Special Relativity induced by Granular Space

TL;DR

This paper proposes that special relativity can emerge from non-relativistic stochastic processes in granular space, linking quantum mechanics, superstatistics, and spacetime granularity to fundamental physics phenomena.

Contribution

It introduces a novel interpretation of relativistic dynamics as arising from interlocked non-relativistic stochastic processes at different energy scales, connecting granular space to relativistic symmetries.

Findings

Feynman amplitudes match transition probabilities in granular space

Spacetime granularity may explain emergence of symmetries

Implications discussed for quantum gravity and cosmology

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 interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.