Light Cone in a Quantum Spacetime

Abstract

Noncommutative spacetimes are a proposed effective description of the low-energy regime of Quantum Gravity. Defining the microcausality relations of a scalar quantum field theory on the $κ$-Minkowski noncommutative spacetime allows us to define for the first time a notion of light-cone in a quantum spacetime. This allows us to reach two conclusions. First, the majority of the literature on $κ$-Minkowski suggests that this spacetime allows superluminal propagation of particles. The structure of the light-cone we introduced allows to rule this out, thereby excluding the possibility of constraining the relevant models with observations of in-vacuo dispersion of Gamma Ray Burst photons. Second, we are able to reject a claim made in [Phys. Rev. Lett. 105, 211601 (2010)], according to which the light-cone of the $κ$-Minkowski spacetime has a "blurry" region of Planck-length thickness, independently of the distance of the two events considered. Such an effect would be hopeless to measure. Our analysis reveals that the thickness of the region where the notion of timelike and spacelike separations blurs grows like the square root of the distance. This magnifies the effect, e.g. in the case of cosmological distances, by 30 orders of magnitude.