Laboratory Experiments: A 14 ppm G measurement,
a new sub-mm gravity constraint,
and other news from MG9

Riley Newman, University of California, Irvine
G to 14 ppm. An elegant new G measurement by Jens Gundlach and Stephen Merkowitz of the U. Washington ``Eöt-Wash" group was reported at the April APS meeting in Long Beach, and at the Marcel Grossmann meeting (MG9) in Rome this summer. The reported result, $G=
(6.674215 \pm 0.000092)\times 10^{-11} m^3 kg^{-1} s^{-2}$, carries an assigned uncertainty two orders of magnitude smaller than the 1500 ppm uncertainty associated with the current recommended ``CODATA" G value (the CODATA uncertainty reflects large discrepancies in G values reported in the last decade - see MOG Number 13). Gundlach's measurement has a number of novel features. A PRL paper in press and available in preprint form [1] describes the experiment. At the heart of the apparatus is a torsion balance placed on a turntable located between a set of attractor spheres. The turntable is first rotated at a constant rate so that the pendulum experiences a sinusoidal torque due to the gravitational interaction with the attractor masses. A feedback is then turned on that changes the rotation rate so as to minimize the torsion fiber twist. The resulting angular acceleration of the turntable, which is now equal to the gravitational angular acceleration of the pendulum, is determined from the second time-derivative of the turntable angle readout. Since the torsion fiber does not experience any appreciable deflection, this technique is independent of many torsion fiber properties, including anelasticity, which may have led to a bias in previous measurements. The attractor masses revolve around the pendulum on a second turntable whose constant angular velocity differs from that of the pendulum's turntable. This motion of the attractor masses makes their torque on the pendulum readily distinguishable from torque due to ambient lab-fixed gravitational fields. Another key feature described in the forthcoming paper and earlier papers [2,3] is a pendulum in the form of a thin rectangular plate. The gravitational torque on the pendulum is dominantly determined by the ratio of its quadrupole moment to moment of inertia - a ratio which is independent of the shape and mass distribution of the pendulum in the limit that it has negligible width. This greatly eases the metrology requirement for the pendulum, in contrast to earlier experiments where pendulum metrology has been a limiting factor. G at MG9. A session at MG9 was devoted primarily to G measurements, several of which target accuracy comparable to that of Gundlach and Merkowitz. Gundlach reported the measurement described above. Tim Armstrong reported measurements made at the New Zealand Measurement Standards Laboratory using a torsion pendulum in two modes: one in which a servo system and rotating platform ensured that there was no significant fiber twist, yielding $G= (6.6742 \pm
0.0007)\times 10^{-11} m^3 kg^{-1} s^{-2}$ [4], and a more recent one using the dynamic (``time-of-swing") method yielding $G= (6.675 \pm
0.01)\times 10^{-11} m^3 kg^{-1} s^{-2}$. The latter value has much larger uncertainty but is consistent with the former, and both values are consistent with that of Gundlach and Merkowitz. Jun Luo described a new G measurement being developed by his lab in China, which should improve on his measurement published recently [5]: $G= (6.6699 \pm
0.0007)\times 10^{-11} m^3 kg^{-1} s^{-2}$. Stephan Schlamminger gave a progress report on the University of Zürich G measurement using a beam balance and mercury-filled steel tank source masses. This experiment [6], which has been troubled in the past by systematic error, shows encouraging progress toward a 10 ppm measurement. Jim Faller reported progress of a G determination based on measurement of the differential deflection of a pair of suspended masses which form a Fabry-Perot cavity; this experiment expects 50 ppm G accuracy, significantly improving on an earlier G measurement by Faller's group [7]. Michael Bantel reported progress of the UC Irvine G measurement using a high-Q cryogenic torsion pendulum operating in the dynamic (``time-of-swing") mode. Ho Jung Paik described his proposed cryogenic G measurement in which a set of four magnetically suspended test masses would be located symmetrically on the periphery of a slowly rotating turntable. Paik's determination of G would be made by measuring the turntable rotation speed required to keep the masses at a fixed radius when an attracting mass is lowered into the center of the array of test masses. Paik's proposed experiment targets 1 ppm accuracy. In the one non-G talk of the session, Andrej Cadez with Jurij Kotar described the University of Ljubljana inverse square law test, in which two pairs of source masses rotate continuously about a torsion pendulum - one pair at opposite 971 mm radii and another at 383 mm radii along an axis perpendicular to that of the first pair. The masses of the pairs are chosen to produce null pendulum excitation at twice the rotation frequency for a Newtonian force law. The group expects to improve on their previous limit [8] which constrained a Yukawa interaction term to be $(-0.2 \pm 6) \times
10^{-3}$ relative to gravity over a distance range 0.2 m to 0.45 m. It seems increasingly clear that the anomalous PTB G measurement [9] must be in error. However, new measurements have yet to converge satisfactorily. At the ``CPEM2000" metrology conference in Australia in May this year, a BIPM group led by Terry Quinn reported (preliminary) results of G measurements using a torsion pendulum suspended by a strip fiber. Such a pendulum is minimally subject to systematic error associated with fiber anelasticity, because the dominant part of its effective torsion constant is gravitational in origin and hence lossless. The measurements were made in two modes: an unconstrained static measurement, yielding $G= (6.6693 \pm 0.0009)\times
10^{-11} m^3 kg^{-1} s^{-2}$ and a static measurement in which the pendulum was servoed to zero displacement with a calibrated electrostatic force, yielding $G= (6.6689 \pm 0.0014)\times 10^{-11}
