Table of contents

We live in exciting times, from a scientific viewpoint, for both experimental and observational science now allow us to investigate the fundamental nature of the Universe with hitherto undreamed of accuracy. Bounds can be set, and competing theories can then be tested and evaluated. Nowhere has this progress been more opportune than in the search for the basic structure of space-time and the nature of gravity. Here, considerations of the cosmos at ultra-large scales (e.g. investigations into the cosmological constant, cosmic and galactic dynamics, dark matter, etc) have prompted research into the ultra-small scale—and vice versa—through attempts to quantize gravity, to unify it with the other three known forces, or to resolve outstanding difficulties with the Standard Model of particle physics (e.g. its apparent complexity, CP symmetry, the various unexplained mass scales, etc). New and subtle forces of nature continue to arise naturally out of this theoretical endeavour, and the Equivalence Principle (EP)—the principle of the equivalence of inertial and gravitational mass—is uniquely placed as a sensitive probe of these same putative forces. Therefore, rigorous experimental testing to the highest accuracy possible of the EP, and thereby of General Relativity, is vital to our future understanding of the physical world.

Experimentation on the so-called Weak EP, or the equivalence of free-fall, for different small test bodies falling in the same gravitational field is not a new idea, of course. After two millennia, during which the erroneous views of Aristotle held sway, actual tests of the EP began in the 17th century with those of Galileo: his well-known experiment of dropping a lead musket ball and an iron cannonball (apparently) from the leaning tower of Pisa, for example. Such tests have continued from that time to the present day: firstly with Newton (using pendulums), and subsequently with Eötvös, Dicke, Braginsky, Adelberger, and others—using predominantly torsion balances in various ways—with increasingly greater sophistication, elegance and sensitivity. However, the inescapable micro-seismicity of the Earth, drifting gravity gradients of the locality, and a limited available driving acceleration for the experiment, now make further progress in testing the EP on the Earth extraordinarily difficult—notwithstanding the very great technical advances that have been made. For this reason the greatest potential future gains in measurement accuracy for the EP are likely to be realized through employing the exceptionally quiet and tranquil environment that may be found in space.

It is noteworthy that the title of the Symposium `Testing the Equivalence Principle in Space' was and still is an aspiration for some EP experiments; and many of the experimental papers (which dominated the Symposium) were concerned with ground-based measurements of the EP. Nevertheless, it is worth underlining the fact that advances in Space Science such as (indirectly) `Lunar Laser Ranging', or (directly) `drag-free' control of spacecraft, mean that today Testing the Equivalence Principle in Space lies squarely within the bounds of practical, technical possibility.

The International Symposium on Testing the Equivalence Principle in Space was held over four days (4–7 September 2000) and was organised jointly by the University of Stanford in the USA and the University of Strathclyde in Glasgow, Scotland. The venue for the meeting was Ross Priory on the southern shores of Loch Lomond, this residential conference centre—dating back originally to 1693, and located in 173 acres of grounds with impressive views over the loch and the highlands of Scotland—being owned by the University of Strathclyde. The relative isolation and the splendid tranquillity of the setting certainly helped to draw the delegates together, and to focus discussions in a truly creative and a constructively positive way. 42 delegates attended the meeting.

Whilst the Symposium was called at rather short notice, and therefore was not fully comprehensive in terms of the range of either experiments or theory covered, it nevertheless conveyed fully the excitement of this burgeoning field of scientific endeavour. I hope you will find the Proceedings of interest.

Finally, I should like to thank Dr Paul Worden of Stanford for assisting with the US side of the organisation for the Symposium, Dr Rüdeger Reinhard of ESTEC for assisting with the programme, and Mrs Elsie MacVarish for her invaluable assistance with the local organisation. The Symposium was supported by NASA, ESA and PPARC.

