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

Arkady Bolotin
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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.
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全息原理源于宇宙几何的有限性
几何与信息之间的一种普遍关系--全息原理--作为一种明显的模式被发现,但尚未得到解释。本文阐述了这种关系。本文证明,全息原理的起源在于物理空间的几何图形只有有限个点。此外,本文还证明,全息原理的困惑可以用网格单元的放大来解释,网格单元用于将诸如面积和体积等几何量离散化为点集。也就是说,当普朗克尺度的网格单元从可观测宇宙的表面投射到其内部时,它们就会被放大。因此,可观测宇宙内部的空间是由点集来描述的,而点集的数量等于构成宇宙表面的点数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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