  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.