N A Lockerbie

Guest Editor

Local Organisation

N A Lockerbie

Organisation in USA

P W Worden

Scientific Programme Committee

E Adelberger (USA)

K Nordtvedt (USA)

T Damour (France)

R Reinhard (ESA, The Netherlands)

C W F Everitt (USA; chair)

G Schafer (Germany)

Y Jafry (ESA, The Netherlands)

R Torii (USA)

M C Lee (NASA HQ, USA)

P Touboul (France)

N A Lockerbie (UK)

S Vitale (Italy)

J C Mester (USA)

P W Worden (USA)

Eric Adelberger, University of Washington, Seattle WA, USA

John Anderson, Jet Propulsion Laboratory, Pasadena CA, USA

Jean-Pierre Blaser, PSI, Schneisingen, Switzerland

Daniel Debra, Edward C Wells Professor Em. Dept. of Aero and Astro, Stanford CA, USA

Michael Devirian, Jet Propulsion Laboratory, Pasadena CA, USA

Hansjoerg Dittus, University of Bremen, Bremen, Germany

Gordon Donaldson, University of Strathclyde, Glasgow, UK

Karen Dragon, Jet Propulsion Laboratory, Pasadena CA, USA

Neil Dunbar, Astrium Limited, Stanmore, Middlesex, UK

Francis Everitt, Stanford University, Stanford CA, USA

Ephraim Fischbach, Purdue University, West Lafayette IN, USA

Jim Hough, University of Glasgow, Glasgow, UK

Felix Huber, Steinbeis Transferzentrum Raumfahrt, c/o IRS, Stuttgart, Germany

Barry Kent, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK

Claus Laemmerzahl, University of Konstanz, Konstanz, Germany

Mark Lee, Code Ug, NASA, Washington DC, USA

Nicholas Lockerbie, University of Strathclyde, Glasgow, UK

Guy Man, Jet Propulsion Laboratory, Pasadena CA, USA

Carsten Mehls, ZARM, University of Bremen, Bremen, Germany

John Mester, STEP, Stanford University, Stanford CA, USA

Riley Newman, University of California, Irvine CA, USA

Ken Nordtvedt, Northwest Analysis, Bozeman Mt, USA

Robert Oberto, Jet Propulsion Laboratory, Pasadena CA, USA

Colin Pegrum, University of Strathclyde, Glasgow, UK

Antonio Pulido, University of Birmingham, Birmingham, UK

Bob Reasenberg, Smithsonian Astrophysical Observatory, Cambridge MA, USA

Ruedeger Reinhard, SSD/Estec, Ag Noordwijk, The Netherlands

Manuel Rodrigues, Onera, 29 Avenue De La Division Leclerc, Chatillon, France

Remo Ruffini, Universita Degli Studi Di Roma La Sapienza, Rome, Italy

Mike Sandford, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK

Sachie Shiomi, University of Birmingham, Birmingham, UK

Clive Speake, University of Birmingham, Birmingham, UK

Donald Strayer, Jet Propulsion Laboratory, Pasadena CA, USA

Rodney Torii, Stanford University, Stanford CA, USA

Pierre Touboul, Onera, 29 Avenue De La Division Leclerc, Chatillon, France

Robin Tucker, University of Lancaster, Lancaster, UK

Stefano Vitale, University of Trento, Povo, Trento, Italy

Wolfgang Vodel, Friedrich Schiller University Jena, Jena, Germany

Charles Wang, University of Lancaster, Lancaster, UK

Suwen Wang, HEPL, Stanford University, Stanford CA, USA

Matthius Wiegand, Zarm, University of Bremen, Bremen, Germany

Paul Worden, STEP, Stanford University, Stanford CA, USA

Some remarks by Heinrich Hertz on the nature of inertial and gravitational mass as seen in the context of his scientific work and historical background.

This paper describes recent experimental work by the University of Washington Eöt-Wash group on two different topics: a test of the strong equivalence principle and a search for sub-millimetre scale deviations of the Newtonian 1/r² law. Our strong equivalence principle test was motivated by the resurgence of interest in `gravitational' scalar fields, which typically lead to violation of the equivalence principle for gravitational self-energy. Our sub-millimetre experiment was motivated by predictions of fundamentally new effects from `large' extra dimensions and from the dilaton and moduli scalar particles of string theory.

A torsion pendulum may be used to measure effective differential accelerations of test masses in the field of sources on distance scales below those accessible in a space experiment such as STEP. Operation of a torsion pendulum at low temperature (2 K) offers many benefits, notably: low thermal noise, high fibre stability, highly effective superconducting magnetic shielding and excellent temperature control. With such an instrument it should be possible to detect differential accelerations as small as 10^-14 cm s^-2, or fractional differential accelerations in the field of the Earth as small as η = 10^-14. This paper discusses the sources of noise and systematic error that limit a cryogenic torsion pendulum in such measurements.

