Geometry, pregeometry and beyond

Abstract

This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the pseudo-Riemannian manifold of general relativity is considered a flawed description of spacetime and it is attempted to replace it by theoretical constructs of a different character, ontologically prior to it. However, despite its claims to the contrary, pregeometry is found to surreptitiously and unavoidably fall prey to the very mode of description it endeavours to evade, as evidenced in its all-pervading geometric understanding of the world. The question remains as to the deeper reasons for this human, geometric predilection-present, as a matter of fact, in all of physics-and as to whether it might need to be superseded in order to achieve the goals that frontier theoretical physics sets itself at the dawn of a new century: a sounder comprehension of the physical meaning of empty spacetime.

Emergent Complex Network Geometry

“…In the apparently unrelated field of quantum gravity, pregeometric models, where space is an emergent property of a network or of a simplicial complex, have attracted large interest over the years 36 37 38 39 40 41 42 43 . Whereas in the case of quantum gravity the aim is to obtain a continuous spacetime structure at large scales, the underlying simplicial structure from which geometry should emerge bears similarities to networks.…”

Romanian Studies in Philosophy of Science

“…There are several suggestions and models for a "pregeometry" (a term introduced by Wheeler) that are currently actively investigated (see e.g. Meschini et al 2005 for a non-technical review). This is a question of ongoing investigation and debate, and several research programs in quantum gravity (loops, spinfoams, noncommutative geometry, dynamical triangulations, etc.)…”

Planck-Scale Physics: Facts and Beliefs

“…constants are relevant to the problem. 8 Armed with previous physical experience, one notices that only quantum mechanics and the electrodynamics of the electron are involved, so that the constants to consider must be h, the electron's charge e, the electron's mass m e , and the permittivity of vacuum ǫ 0 . Equipped with these constants, one proposes…”