Current Searches for non-Newtonian Gravity

at Sub-mm Distance Scales

Riley Newman, University of California at Irvine
Preface: The possibility that ``large" compact dimensions may have a detectable effect on the gravitational force at small distances has stimulated many new experiments (see the previous article in this issue of MOG). A short sketch of activity in this field seemed desirable - of interest to general readers, and of potential use to current practitioners. I have found writing this to be a delicate matter, however. Several groups have understandably been hesitant to make public their activity or plans at this stage - I thank those that consented to go public for this report, and respect the wish of others not to be publicized at this time.

The Report:

John Price ( and his postdoc Josh Long at the University of Colorado are developing an apparatus [1] in which a vibrating reed source mass is driven at the resonant frequency (approximately 1 kHz) of a  tungsten plate torsion oscillator separated from it by a gold-plated thin sapphire shield for electrostatic shielding.  Capacitive readout of the torsion oscillator amplitude is used.  The system operates now at room temperature, later to be at 4K. Mass separations from about 0.1 to 1 mm will be explored, with a target peak sensitivity about 1% of gravity at a range of about 0.3 mm, and  equal to gravity at 0.05 mm.

The Padua Group (eg, measures the influence of a stainless steel source mass on the resonance frequency of a piezo-driven silicon cantilever beam monitored by an optical fiber interferometer. An earlier version of this experiment [2] put a limit on a non-Newtonian force at a level of $8 \times 10^7$ of gravity at 0.2 mm. Analysis of results from the current version are underway; Ruoso estimates that the current system is capable of sensitivity at best about 106 of gravity; this may be improved in future modifications of the experiment.

John Lipa ( with S. Wang has built an apparatus at Stanford which, like the current version of the Padua experiment, searches for frequency pulling of a mechanical resonator as a function of field source mass position. A 6.4 mm diameter tungsten disk is attached to a torsional oscillator with resonant frequency 145 Hz and Q 1500, driven capacitively with a phase-locked loop circuit which tracks its resonant frequency. The source mass is a 50 mm diameter tungsten disk, moved at intervals of 20 minutes so that it is alternately 0.1 mm and 1 mm from the test mass. The current sensitivity of the system, operating at room temperature, corresponds to a force magnitude at 0.1 mm less than 105 of gravity. A low temperature version of the system is being considered.

Aharon Kapitulnik ( with Tom Kenny is operating a system at Stanford with the following design: A test mass is mounted on a cantilever with very low spring constant ( <10-4 N/m) within electrostatic shielding, with optical fiber interferometer readout. The source mass is in the form of five squares of mass of alternating specific weight (Al and W), caused to swing periodically laterally about 0.4 mm by a bimorph device. To generate the force signal of interest, the bimorph oscillates at a frequency which is one third of the cantilever's resonance frequency, allowing excellent inertial decoupling. The range of mass separations to be explored is expected to be 0.03 - 0.5 mm. The ultimate sensitivity of the present apparatus design, at 4.2 K, is expected to be better than 5% of gravity at 0.08 mm. Other designs will be explored in the future.

Eric Adelberger ( with Blayne Heckel is doing an experiment at the University of Washington using a planar torsion balance that sits above a rotating attractor. The apparatus is not yet completed. Eric's group hopes to be able to probe with good sensitivity force ranges from 0.05 to 2 mm, and expects to have some results in about a year if unexpected problems are not encountered.

Paul Boynton (, Michael Moore, and graduate student Micah Ledbetter at the University of Washington are considering an experiment in which the signature of non-Newtonian gravity is a torque on a near-planar torsion pendulum suspended above a near-planar source mass. The signal torque is manifested as a second harmonic distortion of the torsional oscillation of the pendulum. The source and pendulum masses are each to be made with opposing halves at a slightly different elevation, in a configuration which gives a nearly null signal for purely Newtonian gravity. Source and test masses are to be separated by a conducting membrane in the gap between them. The expected sensitivity to an anomalous force is at a level of 0.25 of gravity at 0.25 mm and 10-2 of gravity at 1 mm, limited by machining tolerance.

