The Phenomenologically symmetric geometry of two sets of rank (3,2)

TL;DR

This paper defines and analyzes a new phenomenologically symmetric geometry of rank (3,2) on two manifolds, inspired by physical laws like Newton's second law and Ohm's law, revealing underlying geometric structures.

Contribution

It introduces a novel phenomenologically symmetric geometry of rank (3,2) and applies a new approach to analyze its structure, connecting it to fundamental physical laws.

Findings

Defined the PS G2S of rank (3,2)

Linked the geometry to Newton's 2nd law and Ohm's law

Provided a new geometric framework for these physical laws

Abstract

A geometry of two sets (GTS) is given on manifolds $\mathfrak{M}$ and $\mathfrak{N}$ by a metric (two-point) function $f:\mathfrak{M\times N}\to R$. Its phenomenological symmetry (PS) means that for some numbers of points from each manifold all the reciprocal distances are tied to some equation. Such simplest geometry on one-dimensional manifolds was discovered by Yu.I. Kulakov when he was analyzing the structure of Newton's 2nd law. In this note the PS G2S of rank (3,2) that springs up in the process of analysis the structure of Ohm's law is precisely defined and analyzed using a new approach.