Free-fall experiments to test the weak equivalence principle are in progress at the drop tower in Bremen. The differential acceleration of two test masses made from different materials is being measured by means of a superconducting-quantum-interference-device- (SQUID-) based sensing technique. These pseudo-Galilean tests are aimed at determining the Eötvös ratio to an accuracy of better than 10^-12. The free-fall height of the experimental capsules is 110 m, translating into an experimental time of about 4.5 s. The SQUID-based sensing system guarantees a high measuring resolution of 10^-12 m Hz^-1/2 for the relative positions of the test masses.

In this paper we discuss experiments testing gravity in space and at ultrashort distances. We show that the proposed STEP experiment has sufficient sensitivity to test how gravity couples to neutrinos and to higher-order weak interactions. Then, after briefly reviewing the recent interest in ultrashort distance gravity experiments, we describe a preliminary round of atomic force microscope (AFM) experiments which utilize the `iso-electronic effect'. Our experimental results set new limits on proposed gravity-like forces over distance ranges ~1-4 nm.

We are developing a Galilean test of the equivalence principle in which two pairs of test mass assemblies (TMA) are in free fall in a comoving vacuum chamber for about 0.9 s. The TMA are tossed upward, and the process repeats at 1.2 s intervals. Each TMA carries a solid quartz retroreflector and a payload mass of about one-third of the total TMA mass. The relative vertical motion of the TMA of each pair is monitored by a laser gauge working in an optical cavity formed by the retroreflectors. Single-toss precision of the relative acceleration of a single pair of TMA is 3.5×10^-12 g. The project goal of Δg/g = 10^-13 can be reached in a single night's run, but repetition with altered configurations will be required to ensure the correction of systematic error to the nominal accuracy level. Because the measurements can be made quickly, we plan to study several pairs of materials.

The equivalence principle can be tested using accurate tracking of the Moon, planets, and interplanetary spacecraft. Tests with solar system bodies probe the dependence of the equivalence principle on self-energy. Analysis of lunar laser ranges yields the difference in the ratio of the gravitational and inertial masses for the Earth and Moon of ({-0.7}±1.5)×10^-13. In conjunction with laboratory tests of the equivalence principle and spacecraft and VLBI tests of PPN γ, one derives |β-1|⩽0.0005. Planetary tests are feasible, in particular tests using Mars. Improvements in Doppler accuracies under development may allow tests with interplanetary spacecraft.

Einstein's weak equivalence principle (WEP) states that gravitational mass is identical to inertial mass. This hypothesis has withstood experimental tests to an impressive accuracy of one part in 10¹¹. Various hypotheses based on theory and observations with matter suggest violations of WEP for antimatter may exist anywhere from the one part in 10⁶ to the 200% level. An observed violation at any level would have a profound impact, e.g. it would offer an explanation as to why matter and antimatter are so distinctly separated in the cosmos. We propose a precise test of WEP for antiprotons in microgravity. We expect to test WEP for antimatter to about one part in 10⁶, and foresee that additional advancements of several orders of magnitude in precision could follow with further technical developments.

Because of Earth's non-sphericity, compositional inhomogeneities and crustal topography, an equivalence principle violation seen in a STEP mission will include multipole fine structure produced by sources effectively independent of the Earth's monopole and quantitatively different from the gravitational multipole structure. If non-universality of gravitational free-fall occurs above STEP's detection threshold of 10^-18, there is good chance (about 40%) that the monopole phenomenon will be robust - between 10^-13 and 10^-15 - permitting measurement of the fine structure which can yield ambiguity-breaking information about the absolute coupling strength of the newly discovered interaction.

The Satellite Test of the Equivalence Principle (STEP) will test the equality of fall of objects in Earth orbit to an accuracy approaching one part in 10⁸ by measuring the difference in rate of fall of test cylinders in cryogenic differential accelerometers in a drag-free satellite. This paper describes the current baseline design and principles used in the design of the STEP mission.