m^3 kg^{-1} s^{-2}$. The two methods yield consistent results which are however more than 5 of their own standard deviations from the G value obtained by Gundlach and Merkowitz. Sub-mm gravity at MG9. The highlight of the MG9 session on short-range tests of gravity was preliminary results of the ``Eöt-Wash" group's test, reported by Jens Gundlach. The instrument of this experiment is a torsion pendulum in the form of a horizontal disk with ten holes arranged symmetrically azimuthally, suspended above a rotating attractor, with a thin copper electrostatic shield between. The attractor is in the form of two copper disks, each with a set of ten holes. The lower of these rotating disks has a fixed angular displacement relative to the upper and is more massive, arranged so that for a particular pendulum-attractor separation the pendulum experiences no torque modulation at the signal frequency of ten times the attractor rotation frequency if gravity is Newtonian. Gundlach presented preliminary results in the form of a sketched plot indicating a one sigma limit on the order of 2% of gravity at a range of about 1.5 mm. The test is expected to yield still better constraints soon. John Price reported a current sensitivity about 100 times gravitational strength at 0.1 mm, expected to improve to 1 times gravitational strength at that distance using his existing room temperature instrument and to improve still further with a planned cryogenic instrument. Michael Moore discussed the short-range test he is developing with Paul Boynton, which uses a near-planar torsion pendulum suspended above a near-planar source mass, configured to give a nearly null signal for purely Newtonian gravity. The expected sensitivity of their apparatus to an anomalous force is about 0.25 of gravity at 0.25 mm and 0.01 of gravity at 1 mm. Aharon Kapitulnik described his present cantilever-based instrument at Stanford, which has projected sensitivity better than .05 of gravity at 0.08 mm, and discussed possible future improvements. Giuseppe Ruoso discussed the apparatus of the Padua group. Currently optimized for Casimir force measurements, the instrument does not yet have good sensitivity for short-range gravity measurements. When the Casimir tests are completed the group expects to optimize it for gravity tests, and expects sensitivity on the order of $\alpha = 10^7$ to 108 for ranges of a few microns, in a yet-unexplored region of the $\alpha - \lambda $ plane. Ho Jung Paik reported the design of a cryogenic null test of the inverse-square law, with expected sensitivity at a level 0.0001 of gravity at 1 mm and 0.01 of gravity at 0.1 mm. Ephraim Fischbach reviewed the motivations for short-distance gravity tests, and discussed prospects for very short range tests using atomic force microscopy. Dennis Krause as well as Ephraim discussed ways of dealing with the severe problems of molecular background forces in extremely short range tests. Christian Trenkel reported the development of a torsion balance using a Meissner effect suspension, and this instrument's prospective applications in weak force physics such as a spin-mass coupling experiment. A list including other current mm-scale gravity tests, with a little more detail on some of the projects reported above, is available in MOG number 15. Laboratory equivalence principle tests at MG9. A session on equivalence principle tests, chaired by Ramanath Cowsik, included talks on both space and laboratory tests; I report here only on the latter. Nadathur Krishnan reported the status of the TIFR equivalence principle experiment, which employs a torsion pendulum with a 3.6 meter long torsion fiber of rectangular cross section, operating in a chamber deep underground in a seismically very quiet region of India. The test operates in a Dicke mode, using the sun as acceleration source, targeting a sensitivity at a level of $\eta \approx 10^{-13}$. Continuous operation of the instrument is about to begin. Paul Boynton discussed a novel mode in which a torsion pendulum may be used to measure anomalous forces, based on measurement of the second harmonic component of the pendulum's oscillatory motion. This method, introduced by Michael Moore in Paul's group, has the great advantage that it is extremely insensitive to variation of the fiber temperature, in contrast to force measurements based on measurement of a pendulum's oscillation frequency or static displacement. I gave a short talk on prospects for improved terrestrial equivalence principle tests using a cryogenic torsion pendulum, taking advantage of the high Q and good temperature control achievable with such an instrument. In principle such an instrument should be capable of $\eta$ sensitivities of 10-14 or better, although many practical difficulties are to be encountered. Wolfgang Vodel gave a progress report on the Bremen Drop Tower test of the equivalence principle, in which a superconducting differential accelerometer falls 109 meters in an evacuated tube. This system is expected to be capable of $\eta$ sensitivity at a 10-14 level, with a theoretical limit at a 10-16 level and a near-term result anticipated at a 10-13 level. Cliff Will reviewed tests of the three ingredients of the Einstein Equivalence Principle - universality of free fall, local Lorentz invariance, and local position invariance - and discussed their theoretical implications.


[1] Jens Gundlach and Stephen Merkowitz, PRL in press, preprint at

[2] J.H. Gundlach, E.G. Adelberger, B.R. Heckel and H.E. Swanson, , Phys. Rev. D54, R1256 (1996)

[3] J.H. Gundlach, Meas. Sci. Technol. 10, 454 (1999)

[4] M.P. Fitzgerald and T.R. Armstrong, Meas. Sci. Technol. 10, 439 (1999)

[5] Jun Luo et al., Phys. Rev. D59, 042001 (1998)

[6] F. Nolting, J. Schurr, S. Schlamminger and W. Kündig, Meas. Sci. Technol. 10, 487 (1999)

[7] J.P. Schwarz, D.S. Robertson, T.M. Niebauer and J.E. Faller, Meas. Sci. Technol. 10, 478 (1999)

[8] A. Arnsek and A. Cadez, Proceedings of the 8th Marcel Grossmann Meeting, 1174 (World Scientific, 1999)

[9] W. Michaelis, H. Haars, and R. Augustin, Metrologia 32, 267 (1996)