Space tests of the generalized uncertainty principle

Abstract

A generalized uncertainty principle admitting a minimal measurable length contains a parameter of which the numerical value needs to be fixed. In fact, the application of the Generalized Uncertainty Principle (GUP) to some quantum mechanical problems offers different values for the upper bound of the GUP dimensionless parameter $\alpha_{0}$. In this work, by applying a GUP which is linear and quadratic in the $\Delta P$ correction to Newton’s law of gravity, and then using the stability condition of the circular orbits of the planets, we propose an upper bound for $\alpha_{0}$. By using the astronomical data of the Solar System objects, a new and severe constraint on the upper bound of the parameter $\alpha_{0}$ is derived. Also, using the modified Newtonian potential, inspired by a GUP which is linear and quadratic in $\Delta P$, we investigate the possibility of measuring the relevant parameter $\alpha_{0}$ through observables provided by the Galileo Navigation Satellite System.