A geometry of space that satisfies the holographic principle

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.

arXiv comment12 pages