P-Structures, P-Geometry and Observer's Perceptive Space

TL;DR

This paper develops a mathematical framework for an observer's perceptive space based on P-structures and P-geometry, extending reference frames in general relativity and linking physical invariance to geometry.

Contribution

It introduces P-structures and P-geometry as new concepts for describing physical invariance and observer's perceptive space, generalizing existing reference frame theories in GR.

Findings

Experimental data on observer's visual space geometry

Affine model of visual geometry for data interpretation

Discussion of implications for theoretical physics

Abstract

Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure (P-structure) and corresponding physical geometry (P-geometry) notions, representing properties invariance of some physical objects and their relations, are introduced. P-structure of classical physical time and its corresponding chronogeometry is considered as an example. Some quantitative characteristics of observer's visual space geometry are experimentally determined. The affine model of visual geometry is offered to interpret experimentally sampled data. The connection of the obtained results with some problems of theoretical physics is being discussed.