Noninteger dimensionality, nonlocal noise and self-decoherence

This paper argues that noninteger dimensionality creates a hitherto unexplored source of nonlocal noise, called ND noise or NDN, that is likely to play a role in measurements at very small distances. New analysis on scale invariant probability distributions arising from noninteger dimensionality is presented. The significance of this when considering performance and noise-correction coding in models of quantum computing is indicated. It is argued that NDN noise will lead to decoherence even without interaction with the environment and it is likely to be relevant also in models of cognition.