Abstract
This paper addresses a simple question: how small can one make a gravitational source mass and still detect its gravitational coupling to a nearby test mass? We describe an experimental scheme based on micromechanical sensing to observe gravity between milligram-scale source masses, thereby improving the current smallest source mass values by three orders of magnitude and possibly even more. We also discuss the implications of such measurements both for improved precision measurements of Newton’s constant and for a new generation of experiments at the interface between quantum physics and gravity.
Highlights
Measuring gravitational forces between non-celestial bodies started with the pioneering experiments of Maskelyne [1] and Cavendish [2] and has remained a challenging task ever since
We provide an outlook on future possible applications of such an apparatus for improved precision measurements of Newton’s constant and for a new generation of experiments at the interface between quantum physics and gravity, in which the quantum system itself can act as a gravitational source mass
We have introduced a micromechanical method to measure gravitational coupling between small masses
Summary
Measuring gravitational forces between non-celestial bodies started with the pioneering experiments of Maskelyne [1] and Cavendish [2] and has remained a challenging task ever since. Let us consider a spherical mass, say a 1 mm radius lead sphere (m » 40 mg), trapped harmonically at a frequency of wm = 100 Hz with a quality factor of Q = 10 000 at room temperature (T = 300 K) This results in a thermal noise limit of Fth » 1 ́ 10-14 N, which corresponds to the gravitational force exerted by a mass of the same size separated by 3 mm in distance. As an order of magnitude estimate, it suggests that in principle it should be possible to exploit the sensitivity of state-of-the-art micro-mechanical devices to measure gravity between mm-sized objects of mg-scale mass, possibly even below that Note that this is different from experiments that probe possible deviations from Newtonian gravity at short distances and that involve small source masses [16, 17]. We provide an outlook on future possible applications of such an apparatus for improved precision measurements of Newton’s constant and for a new generation of experiments at the interface between quantum physics and gravity, in which the quantum system itself can act as a gravitational source mass
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