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.