Granular universe: statistical origin of special and doubly special relativity

Abstract

Abstract. We present a new theoretical evidence that a relativistically invariant quantum dynamics at large enough space-time scales can be derived from two inter-correlated genuinely non-relativistic stochastic processes that operate at different energy scales. This leads to Feynman amplitudes that are, in the Euclidean regime, identical to transition probability of a Brownian particle propagating through a granular space. Our observation implies a preferred frame and can have distinct experimental signatures. Ensuing implications for special and doubly-special relativity, quantum field theory, quantum gravity and cosmology are discussed.