ANNUAL REPORT 2005 - Universiteit Utrecht

ANNUAL REPORT 20052 Scientific highlightsperturbative methods unsuitable, the system can be investigated numerically withMonte Carlo methods. Thirdly, and somewhat unusually in this area of research, theapproach has produced some new and unexpected results.Figure 2.2: In the described quantum gravity theory, the dimension of spacetimechanges smoothly from 2 to 4 dimensions. Also the Dutch artist M.C. Escher wasfascinated by such transitions in dimensionality.Understanding the geometric and physical properties of the quantum spacetime generatedby the method is a challenging task. Most recently, a surprising result wasfound by studying a diffusion process on the quantum-fluctuating spacetime: its spectraldimension, which characterizes how other fields will propagate in it, turns out tobe scale-dependent, an effect not previously observed in quantum gravity. At largedistances, this dimension is four, as one would expect from a quantum gravity theorywith the correct classical limit. However, at short distances, where quantum effectsdominate, it is found to be close to two, with further indications that spacetime atand below this so-called Planck scale has a fractal structure [2]. This is exciting