Ho Jung Paik ( at the University of Maryland has proposed to NSF a mm-scale test for non-Newtonian gravity. The proposed system uses two magnetically levitated 2.1 g Nb test masses 11.6 cm apart, with SQUID readout of their differential motion. Two nearly planar 1.4 kg source masses would be shaped and positioned so that when they are moved in opposite directions their Newtonian effect on the differential motion of the test masses is null. The opposite motion of the source masses cancels inertial reaction forces on the apparatus as a whole, easing vibration rejection requirements for the experiment. The source masses positions will be modulated at about 0.1 Hz. Test masses will be shielded from source masses and environment by superconducting shields. The design sensitivity of the system is 10-4 of gravity at 2 mm and 10-2 of gravity at 0.1 mm.

Measurements at very short distances. Experiments designed to measure the Casimir force can in principle constrain non-Newtonian gravity, but this is made perilous by uncertainties in accounting for finite conductivity corrections, surface roughness, dirt, etc. Two Casimir force measurements have been made recently:

Steve Lamoreaux (, used a torsion balance [3] at the University of Washington to measure the force between a 11.3 cm spherical lens and a quartz plate, both plated with copper and then gold, exploring a separation range from 0.6 to 10 microns with results within about 5% of the Casimir prediction. This data has been used by Price and Long [1] and also by Bordag et al. [4] to constrain non-Newtonian gravity - the two analyses appear to disagree somewhat. The figure in [1] suggests a limit of about 105.7 of gravity at 100 microns and 107.3 of gravity at 10 microns, while a figure in [4] implies tighter respective limits of about 103.4 and 106.2 of gravity.

Umar Mohideen ( with Anushree Roy used an AFM system at UC Riverside to measure [5] the force between a 0.2 mm polystyrene sphere and a sapphire plate, both aluminum coated, over a separation range 100 to 500 nm. The force was measured with an average statistical precision over this range equal to about 1% of the Casimir force at the smallest surface separation, and was found to be consistent with the Casimir force using theoretical corrections calculated to date. Refinements of this work continue.

Michael George ( and his student Lelon Sanderson at the University of Alabama, Huntsville, are also conducting AFM measurements, and exploring with theorist Al Fennelly the possibility of extracting useful limits on non-Newtonian gravity from these measurements.

M. Bordag et al. ( have attempted [6] to constrain sub-micron scale anomalous interactions, using data from Casimir measurements by others. However, Lamoreaux believes that reliable tests for non-Newtonian gravity can only be made for mass separation greater than 5 or 10 microns, because of uncertainty in corrections at shorter distances.

Ephraim Fischbach ( and his colleagues are exploring ideas for circumventing some of the perils in very short distance force measurements, for example by comparing results obtained using different isotopes of the same materials, which should have identical electronic properties but differing gravitational interaction.

Other experiments. There are undoubtably other sub-mm force experiments underway or planned. Mark Kasevich ( at Yale, for example, indicated that he didn't mind being mentioned by name and affiliation, but preferred not to talk in public about his plans which are still somewhat ill defined.

I hope that this sketch of current activity in short distance gravity measurements may be helpful in encouraging communication in an important field.


[1] J.C. Long, H.W. Chan, J.C. Price, Nuclear Physics B 539, 23 (1999).

[2] C. Carugno, Z. Fontana, R. Onofrio, and C. Rizzo, Phys. Rev. D 55, 6591, (1997).

[3] S.K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997), and Phys. Rev. Lett. 81, 5475 (1998).

[4] M. Bordag, B. Geyer, G.L. Klimchitskaya, and V.M. Mostepanenko, Phys. Rev. D 58, 075003 (1998).

[5] A. Roy, C-Y Lin, and U. Mohideen, Phys. Rev. D 60, 111101 (1999).

[6] M. Bordag, B. Geyer, G.L. Klimchitskaya, and V.M. Mostepanenko, Phys. Rev. D 60, 055004 (1999).

Jorge Pullin