Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

Abstract

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length, ${l_p = \sqrt{\hbar G}}$. The classical and quantum dynamics of a particle propagating in κ-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 transformations 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 it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which ${\hbar =0}$ but ${l_p = \sqrt{\hbar G}\neq 0}$. This may be relevant for phenomenology such as observations by FERMI, because at leading order in l _p × distance there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.