(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

Abstract

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.

25 pages, Latex, no figures, some references added, some minor changes added relating to previous work

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• Strings, loops and others: a critical survey of the present approaches to quantum gravity
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• (Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks
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• About the Minimal Resolution of Space-Time Grains in Experimental Quantum Gravity
• A dynamical evolution model on the black hole horizon
• A metageometric enquiry concerning time, space, and quantum physics
• Planck Scale Physics, Pregeometry and the Notion of Time
• On the dynamics between gravity and entanglement