The No-Rush Theorem, first formulated by independent theoretical physicist John Onimisi Obidi as part of his Theory of Entropicity (ToE), is the principle that no physical process can occur instantaneously. The theorem asserts that every physical interaction requires a finite, non-zero amount of time to unfold. 

The theorem is a core tenet of the Theory of Entropicity, which proposes that entropy is not a statistical concept but a fundamental field that governs all physical dynamics. The No-Rush Theorem provides a causal mechanism for why the universe has a fundamental speed limit, as interactions must be processed by this "entropic field". 

Key aspects of the No-Rush Theorem 

A universal time limit: The theorem posits a minimum duration for any physical interaction, no matter how small or large. This contrasts with some conventional physics models where certain interactions are assumed to be instantaneous.

The origin of the speed of light: In ToE, the universal speed limit—the speed of light (\(c\))—is not a postulate but an emergent property of the entropic field. The No-Rush Theorem explains that \(c\) is the maximum possible rate at which the entropic field can rearrange itself and propagate information.

Explaining relativistic effects: The theorem offers a physical explanation for phenomena like time dilation and length contraction. As an object moves faster, it reallocates more of its "entropic budget" to motion, leaving less for internal processes like the ticking of a clock.

Explaining quantum phenomena: The theorem extends to quantum mechanics, where it suggests that events like quantum entanglement and wave function collapse also occur within a finite time frame, governed by the same entropic speed limit. This provides an interpretation of recent experimental measurements showing entanglement formation takes time (attoseconds).

"Nature cannot be rushed": Obidi summarizes the theorem with the phrase "Nature cannot be rushed," encapsulating the idea that the universe, at its most fundamental level, operates at a finite "processing speed". 

The famous equation is $$E = mc^2$$.

$$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$

“The Limit of the Speed of Light (c) is a Consequence of [Thermodynamic] Entropy Rather Than the Geometry of Einstein’s Theory of Relativity”

The above title is actually one of the boldest and most thought-provoking proposals in John Onimisi Obidi’s Theory of Entropicity(ToE), because it shifts the meaning of the speed of light,(c), from a purely geometric role in relativity to a thermodynamic/entropic one.

Let us expand this innovative and groundbreaking idea carefully:

1. Standard View of the Speed of Light c

In Special Relativity, c is the invariant speed built into the Minkowski metric — a geometric axiom about spacetime itself.

In General Relativity, c retains that role as the fundamental conversion factor linking space and time.

In Quantum Field Theory, it sets the causal structure: no signals faster than c.

So, in conventional physics, c is axiomatic and not explained further. It is “just there.”

2. ToE’s Entropic Reinterpretation of the Speed of Light c

The Theory of Entropicity(ToE) proposes that c is not a geometric postulate but the maximum rate at which entropy can be rearranged, exchanged, or propagated through the universal entropic field.

That is:

Entropy rearrangement = physical interaction

Thus, the Theory of Entropicity(ToE) compels us to think differently and to demand that:

Every interaction (electromagnetic, gravitational, quantum entanglement, etc.) is a redistribution of entropy.

That is:

Finite speed = constraint of the field

Which is:

No entropic rearrangement — and hence no causal process — can occur faster than this fundamental rate.

New Meaning of The Speed of Light c:

The speed of light c thus becomes the ceiling imposed by the irreversibility and finite responsiveness of the entropic field itself.

So in the Theory of Entropicity(ToE), the speed of light c = “the fastest possible entropic handshake.”

3. Why This Paradigm Shift of the Theory of Entropicity(ToE) Is Provocative

Unification: It ties relativity’s speed limit to thermodynamics, two pillars of physics that are usually separate.

Explanation instead of axiom: Instead of saying “the speed of light c is maximum by geometry,” the Theory of Entropicity(ToE) says why there is a maximum: because entropy rearrangement itself cannot be instantaneous.

Testable outlook: If entropic rearrangement defines the causal limit, then subtle deviations or entropic thresholds might be observable in extreme conditions (black holes, quantum entanglement formation times, cosmological horizons).

4. Comparison with Other Views

Jacobson (1995): Derived Einstein’s equations as equations of state from thermodynamics.

Verlinde (2011): Proposed gravity as an entropic force.

John Onimisi Obidi (2025): Goes further by proposing a full blown Theory of Entropicity(ToE) to give us a new world view with entropy as the center stage for all phenomena and interactions: Not only are gravity and mass emergent from entropy, but that even the speed of light itself is entropic in origin.

5. In Plain Words

What the Theory of Entropicity(ToE) is saying is:

“The universe cannot rearrange its entropy faster than a certain rate. That rate is what we call the speed of light c.”

This reframes the speed of light(c) as the operational limit of nature’s entropic field, not an arbitrary constant built into spacetime geometry.

