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

TL;DR

This paper explores classical paradoxes of locality in deformed special relativity and suggests that quantum effects may resolve these paradoxes, with implications for high-energy astrophysical observations.

Contribution

It proposes that locality paradoxes in DSR are classical artifacts and can be resolved by considering quantum dynamics, highlighting the importance of quantum effects in Planck-scale physics.

Findings

Classical locality paradoxes depend on observer frame.

Quantum dynamics can resolve these paradoxes.

Implications for astrophysical observations like FERMI.

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. The classical and quantum dynamics of a particle propagating in kappa-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 Planck's constant is zero but the Planck length is non-vanishing. This may be relevant for phenomenology such as observations by FERMI, because at leading order there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.