A geometry of space that satisfies the holographic principle

TL;DR

This paper demonstrates that the holographic principle implies that any finite region of 3-space contains only a finite number of points, challenging the traditional view of continuous space.

Contribution

It establishes a logical equivalence between the holographic principle and the finiteness of points in a spatial region, proposing a geometric framework consistent with holography.

Findings

Holographic principle implies finite points in any spatial region.

Continuous 3-space with infinite points contradicts holography.

Finite point count aligns with holographic constraints.

Abstract

Conventional wisdom holds that any region of 3-space contains infinitely many points, and the Planck length scale determines the uncertainty in every measurement of distance between two separate points. Against such a backdrop, this uncertainty may be interpreted as resulting from either foaminess or discreteness of 3-space. But, as it is demonstrated in the present paper, neither of those interpretations is consistent with the holographic principle. In the paper it is shown that the statement ``The holographic principle holds true'' and the statement ``Each region in 3-space contains only a finite number of points'' are logically equivalent.