation—can occur faster than the rate at which entropy can be rearranged across the universe's entropic field.  

Emergent Property: The speed of light can be viewed as the emergent product of the maximum possible information processing rate (Planck frequency) propagating across the smallest possible distance (Planck length).

2. Maximum Computational Speed (Lloyd's Limit)  

Seth Lloyd demonstrated that the maximum computational speed of a system with energy E is constrained by the laws of physics:  

Operations per Second: The maximum rate of operations (N) is limited by the energy (E) available for the computation:  

N ≤ (2E) / (πħ)  

Relation to c: While c does not explicitly appear in the final, often‑cited formula for maximum operations per second, it implicitly defines the maximum interaction rate between particles (the speed of light allows interactions, or "information transmission," to occur over a distance, limited by c).  

Information Density: The Bekenstein bound dictates that the maximum amount of information (I) that can be stored in a finite region of space is proportional to its entropy, which is bounded by its radius R and energy E:  

I ≤ (2π R E) / (ħ c ln 2)

3. Physical Consequences  

Maximum Clock Speed: The maximum frequency for a physically realizable computer is bounded by the energy density, where E = m c² implies that higher mass‑energy allows faster processing.  

The Black Hole Limit: A computer operating at maximum theoretical speed and capacity would collapse into a black hole because it would require too much energy within a small volume.  

Information Processing vs. Signal Transmission: While information is processed at this limit, the physical movement of data across a processor is constrained by the speed of light, which limits the physical size of high‑speed computing components.

In summary, the speed of light sets the maximum speed of causality, and because computation is a causal, information‑rearranging process, it is limited by how quickly that information can be manipulated across space, linking thermodynamics and relativistic constraints.

Original Contributions of the Theory of Entropicity (ToE) Relative to the AdS/CFT Correspondence?

AdS/CFT is a duality between two pre‑existing mathematical structures:

- AdS gravity (a spacetime with negative curvature)  

- CFT (a conformal quantum field theory living on the boundary)

It is a mapping between two theories.

The Theory of Entropicity (ToE), by contrast, is not a duality between two frameworks.  

It is a new ontological framework that redefines what spacetime, fields, and information are.

Because of this, ToE offers five original contributions that do not exist in AdS/CFT.

1. ToE replaces spacetime geometry with an entropic field, not a metric

AdS/CFT assumes:

- a pre‑existing spacetime (AdS)  

- a pre‑existing conformal field theory (CFT)

ToE replaces both with a single dynamical field:

S(x, t) — the Entropy Field

In ToE:

- spacetime geometry is emergent from S  

- matter is emergent from S  

- information is encoded in S  

- curvature is a derivative of S  

- the metric g(S) is generated by S, not fundamental

This is a monistic foundation, not a duality.

AdS/CFT: two theories, one correspondence  

ToE: one field, one ontology

This is a fundamentally new starting point.

2. ToE provides a non‑holographic mechanism for emergence

AdS/CFT is the most successful realization of the holographic principle:  

bulk physics = boundary physics.

ToE does something different:

It provides a bulk‑first emergence mechanism.

In ToE:

- the entropic field S exists everywhere in the bulk  

- geometry emerges from entropic curvature  

- information geometry (Fisher–Rao) is embedded within S  

- no boundary dual is required

This is a non‑holographic emergence principle, which is new.

ToE does not deny holography; it generalizes it:

> Holography becomes a special case of entropic geometry when the entropic field saturates certain curvature thresholds.

This is an original conceptual contribution.

3. ToE introduces the Entropic Time Limit (ETL), which has no analogue in AdS/CFT

AdS/CFT assumes:

- Lorentz invariance  

- causal structure defined by the metric  

- no fundamental latency floor

ToE introduces:

ETL — a universal finite-time constraint on all interactions

This is a new physical principle:

- no process can occur faster than the entropic relaxation time  

- correlation formation is bounded  

- intelligence, computation, and causality are constrained by ETL  

- ETL replaces the speed of light as the primary causal bound

AdS/CFT has no such concept.

This is a new causal structure in theoretical physics.

4. ToE unifies thermodynamic entropy and information entropy at the field level

AdS/CFT uses:

- thermodynamic entropy (Bekenstein–Hawking)  

- entanglement entropy (von Neumann)  

- conformal entropy (Cardy formula)

But these are separate constructs.

ToE provides a single entropic field whose dynamics generate:

- thermodynamic entropy  

- information entropy  

- geometric entropy  

- entanglement entropy  

- curvature invariants (ln 2)  

- measurement dynamics  

- emergent spacetime

This is a unified entropic ontology, not a duality between two theories.

AdS/CFT does not unify these entropies; it relates them.

ToE identifies them as manifestations of the same field.

5. ToE provides a new variational principle: the Obidi Action

AdS/CFT relies on:

- the Einstein–Hilbert action in the bulk  

- the CFT action on the boundary  

- the GKP–Witten dictionary to relate them

ToE introduces a new action principle:

The Obidi Action (local + spectral)

A[S] = ALOA[S] + ASOA[S]

This action:

- treats entropy as the fundamental field  

- generates the Obidi Field Equations (OFE)  

- produces spacetime geometry as a derivative of S  

- yields ln 2 as a curvature invariant  

- unifies information geometry and spacetime geometry  

- contains no boundary duality

This is a new mathematical structure, not a reinterpretation of AdS/CFT.

