(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

Abstract

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.

35 pages, Latex, under consideration by CQG

References in corpus (3)

• Cellular Networks as Models for Planck-Scale Physics
• Pregeometric Concepts on Graphs and Cellular Networks as Possible Models of Space-Time at the Planck-Scale
• Space-Time as an Orderparameter Manifold in Random Networks and the Emergence of Physical Points

Cited by in corpus (16)

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• (Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
• Statistical Mechanics of Graphity Models
• A Geometric Renormalisation Group in Discrete Quantum Space-Time
• The Continuum Limit of Discrete Geometries
• The running of the Universe and the quantum structure of time
• Emergent Space-Time via a Geometric Renormalization Method
• Let's call it Nonlocal Quantum Physics
• Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs
• Scale Free Small World Networks and the Structure of Quantum Space-Time
• Wormhole Spaces: the Common Cause for the Black Hole Entropy-Area Law,the Holographic Principle and Quantum Entanglement
• Relational interpretation of the wave function and a possible way around Bell's theorem
• Multicoloured Random Graphs: Constructions and Symmetry
• Wormhole Spaces, Connes' "Points, Speaking to Each Other", and the Translocal Structure of Quantum Theory
• Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional
• A dynamical evolution model on the black hole horizon