Emergent Lorenz Symmetry in Quantum Mechanics and Doubly Special Relativity

Department of Physics
National Taiwan University
Taipei - Taiwan

In this talk we show how a classical Brownian motion on a short scale can originate a relativistic motion on scales 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. We also present the modifications necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, an unsuspected, common statistical origin of the two frameworks is brought to light for the first time. Salient issues such as generalized commutation relations, Hausdorff dimensions of path-integral trajectories, and a connection with graphene theory are also discussed.

Reference paper: arXiv: 1105.3930