Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity Lee Smolins Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada July 5, 2010 Abstract In deformed or doubly special relativity (DSR) the action of the Lorentz group on momen- tum eigenstates is deformed to preserve a maximal momentum or minimal length, supposed equal to the Planck length, to, = VO. The classical and quantum dynamics of a particle prop- agating in ti-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the Lorentz transfor- mations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here we discuss two issues which may contribute to the resolution of these apparent paradoxes. First it may be that the paradox arises only in the classical picture, because it is inconsistent to study physics in which h = 0 but Ir = R ;‘ 0. Second, there may still be an observer independent notion of a local interaction, which slightly extends the usual notion without coming into conflict with the observed locality of interactions in nature. These considerations may be relevant for phenomenology such as observations by the Fermi observatory, because at leading order in 4 x distance there is both a direct and a stochas- tic dependence of arrival time on energy, due to an additional spreading of wavepackets. lsmolineperimeterinstitute.ca 1 EFTA_R1_01441413 EFTA02403023