The MICROSCOPE mission aims to test the equivalence principle (EP) up to an accuracy of 10^-15 using its well known manifestation: the universality of free-fall. The mission, implemented in the Cnes programme of 2000, schedules the launch of the microsatellite for 2004. The satellite payload comprises four gravitational sensors operating at finely stabilized room temperature. The masses of the sensors are controlled to the same orbital motion on-board the satellite, which compensates external surface forces in real time by actuation of electrical thrusters. Accurate measurements of the electrostatic forces applied to the masses, so that they follow the same gravitational orbit, are processed in order to reject any common effects on the masses; then the differential outputs are observed with high precision along the Earth-pointing axis, with an expected resolution of 5×10^-15 m s^-2. The quasi cylindrical test masses are concentric in order to reject gravity gradient effects, and are made of platinum or titanium alloys. The instrument's concept and design are presented, and the rationale of the space experiment is explained.

A new satellite-based test of special and general relativity is proposed. For the Michelson-Morley test we expect an improvement of at least three orders of magnitude, and for the Kennedy-Thorndike test an improvement of more than one order of magnitude. Furthermore, an improvement by two orders of magnitude of the test of the universality of the gravitational redshift by comparison of an atomic clock with an optical clock is projected. The tests are based on ultrastable optical cavities, lasers, an atomic clock and a frequency comb generator.

The orbit of a free-flying test mass having differing inertial and gravitational masses relative to a reference mass obeying the equivalence principle (EP), depends on the EP-violation e as well as on the release conditions. For every orbit a release error does exist which compensates for the EP effect. The secular term in the relative distance of the masses (due to orbit period changes) is also dependent on a combination of e and release errors in a non-separable way.

The influence of the choice of the test mass materials in equivalence principle experiments like STEP on the sensitivity for detection of violations or new interactions is evaluated. Selection criteria, also taking into account the many technical conditions, are discussed.

This paper reports and discusses the first experimental results obtained using a novel dynamical method for measuring the inertial imbalance ΔI/I of three reference test masses. Good agreement between experiment and theory is found, and a measurement precision for ΔI/I of better than one part in 10⁴ is demonstrated. The measured values of ΔI/I can be converted with high sensitivity into gravitational quadrupolar coupling, e.g. for assessing masses intended for use in equivalence principle experiments. Some future developments for quantifying systematic error are discussed, in order to convert the current level of precision into measurement accuracy.

We have determined the inhomogeneities in the density of prototype STEP test masses made from HIPed beryllium and niobium using the hydrostatic weighing method developed at BIPM. 13 samples are taken from a HIPed beryllium rod (approximately 140 mm long by 90 mm) and 24 samples from a niobium rod (approximately 225 mm long by 45 mm). The maximum relative difference of density is found to be approximately 240 ppm in the beryllium samples and 60 ppm in the niobium samples. Assuming that there is a 10 g helium bubble at 250 mm from the test masses acting as a source, these inhomogeneities of density would produce a disturbance of Δa/a = (1.1±0.7)×10^-18 in a beryllium outer test mass and (5.1±0.5)×10^-20 in a niobium inner test mass, in the STEP experiment. The inhomogeneities of density in the HIPed beryllium rod appear to be too large for the STEP experiment, which aims at a sensitivity of one part in 10¹⁸. We suggest that it is important to find a way to fabricate more homogeneous HIPed beryllium.

We describe the ongoing development of a comprehensive error model for the satellite test of the equivalence principle, STEP. The goal is to employ a model of the experiment and apparatus as a self-consistent whole. The model uses a set of input parameters based on experiment design and the measured characteristics of STEP sensor systems. The output of the model evaluates specific disturbances to the test masses in the general categories of thermal noise, gas pressure forces, electrical forces, magnetic forces, gravitational forces, radiation pressure and vibration. Use of the model to set experiment requirements and to evaluate design trade-offs are briefly discussed.

As has been shown in previous experiments (Dolesi R et al 2000 J. Low Temp. Phys. 118 219), a porous silica aerogel network can adequately constrain on-orbit motion of superfluid helium, and subsequently remove the possibility of a `helium tide' gravitational disturbance appearing in the Satellite Test of the Equivalence Principle (STEP) signal bandwidth. Silica aerogel is used to decouple the superfluid helium from the Earth (STEP source field). This paper addresses two key issues for flight implementation. The first is to see whether the litre size samples of aerogel needed to fill the flight Dewar behave significantly differently to the millilitre size samples that have been extensively studied in the literature. We have found no significant difference. The second issue is to see whether silica aerogel filled with superfluid helium will survive launch. Based on the tests reported here, we have found no intrinsic property of the silica aerogel/superfluid helium system that would cause it to fail in a launch environment.