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