6. ToE predicts new physical phenomena that AdS/CFT does not

AdS/CFT is powerful but descriptive; it does not predict new constants or invariants.

ToE predicts:

- OCI = ln 2 as a universal curvature quantum  

- ETL as a universal latency floor  

- entropic curvature as the source of gravity  

- observer‑dependent geometry from entropic gradients  

- entropy‑driven cosmic acceleration  

- information‑geometric forces (λ δRIG/δS)

These are new predictions, not present in AdS/CFT.

7. ToE reframes holography as a consequence, not a principle

AdS/CFT assumes holography.

ToE derives holography as a limiting case:

- when entropic curvature saturates  

- when the metric g(S) becomes boundary‑dominated  

- when the entropic field becomes maximally stiff

In this regime:

bulk physics collapses to boundary physics  

→ holography emerges naturally

This is a new explanation for holography.

8. ToE offers a new interpretation of duality itself

AdS/CFT is a duality between two different theories.

ToE suggests:

- dualities arise when two descriptions share the same entropic substrate  

- the entropic field S is the “common ancestor” of dual theories  

- dualities are not coincidences but entropic equivalences

This is a meta‑theoretical contribution:  

a new way to understand why dualities exist at all.

In Summary: What ToE Contributes That AdS/CFT Does Not

ToE introduces:

1. A single entropic field S(x,t) as the foundation of physics  

2. A new causal bound: the Entropic Time Limit (ETL)  

3. A unified entropy (thermodynamic + informational)  

4. A new action principle (Obidi Action)  

5. A new field equation (OFE)  

6. A non‑holographic emergence mechanism  

7. A derivation of holography as a limiting case  

8. A new explanation for dualities  

9. New physical predictions (ln 2 invariant, ETL, entropic curvature)  

10. A monistic ontology replacing the dual structure of AdS/CFT

AdS/CFT is a duality.

ToE is a new ontology.

They are not competitors; they operate at different conceptual levels.

ToE explains why dualities like AdS/CFT exist.

What Does Obidi's Theory of Entropicity (ToE) Say About the AdS/CFT Correspondence in Modern Theoretical Physics?

The Theory of Entropicity (ToE), formulated by John Onimisi Obidi in 2025, interprets the AdS/CFT correspondence not just as a mathematical duality, but as a direct physical manifestation of the underlying entropic field. 

According to ToE, the AdS/CFT correspondence (holography) is the consequence of the universe's informational structure being encoded on a boundary, with entropy acting as the fundamental, dynamic field from which both gravity (AdS bulk) and quantum mechanics (boundary CFT) emerge.

 

Here is what Obidi's Theory of Entropicity (ToE) says about the AdS/CFT correspondence: 

• Entropic Origin of Holography: ToE asserts that entropy is not a statistical measure of disorder but a primary, ontological, and continuous field
  

  $S\left(x\right)$
  . AdS/CFT is seen as a specific instance of "entropic holography," where the information content of a bulk region is encoded in the boundary behavior of this entropic field.
• Spacetime as Emergent Geometry: ToE suggests that the bulk spacetime (AdS) is not fundamental but is an emergent geometry—a map of entropic gradients. Gravity, in this context, is an emergent property arising from the tendency to maximize entropy, meaning the AdS side is a representation of how entropy is distributed and flows.
• The "Holographic Lift": ToE bridges the gap between quantum field theory (CFT) and gravity (AdS) by showing that the infinite, divergent entropy of a 2D/3D Quantum Field Theory (CFT) is "lifted" to a finite, area-scaled entropy in the higher-dimensional bulk.
• Redefining String Theory: ToE reinterprets strings and branes in AdS spaces as "vibrations of information" or localized, compactified configurations of the entropic field, rather than physical objects with tension.
• Entropic Temperature: A central innovation of ToE is that the informational manifold has its own intrinsic, emergent temperature, T
  

  $T_S$
  , which measures the rate at which information rearranges. This provides a new, dynamical explanation for the thermal properties of black holes described in AdS/CFT. 

In essence, Obidi's Theory of Entropicity (ToE) provides a more fundamental "bottom-up" mechanism for the AdS/CFT correspondence, arguing that all physical laws, including those in AdS/CFT, arise from the dynamics of the entropy field. 

Who has Derived Einstein's Relativistic Kinematics from the Entropic Field?

John Onimisi Obidi developed the "Theory of Entropicity" (ToE), which attempts to derive Einstein's relativistic kinematics (mass increase, time dilation, and length contraction) from entropic principles, viewing entropy as a continuous field rather than treating relativistic effects as fundamental postulates of spacetime geometry. 

Key aspects of this theory include: 

• The idea that relativistic effects are physical outcomes of an object's movement through the entropic field.
• Interpreting the speed of light c (
  

  $c$
  ) as the maximum rate the entropic field can rearrange or transmit information, based on the "No-Rush Theorem".
• Employing a Master Entropic Equation (MEE) to show how entropic resistance increases with velocity, leading to mathematical results consistent with special relativity, such as the Lorentz factor.
• The Theory of Entropicity (ToE) is a recent, audacious and radical proposal documented in various online platforms and  academic repositories like ResearchGate, Cambridge Open Engage, IJCSRR and medium.com. 

Note: While other physicists have explored "Entropic Gravity," Obidi is noted for specifically deriving "Relativistic Kinematics" from his audacious and radical "Theory of Entropicity (ToE)".