POINTLESS SPACES IN GENERAL RELATIVITY

TL;DR

This paper proposes a novel approach to quantize gravity using differential algebra, emphasizing the non-point-like nature of geometric structures in general relativity and exploring the implications of spatialization.

Contribution

It introduces a differential algebra framework for quantum gravity that challenges the traditional point-based differential geometry.

Findings

Differential algebra cannot be described in terms of points.

Spatialization leads to loss of geometric structure.

Traditional differential geometry objects are reinterpreted.

Abstract

The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise to points by loosing a part of the entire structure is discussed. The counterpart of the traditional objects of differential geometry are studied.