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

1. What Maxwell Actually Derived

Maxwell showed that electromagnetic waves propagate at a speed determined by the electric and magnetic constants:

c = 1 / √(μ₀ ε₀)

This was revolutionary because:

• μ₀ and ε₀ were already known from experiments

• Maxwell’s equations predicted a wave with that speed

• that speed matched the measured speed of light

So, Maxwell concluded:

light is an electromagnetic wave

But notice something crucial:

Maxwell did not explain why μ₀ and ε₀ have the values they do.

He did not explain why the universe has a maximum speed at all. He did not explain why causality is limited by c.

He discovered that EM waves travel at c. He did not derive c as a fundamental property of reality.

2. Maxwell’s derivation is within electromagnetism, not beneath it

Maxwell’s result is:

• conditional

• theory‑internal

• dependent on EM constants

• not universal

If the universe had different μ₀ and ε₀, Maxwell’s “derived” speed would be different.

So Maxwell’s c is:

• the speed of EM waves

• not the speed of causality

• not the speed of information

• not the speed of spacetime

• not the speed of entropic propagation

Einstein later elevated c to a universal constant, but Einstein did not derive it — he postulated it.

3. What Seth Lloyd derived

Lloyd derived:

• the maximum computational rate

• the maximum information density

• the maximum causal update rate

But Lloyd assumes c as a fundamental limit. He does not explain why c exists.

4. What the Theory of Entropicity (ToE) claims to derive

ToE is doing something neither Maxwell nor Lloyd attempted:

ToE derives c as the maximum rate of entropic reconfiguration of the universe’s substrate.

In ToE:

• c is not a property of electromagnetism

• c is not a property of spacetime geometry

• c is not a postulate

• c is not a constant inserted by hand

Instead:

c emerges from the stiffness and finite‑rate dynamics of the Entropy Field S(x).

This is a deeper level of explanation.

5. The hierarchy of “derivations” of c

Here is the difference summarized in tabular form:

Level	Who	What is c?	Derived or Assumed?
Electromagnetic	Maxwell	Speed of EM waves	Derived from μ₀, ε₀
Relativistic	Einstein	Universal speed limit	Assumed as postulate
Computational	Lloyd	Max info‑processing rate	Derived given c
Entropic (ToE)	Obidi	Max entropic update rate of reality	Emergent from S(x)

So:

• Maxwell: c is the speed of light

• Einstein: c is the speed of causality

• Lloyd: c is the speed of computation

• ToE: c is the speed of the universe’s entropic substrate

These are not the same.

6. The key distinction

Maxwell derived the speed of light.

ToE derives the speed limit of reality, which light happens to saturate.

Maxwell’s derivation is phenomenological. ToE’s derivation is ontological.

Maxwell explains why light travels at c. ToE explains why c exists at all.

7. The simplest way to put it

Maxwell derived c from electromagnetism. ToE derives electromagnetism from c.

That’s the difference.