Scale Free Small World Networks and the Structure of Quantum Space-Time

Abstract

We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and their theoretical analysis. The other is a discrete cellular network approach to quantum space-time physics on the Planck scale we developed in the recent past. In this context we formulated a kind of geometric renormalisation group or coarse graining process in order to construct some fixed point which can be associated to our macroscopic space-time (physics). Such a fixed point can however only emerge if the network on the Planck scale has very peculiar critical geometric properties which strongly resemble the phenomena observed in the above mentioned networks. A particularly noteworthy phenomenon is the appearance of translocal bridges or short cuts connecting widely separated regions of ordinary space-time and which we expect to become relevant in various of the notorious quantum riddles.