The Alemoh-Obidi Correspondence (AOC): Daniel Alemoh's Central Contribution to the Theory of Entropicity (ToE): The Question of c

The Alemoh-Obidi Correspondence (AOC): Daniel Alemoh's Central Contribution to the Theory of Entropicity (ToE): The Question of c

Among the most consequential themes in the Alemoh-Obidi correspondence is the question of the speed of light. Daniel Alemoh identified early in the exchanges that the Theory of Entropicity does not regard c as a primitive constant of nature — a fixed parameter embedded in the structure of Lorentz symmetry and the geometry of Minkowski spacetime — but rather as an emergent quantity, a limit imposed by the finite rate at which the entropic field can redistribute its content [33].

This is a radical departure from the Einsteinian framework. In special relativity, c is the invariant speed — the same in all inertial frames — and its constancy is elevated to the status of a postulate. In general relativity, c remains fundamental: it appears in the Einstein field equations, in the definition of the metric signature, and in the structure of the light cone that determines causal ordering. To suggest that c is emergent rather than fundamental is to suggest that the very architecture of Lorentz symmetry is itself a consequence of a deeper entropic structure.

The ToE position on c may be stated as follows:

c = maximum current rate of entropic redistribution (8)

This equation asserts that the speed of light is not a geometric constant but a dynamical ceiling — the maximum rate at which the entropic field can transfer information, energy, or configurational content from one region to another. The observed numerical value of c ≈ 3 × 10⁸ m/s reflects the specific properties of the current cosmic entropic phase: the entropy density, the field responsiveness, and the topological connectivity of the entropic manifold in the present epoch.

Daniel Alemoh's decisive contribution to this theme came in the form of a question that penetrated to the deepest structural issue of any emergent-space theory:

 

"If space itself emerges from the entropic field, what does cosmic expansion mean when the recession velocity of distant galaxies exceeds c?"

 

This question is technically deep. It is not a naive confusion between velocity and expansion; it is a probe of whether ToE can consistently maintain that c is a universal causal limit while simultaneously accounting for the observed fact that galaxies beyond the Hubble sphere recede at superluminal velocities. In standard cosmology, this is resolved by distinguishing between the velocity of objects through space (which is limited by c) and the expansion of space itself (which is not). But if space is emergent from the entropic field, this distinction must be rederived — and its validity is not guaranteed.

5.1 The Two-Layer Resolution: Propagation vs. Background Evolution

The resolution developed in the correspondence — and subsequently formalized in the published Letters — involves the recognition that the entropic field supports two categorically distinct dynamical processes [5, 33, 34]:

Layer I — Internal Propagation: This layer encompasses all processes that involve the transmission of information, energy, or physical influence through the entropic field: particles, photons, causal signals, local forces, and measurement chains. All such processes are constrained by the entropic transfer ceiling:

v ≤ c_ent (9)

where c_ent is the local value of the entropic speed limit, determined by the local properties of the entropic field. No information can be transmitted faster than the entropic field can process it. This is the content of the No-Rush Theorem, and it is the ToE analog of the light-speed limit of special relativity.

Layer II — Background Manifold Evolution: This layer encompasses processes that involve changes in the structure of the entropic manifold itself: cosmological scaling, entropy vacuum restructuring, relational node growth, and topological re-indexing. These processes are not signal transmissions; they are changes in the field architecture from which space is inferred. The expansion of the universe is not a motion of galaxies through space; it is a reconfiguration of the entropic manifold that increases the relational distances between entropic nodes without any local signal exceeding c_ent.

The distinction is precise: Layer I dynamics are governed by the wave equation on the entropic manifold; Layer II dynamics are governed by the evolution equation of the manifold itself. These are different equations with different causal structures, and there is no contradiction in the former being bounded while the latter is not.