Probing modified gravity with magnetically levitated resonators

TL;DR

This paper proposes an experimental setup using magnetically levitated resonators to measure gravitational interactions at small scales, aiming to test models of modified gravity with high sensitivity.

Contribution

It introduces a novel levitation-based method for measuring weak gravitational forces between small masses, enabling tests of modified gravity theories.

Findings

Potential to measure gravitational attraction from 30 μg masses

Feasibility of testing modified Newtonian dynamics models

High sensitivity of the proposed experimental scheme

Abstract

We present an experimental procedure, based on Meissner effect levitation of neodymium ferromagnets, as a method of measuring the gravitational interactions between mg masses. The scheme consists of two superconducting lead traps, with a magnet levitating in each trap. The levitating magnets behave as harmonic oscillators, and by carefully driving the motion of one magnet on resonance with the other, we find that it should be easily possible to measure the gravitational field produced by a 4~mg sphere, with the gravitational attraction from masses as small as 30~$\mu$g predicted to be measurable within realistic a realistic measurement time frame. We apply this acceleration sensitivity to one concrete example and show the ability of testing models of modified Newtonian dynamics.