Hypothesis on the Nature of Time

Abstract

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behaviour is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.