Local and Global Properties of the World

TL;DR

This paper explores the relationship between local and global properties in physics, proposing that noncommutative geometry offers a promising framework to understand the transition from pregeometry to spacetime at the Planck scale.

Contribution

It introduces noncommutative geometry as a novel approach to unify local and global properties in physics, especially in quantum gravity and pregeometry theories.

Findings

Noncommutative spaces are inherently non-local.

Noncommutative geometry provides conceptual insights into quantum gravity.

A transition from pregeometry to spacetime may occur at the Planck scale.

Abstract

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the necessity of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a ``noncommutative pregeometry'', and only when crossing this threshold the usual space-time geometry emerges.