Measurement of Gravitational Coupling between Millimeter-Sized Masses

TL;DR

This paper reports the first measurement of gravitational coupling between millimeter-sized gold spheres, demonstrating the ability to detect gravity at microscopic scales with high precision over extended periods.

Contribution

It introduces a novel experimental setup capable of measuring gravitational interactions between millimeter-scale masses with unprecedented accuracy.

Findings

Successful detection of gravitational coupling at 400μm separation

Achievement of systematic accuracy of 4×10⁻¹¹ m/s²

Observation of both linear and quadratic gravitational signals

Abstract

We demonstrate gravitational coupling between two gold spheres of approximately 1mm radius and 90mg mass. By periodically modulating the source mass position at a frequency f=12.7mHz 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 4E-11m/s^2 and a statistical precision of 4E-12m/s^2. This is sufficient to resolve the gravitational signal at a minimal surface distance of 400mum 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.