Measurement of Gravitational Coupling between Millimeter-Sized Masses

Abstract

We demonstrate gravitational coupling between two gold spheres of radius r ≈ 1 mm and mass m ≈ 90 mg. By periodically modulating the source mass position at a frequency f mod = 12.7 mHz we generate a time-dependent gravitational acceleration at the location of the test mass, which is measured off resonance in a miniature torsional balance configuration. Over an integration time of 350 hours the test mass oscillator enables measurements with a systematic accuracy of 4×10 −11 m/s 2 and a statistical precision of 4 × 10 −12 m/s 2 . This is sufficient to resolve the gravitational signal at a minimal surface distance of 400 µm between the two masses. We observe both linear and quadratic coupling, consistent in signal strength with a time-varying 1/r gravitational potential. Contributions of non-gravitational forces could be kept to less than 10 % of the observed signal. We expect further improvements to enable the isolation of gravity as a coupling force for objects well below the Planck mass. This opens the way for precision tests of gravity in a new regime of isolated microscopic source masses.

On Lorentz invariant complex scalar fields

“…Moreover, by tuning the values of the charges q and Q, we can also obtain manageable values for the masses m and M that might lead to an experimental test of Eq. (208) if we build on stateof-the-art experimental techniques that can detect the gravitational attraction between millimeter-sized particles with masses of the order of 100 mg [24].…”

Searching for Chameleon Dark Energy with Mechanical Systems

“…We then discuss two classes of spherical mechanical systems: levitated microspheres and Cavendish-style torsion balances. Both systems have demonstrated exceptional sensitivity to weak forces [33][34][35] and there has been some work considering microspheres as potential probes for scalar and screened-scalar fields [36][37][38][39]. Using a novel analytical treatment allowing us to consider systems with larger masses, we show that for both mechanical systems, the current generation of experiments have the sensitivity to put new constraints in a region of interest to cosmology, possibly ruling out chameleons as DE.…”

“…To supplement the potential constraints from levitated microspheres, we also consider torsion balances, whose larger test masses enable them to probe weaker chameleon-matter couplings (larger M). A simple Cavendish-style torsion balance [35] consists of equally-sized spheres, connected by a rod of negligible mass, which is suspended at its center by a torsion fiber and placed in a vacuum chamber. One of the spheres serves as the test mass M 2 , while the balance as a whole forms a harmonic oscillator with effective mass m 0 ≈ 2M 2 and quality factor Q 0 = 2π f 0 /Γ 0 .…”

“…One of the spheres serves as the test mass M 2 , while the balance as a whole forms a harmonic oscillator with effective mass m 0 ≈ 2M 2 and quality factor Q 0 = 2π f 0 /Γ 0 . Westphal et al [35] have demonstrated that such torsion balances have the ability to make measurements near the thermal limit, achieving piconewton / √ Hz force sensitivity. In Figs.…”

“…A common component in torsion balance experiments is an electromagnetic shield placed between the source and test masses [31,35]. These shields can also be used to control Casimir forces which are relevant for the geometries proposed here [39,47].…”