Abstract
Using the concept known as a superstatistics path integral we show that a Wiener process on a short spatial scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Here we place a special emphasis on the modifications that are necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, a previously unsuspected, common statistical origin of the two frameworks is revealed. Salient issues such as generalized commutation relations and a connection with Feynman chessboard model are also discussed.
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