Tabletop gravity experiments

Jens Gundlach, University of Washington

The past fifteen years of laboratory-scale gravitational experimentation have been marked by many new and exciting developments. The field received a lot of impetus by the hypothesis of a "fifth force" [1] in 1986. This very testable new force would have been a blatant violation of the equivalence principle. The evidence for the 5$^{th}$ force was partially based on a reanalysis of the torsion balance data of Baron Eötvös of the early 1900's. Immediately several groups around the world started to do Eötvös-type experiments. The availability of new technologies combined with many new and creative ideas quickly led to several refined measurements by which the 5$^{th}$ force in its postulated form could be conclusively ruled out. However, the physics community was once again reminded of the importance of the equivalence principle which lies at the foundation of general relativity. Tests of the equivalence principle become particularly important for grand unification schemes, most of which predict an equivalence principle breakdown at some level. In addition it is generally believed that the standard model of particle physics can only be complete with the existence of new particles which could exist at high masses as well as at the ultra low energies. The latter frontier being covered by laboratory-gravity tests.

Most equivalence principle tests compare the acceleration of different materials towards another source mass. The difference in test mass composition is chosen to maximize the new interaction's charge, which could be e.g. baryon number, lepton number or combinations thereof. The source mass could be a mass in the lab, a nearby hill, mountains, the entire earth, the Sun, the Milky Way or even cosmological structures. Several types of instruments were developed. One of the more exotic devices consisted of a perfectly buoyant hollow copper sphere in water tank placed at a cliff [2]. Others compared the rate of free fall of different masses [3]. By far the most sensitive and versatile devices proved to be torsion balances. Here new concepts as well as quantitative understanding led to tremendous advances. Our group at the University of Washington, called the Eöt-Wash group, developed a torsion balance that is installed on a continously rotating turntable. As seen from a restframe, turning with the turntable, the signal is modulated at the rotation frequency of the turntable. The technical difficulty lay in producing the required extremely constant rotation rate. We also introduced a multipole analysis that proved very practical in eliminating gravitational torques that could have been mistaken for an equivalence principle violation. The differential acceleration sensitivity between different materials that we are now achieving is $\Delta a < 5\times10^{-15}m/s^{2}$. This limits equivalence principle violations with infinite range and baryon number as its charge to be at least $10^{9}$ times weaker than gravity. Together with another experiment, in which a 3 ton source was rotated about a stationary pendulum, we now can set new limits on equivalence principle violations for ranges from the cm-range [4] to infinity [5]. Riley Newman's group at UC Irvine also has a long and successful tradition of torsion balance experiments probing gravity. He has pioneered cryogenic torsion balances that will have phenomenal intrinsic sensitivity [6].

In the last few years the $1/r^2$-law of gravity at very short ranges came under close scrutiny. Several theorists [7] argued that it might be possible for some of the unobserved extra dimensions in string theory to be compactified close to a mm-radius rather than at Planck length. For two such dimensions the $1/r^2$-force law would break down below the mm-scale, precisely at a length range where limits from previous experiments were weak. A group at the University of Colorado and another group at Stanford University built micromechanical oscillator plates which would be brought into resonance by a close-by parallel moving source plate if the $1/r^2$-law were violated. Both groups use sophisticated mechanical vibration isolation techniques, as well as an electrostatic shield between the source and the sensor. Our approach involved a torsion balance. We built a pendulum consisting of a horizontal disk with 10 holes drilled in it. Below the pendulum we located a similar horizontal disk also with 10 holes. This source disk was mounted on a slowly rotating turntable. Gravity causes the pendulum to be deflected 10 times per revolution. We placed another disk below the source disk that has 10 holes exactly out of phase with the upper disk. This disk was designed to exactly cancel the gravity signal, assuming $1/r^2$ holds. With this setup we were able to tell that a $1/r^2$-violation must have a Yukawa range shorter than $\approx$0.2mm for a strength about equal to gravity [8].

Contrary to the equivalence principle and the $1/r^{2}$-tests several new measurements of the gravitational constant G were motivated by a disagreement in experimental results. One well respected measurement deviated by $\approx42\sigma$ from the accepted value. This situation forced an increase in the uncertainty of the accepted value of G by a factor of 12 (now 0.15%) [9]. In addition Kuroda [10] discovered that torsion fiber anelasticity, a material property, had led to a bias in many previous measurements. Several measurements were initiated, each with new approaches to minimize systematic uncertainties. Torsion balances continued to dominate. Using our experience from the equivalence principle tests we built a continuously rotating balance. Uncertainties with the torsion fiber were avoided by regulating the turntable velocity so that the fiber was not twisted. The gravitational signal was derived from the turntable acceleration. We discovered that a thin vertical plate pendulum eliminated the difficult pendulum metrology issues most measurements had. Rotating the attractor masses on a coaxial turntable transformed our signal to a higher frequency. Our result is about 250ppm higher than the accepted value and has an uncertainty of 14ppm [11]. Another group [12] led by Terry Quinn at the BIPM in Paris eliminates the anelasticity problem by using a torsion strip instead of a round fiber. A four-fold attractor-pendulum configuration is used. The likelihood of unknown systematic error is reduced by using two independent torque measurements: electrostatic feedback and a calibrated deflection. Their result has been submitted for publication. Riley Newman's group has operated a torsion balance at 2K [13]. The group was able to show that at these temperatures anelasticity corrections are small and well understood. They also use a flat plate pendulum. Two copper rings as attractors simplify their metrology issues. The apparatus is located at a remote site to reduce noise. The group expects to announce results soon.


[1] E. Fishbach et al., Phys. Rev. Lett. 56, 3 (1986).

[2] P. Thieberger, Phys. Rev. Lett. 58, 1066 (1987).

[3] K. Kuroda and N. Mio, Phys. Rev. D42, 3903 (1990), T.M. Niebauer, M.P. McHugh, J.E. Faller, Phys. Rev. Lett. 59, 609 (1987).

[4] G. L. Smith et al., Phys. Rev. D61, 022001 (1999).

[5] Y. Su et al., Phys. Rev. D50, 3614 (1994).

[6] M.K. Bantel and R.D. Newman, Class. Quantum Gravity 17, 2313 (2000).

[7] For example: N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett B429, 263 (1998).

[8] C.D. Hoyle et al., Phys. Rev. Lett. 75, 2796 (2001).

[9] P.J. Mohr and B.N. Taylor, J. Phys. Chem. Ref. Data 28, 1713(1999).

[10] K. Kuroda, Phys. Rev. Lett. 75, 2796 (1995).

[11] J.H. Gundlach and S.M. Merkowitz, Phys. Rev. Lett. 85, 2869 (2000).

[12] T. Quinn et al., Meas. Sci. Technol. 10, 460 (1999).

[13] R. Newman and M. Bantel, Meas. Sci. Technol. 10, 445 (1999).

Jorge Pullin