Pregeometric Concepts on Graphs and Cellular Networks as Possible Models of Space-Time at the Planck-Scale

Abstract

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of the building blocks of continuum physics and mathematics. In the following we embark on developing such concepts for irregular structures like (large) graphs or networks which are intended to emulate (some of) the generic properties of the presumed combinatorial substratum from which continuum physics is assumed to emerge as a coarse grained and secondary model theory. We briefly indicate how various concepts of discrete (functional) analysis and geometry can be naturally constructed within this framework, leaving a larger portion of the paper to the systematic developement of dimensional concepts and their properties, which may have a possible bearing on various branches of modern physics beyond quantum gravity.

16 pages, Invited paper to appear in the special issue of the Journal of Chaos, Solitons and Fractals on: "Superstrings, M, F, S ... Theory" (M.S. El Naschie, C. Castro, Editors)

References in corpus (2)

• Dimension Theory of Graphs and Networks
• The future of spin networks

Cited by in corpus (6)

• (Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
• Cellular Networks as Models for Planck-Scale Physics
• (Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks
• A Geometric Renormalisation Group in Discrete Quantum Space-Time
• Space-Time as an Orderparameter Manifold in Random Networks and the Emergence of Physical Points
• Positive expansiveness versus network dimension in symbolic dynamical systems