Speaker
Prof.
Petr Jizba
(Czech Technical University of Prague)
Description
In this talk I will show how a Brownian motion on a short scale can originate a relativistic motion on scales that larger than particle's Compton wavelength. I start by discussing complex dynamical systems whose statistical behavior can be explained in terms of a superposition of simpler underlying dynamics ? the so-called superstatistics paradigm. Then I go on by showing that the combination of two cornerstones of contemporary physics ? namely Einstein?s special relativity and quantum-mechanical dynamics is mathematically identical (when analytically continued to Euclidean regime) to a complex dynamical system described by two interlocked processes operating at different energy scales. The combined dynamic obeys special and doubly special relativity even though neither of the two underlying dynamics does. This implies that Einstein's special relativity might well be an emergent concept in the quantum realm. To model the double-stochastic process in question, I consider quantum mechanical dynamics in a background space consisting of a number of small crystal-like domains varying in size and composition, known as polycrystalline space (or Voronoi tessellation). There, particles exhibit a Brownian motion. The observed relativistic dynamics then comes solely from a particular grain distribution in the polycrystalline space. In the cosmological context such distribution might form during the early universe?s formation. Salient issues such as Hausdorff dimensions of path-integral trajectories, connection with Feynman chessboard model and implications for quantum field theory and cosmology (leptogenesis) will be also briefly discussed.
