Universality of free fall in Planck-scale deformed Newtonian gravity

TL;DR

This paper addresses whether the weak equivalence principle survives Planck-scale deformations in a Newtonian/Galilean regime of doubly special relativity (DSR). By performing a Wigner–Inönü contraction of the κ-Poincaré algebra, the authors derive a deformed Galilean symmetry with deformation parameter ε = m/μ and construct a three-body Hamiltonian for two test masses in the field of a classical Earth, including a symmetry-invariant, Planck-scale–corrected Newtonian potential. They find that, in general, free-fall universality is violated, but a special class of models with h = −(1+2α) can preserve universality, which requires a modified Newtonian potential; they also analyze frame dependence and show that, in the absence of gravity, time delays vanish, ensuring consistency. The results impose nontrivial constraints on Planck-scale gravity phenomenology and motivate further work toward fully relativistic formulations and experimental tests of deformed gravitational dynamics.

Abstract

The universality of free fall is one of the most cherished principles in classical gravity. Its fate in the quantum world is one of the key questions in fundamental physics. We investigate the universality of free fall in the context of Planck scale modifications of Newtonian gravity. Starting from a doubly-special-relativity setting we take the Newtonian limit to obtain deformed Galilean relativity. We study the interaction between two test particles, subject to deformed Galilean relativity, and a classical, undeformed gravitational source, the Earth. Such an interaction is investigated here for the first time. Considering the two test particles falling freely in the source's gravitational field, we examine whether the universality of free fall is affected by deformed relativistic symmetries. We show that, in general, the universality of free fall is violated. Remarkably, we find that there exist distinguished models for which the universality of free fall is realized and which predict a specific modification of the Newtonian potential.

Figures (1)

• Figure 1: Sketch of the positions of the origins of the reference frames used in the main text.