Generalized Uncertainty Principle, Classical Mechanics, and General Relativity

Physics Letters B, vol. 807, pp. 135558

Abstract

The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out here that the two effects are mutually exclusive when compared with experimental bounds. Moreover, the former stems from modified Poisson brackets obtained from a wrong classical limit of the deformed canonical commutators.

Authors 2

1. Roberto Casadio A corresponding

   Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · University of Bologna

   Affiliation as printed

   Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna, via Irnerio 46, 40126 Bologna, Italy

   I.N.F.N., Sezione di Bologna, IS FLAG viale B. Pichat 6/2, I-40127 Bologna, Italy

2. Fabio Scardigli Aachen Institute-Lorentz for Theoretical Physics

   Leiden University · Politecnico di Milano

   Affiliation as printed

   Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

   Institute-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, Leiden, the Netherlands