Eur. Phys. J. C (2013) 73: 2491
https://doi.org/10.1140/epjc/s10052-013-2491-x

Letter

Special relativity induced by granular space

¹ FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague 1, Czech Republic
² ITP, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
³ Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan
⁴ Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

^* e-mail: p.jizba@fjfi.cvut.cz

Received: 20 May 2013
Published online: 6 July 2013

Abstract

We show that the special relativistic dynamics, when combined with quantum mechanics and the concept of superstatistics, can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This framework leads to Feynman amplitudes that are, in the Euclidean regime, identical to the transition probability of a Brownian particle propagating through a granular space. For illustration we consider the dynamics and the propagator of a Klein–Gordon particle. Implications for deformed special relativity, quantum field theory, quantum gravity and cosmology are also discussed.