What we are saying is that the Theory of Entropicity(ToE) is telling us that the speed of light c is not because of light or the electromagnetic field but because of entropy and the Entropic Field and it happens that light is what we see to physically depict that speed, etc.

We explain the above further here under.

6. In Standard Physics

Electromagnetism: The speed of light arises as the propagation speed of electromagnetic waves in Maxwell’s equations.

Relativity: Einstein elevated this to a universal constant of nature, built into spacetime itself — light was the physical phenomenon that first revealed it, but in relativity is not “about light” alone. It is the invariant speed of all causal influences.

7. In the Theory of Entropicity (ToE)

The Theory of Entropicity(ToE) goes one step deeper:

Entropy as the real substrate:

The universal limit is not because of light or electromagnetism, but because the entropic field has a maximum rate at which it can rearrange or redistribute entropy.

Light as a tracer:

Light — being massless and already “at the edge” of interaction — therefore moves at that entropic limit. So when we measure the speed of light, what we are really seeing is the maximum entropic rearrangement rate in action.

Universality:

That’s why the speed of light c shows up not just in electromagnetism but in gravity, relativity, and quantum field theory. This is because all these processes are bounded by the same entropic field constraint.

So in ToE, light does not “cause” the universal speed — it merely reveals it.

8. Plain Language Analogy

Let us think of it and visualize it this way:

Imagine the entropic field as the “road system of the universe.”

The speed limit on all roads is c.

Light is like the (sports) car that can actually drive right at that limit, while everything else (with mass) drives below it.

The speed limit exists because of the road (entropy field), not because of the car (light).

9. Why This Perspective is Profound

This means the Theory of Entropicity(ToE) is shifting the root explanation of causality:

Relativity: c is geometric, a rule of spacetime.

ToE: c is entropic, a rule of how entropy can change in the universe. Order and disorder cannot be processed and cannot take place Instantaneously, but at a speed that respects the Entropic Speed Limit [ESL] encoded as the speed of light c.

So, in conclusion, we can say that:

In the Theory of Entropicity(ToE), c is not fundamentally “about light.” It is the entropic field’s universal rate limit, and light is just what saturates it — giving us a physical window into entropy’s deepest law.

\[

\int_0^\infty e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}

\]

## No-Rush Theorem (NRT)

### 1. Entropic Time Limit (ETL)

$$\Delta t \;\geq\; \Delta t_{\min} \;>\; 0$$

where $\Delta t_{\min}$ is the Entropic Time Limit (ETL).

---

### 2. Master Entropic Equation (MEE)

$$\frac{\partial S}{\partial t} + \nabla \cdot \mathbf{J}_S = \sigma_S$$

with $\mathbf{J}_S$ the entropy flux and $\sigma_S$ the entropy production density.

---

### 3. Cumulative Delay Principle

$$T_N - T_0 \;\geq\; \Delta t_{\text{tot}} \;\geq\; N \cdot \Delta t_{\min}$$

for a sequence of $N$ interactions between $T_0$ and $T_N$.

---

### 4. Non-Markovian Memory (Entropic Backlog)

$$\frac{d\rho(t)}{dt} = L_0[\rho(t)] + \int_0^\infty \Pi(\tau)\,\rho(t-\tau)\,d\tau$$

where $\rho(t)$ is the system density operator, $L_0$ the instantaneous generator, and $\Pi(\tau)$ the delay distribution.

---

### 5. Formal Statement of the No-Rush Theorem

$$\forall \;\; \text{physical interactions}, \quad

\Delta t \;\geq\; \Delta t_{\min}(S,\nabla S,\ldots)$$

with $\Delta t_{\min}$ determined by the local entropy field $S$ and its gradients.

============

<div style="border:1px solid #aaa; padding:12px; border-radius:6px; background:#fafafa;">

<strong>No‑Rush Theorem (NRT)</strong>

<p><strong>1. Entropic Time Limit (ETL)</strong></p>

$$

\Delta t \ge \Delta t_{\min} > 0

$$

<p><strong>2. Master Entropic Equation (MEE)</strong></p>

$$

\frac{\partial S}{\partial t} + \nabla \cdot \mathbf{J}_S = \sigma_S

$$

<p><strong>3. Cumulative Delay Principle</strong></p>

$$

T_N - T_0 \ge \Delta t_{\text{tot}} \ge N \cdot \Delta t_{\min}

$$

<p><strong>4. Non‑Markovian Memory</strong></p>

$$

\frac{d\rho(t)}{dt} = L_0[\rho(t)] + \int_0^\infty \Pi(\tau)\,\rho(t-\tau)\,d\tau

$$

<p><strong>5. Formal Statement</strong></p>

$$

\forall \ \text{physical interactions}, \quad

\Delta t \ge \Delta t_{\min}(S,\nabla S,\ldots)

$$

</div>