The Ulianov Sphere Network - A Digital Model for Representation of Non-Euclidean Spaces

Abstract

Policarpo Yoshin Ulianov

This article introduces a new model for the non-Euclidean spaces’ representation, in which the coordinates and distances are considered as digital nature. This model, called the Ulianov Sphere Network (USN), presents a new way for visualizing the curved spaces, such as those defined in the context of the General Relativity Theory (GRT).

The USN model has the potential to facilitate the calculation procedures concerning the problems handled by the GRT, since it relies on a very simple mathematical formulation, which can be easily implemented in numerical computing systems.

The proposed model is a mathematical tool that facilitates the manipulation of non-Euclidean spaces, for the simple expedient of constructing over a continuous plain space, a network of hyperspheres that behaves as a non-Euclidean digital space.

Initially, the USN model has no real connection with the observed physics in our universe, being basically a theoretical abstraction. However, as will be shown in this article, the application of the UNS model allows inferring some formulas related to the GRT and also with Newton’s Law of Gravitation. Thus, the hypothesis that the USN model is actually somehow related to the physical basis of operation in our universe is not discarded.

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