Particle processes in a discrete spacetime and GW170814 event

Abstract

Standard quantum mechanics is not capable of solving properly the Planck scale problems. A quantum theory of spacetime, Quantum Gravity, which could be in essence a combination of general relativity and quantum mechanics, is necessary to address the Planck scale phenomena. Natural cutoffs as fundamental characteristics of quantum spacetime are phenomenological outcomes of approaches to quantum gravity proposal. These natural cutoffs are encoded as a minimal length, a maximal momentum and a minimal momentum. These are indeed technically related to compactness of corresponding symplectic manifold in Snyder noncommutative phase space. Here we focus on the issue of particle processes and photon’s propagation in the presence of all natural cutoffs. We firstly derive a modified dispersion relation encoding these cutoffs in a massive particle process and then pay our attention to the massless photon’s dispersion relation. As a novel achievement, we show that photon’s propagation, in addition to photon’s energy, depends also on the position due to existence of a minimal measurable momentum. This novel position dependence of quantities in this framework provides new physics in the infrared regime of the background gravitational theory. We also consider frequency at the peak GW strain based on event GW170814 and investigate the possible constraints on the model parameters in this setup by treating graviton’s group velocity.