The holographic principle comes from finiteness of the universe's geometry

TL;DR

This paper explains the holographic principle as a consequence of the finite number of points in the universe's geometry, linking it to the discretization of space at the Planck scale and the projection of surface points inward.

Contribution

It demonstrates that the holographic principle originates from the finite point set of the universe's geometry and the magnification of discretized grid cells.

Findings

The universe's geometry has a finite number of points.

Holographic relation arises from surface-to-volume projection.

Discretization at Planck scale explains holographic behavior.

Abstract

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe's surface.