The Holographic Principle Explained by the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE), formulated by John Onimisi Obidi, explains holography by positing that entropy, 

$S\left(x\right)$

, is not merely a measure of disorder, but the fundamental, dynamic, physical field from which spacetime, geometry, and physical laws emerge. Instead of treating holography as a specialized correspondence between a bulk and a boundary, ToE interprets it as a direct consequence of entropic information being encoded in the boundary behavior of this universal entropic field. 

Here is how ToE explains holography: 

• Entropy as the Fundamental Substrate: ToE redefines reality as an entropic, rather than geometric, system. It posits that information content within a 3D bulk volume is encoded in the 2D boundary surface, not as a purely spatial arrangement, but as an encoding within the "boundary behavior of the entropic field" (
  

  $S\left(x\right)$
  ).
• Geometric Emergence (Entropic Holography): ToE proposes that spatial geometry arises from gradients in the entropy field, with higher-order entropic curvature corrections (denoted by
  

  $\alpha$
  ) dictating the relationship between area and entropy. The holographic entropy bound is thus a direct result of this entropic field geometry, where the maximum entropy (
  

  $S_{Holo}$
  ) in a region is
  

  $k_B{c}^{3}A/4G\hslash$
  multiplied by a correction factor.
• Reinterpreting AdS/CFT: ToE considers conventional holography (such as AdS/CFT) as a specialized, lower-dimensional "shadow" or subset of a deeper,, more comprehensive entropic field theory. ToE goes beyond simple AdS/CFT, providing a framework for "Entropic Holographic Quantum Gravity" (HQEG) that operates in a 5D bulk, treating gravity and quantum mechanics as emergent from this entropic flow.
• Dynamic Information Flow: The theory uses the "Obidi Action" (a variational principle) to show that what we perceive as 3D gravity is an emergent manifestation of 2D entropy flow and "entanglement," which acts as a "boundary manifestation" of the deeper entropic dynamics.
• The No-Rush Theorem: ToE links holography to causality via the "No-Rush Theorem," which dictates that information cannot be processed faster than the entropic field can redistribute it, setting a "maximum entropic rearrangement rate" (
  

  $c_E$
  ) that corresponds to the speed of light. 

In summary, ToE interprets the holographic principle as a consequence of the universe being an "accounting mechanism" for entropy, where the 3D world is generated by the 2D boundary encoding of the underlying entropic field.