Table of contents

The 20th Century saw a renaissance in experimental gravitation: some recent results were presented in a symposium organized by Hu Enke and Peter Michelson in Guangzhou, in 1987, followed by the symposium organized by Asghar Qadir and myself in Nathiagali in 1993, and in the latest gathering in Samarkand in August 1999. An interval of six years seems appropriate in reviewing landmarks in this field.

This issue of Classical and Quantum Gravity is devoted to topics covered in the Samarkand symposium. The subject of the symposium is broadly classified as experimental gravitation: included in it are experiments from many different areas of physics, that generally aim to test and interpret Einstein's theory of gravity. Contributors to this issue have provided comprehensive reviews of experiments placing each within a theoretical framework.

Advances in several branches of physics have made possible experiments of unprecedented precision to the extent that one can devise tests of many aspects of general relativity, using in some cases, laboratory-scale apparatuses. Sometimes these advances have occurred in fields as diverse as atomic physics, physics of condensed matter, metrology and measurement theory to name a few; the symposium provided a synergic forum for scientists from different specializations. Experiments were described that test the predictions of general relativity over a range of phenomena from the classical to the quantum, over distances of millimetres to the astronomical, over timescales from the present to the early Universe and from the weak to the strong-field approximation.

Papers in this issue are loosely grouped under the following broad categories: tests of the equivalence principle, with Pound's description of a classic, Bantel and Boynton reporting on new methods to push back the limits of the equivalence principle using the venerable torsion balance, and separate proposals by Iafolla, Sanders and Nobili to refine Galileo's free-fall experiments on Earth and in space. Difficult and ingenious experiments to measure `G' are reviewed by Luo. One can observe the sometimes erratic progress in the measured value; great efforts are underway to improve the accuracy. Ruoso reports on an experiment to verify, on a submillimetre scale, Newton's law of gravity and attempts to link the results to supersymmetry physics. Rotating fields are covered next: Ciufolini describes his discovery of the Lens-Thirring effect using, as a gyroscope, a pair of satellites. Gustavson reports on an atom interferometer gyroscope, a device meant to extend, to general relativity, earlier work on the effect of rotating frames on quantum systems. Mashhoon proposes an experiment to measure the effect of a rotating mass on intrinsic spin. Astrophysical phenomena have revealed new insights associated with strong field effects close to black holes. Chakrabarti describes matter under extreme conditions in the vicinity of black holes and shows that spectral signatures can distinguish between a black hole and a neutron star, and how the centrifugal barrier oscillates to produce the quasi-periodic oscillations of x-rays from black-hole accretion disks. Partridge has reviewed the status of measurements of cosmic background radiation as well as recent observational evidence requiring a cosmological constant, necessitating an accelerating expansion of the Universe. Saulson reports on the status of interferometeric detectors of gravitational radiation. Little is known about quantized fields in curved metrics; the last contribution points to an intriguing possibility.

The symposium provided those engaged in experiments with gravitation an opportunity to exchange ideas with scientists from a part of the World emerging from a long period of isolation.

Samarkand is a city of spectacular monuments, both architectural and intellectual. It was the city where the great medieval astronomer Ulugh Bek (1394 - 1449) established an observatory. His aim was to measure the length of a year in order to revise the calendar. Following the tradition of the scientific method established by Ibn Al-Haytham (d. 1039), he designed and built an instrument before engaging in measurements. His log books have survived, as has his observatory. Among his discoveries were a number of errors in the computations of the 2nd Century Alexandrian astronomer Ptolemy. Ulugh Bek compiled a catalogue of stars (the third such catalogue after Hipparchus (129 BC) and Ptolemy's Almagest (140 AD)) which circulated in Europe in the 1500s. Ulugh Bek was Tycho Brahe's predecessor.

Omar Khayyam also enriched Samarkand's intellectual history. Omar solved the general problem of extracting roots of any desired degree. He was an avid astronomer. As a result of his observations he suggested a scheme which made 8 of every 33 years leap years, with 366 days each, and produced a length of the year closer to the true value than does the present Gregorian calendar. Among his quatrains was one that may describe the typical contemporary relativity conference:

Myself when young did eagerly frequent

Doctor and Saint, and heard great Argument

About it and about: but evermore

Came out by the same Door where in I went.

This symposium, I hope, is an exception.

During the 9th Century the city of Khiva, a day's drive from Samarkand, was home to the mathematician Al-Khwarizmi. Among his many achievements was a book explaining Hindu arithmetic and a systematic introduction to algebra and a theory of quadratic equations. He also made an accurate measurement of 56 2/3 miles/degree. The word algorithm is derived from a Latinized version of his name.

A millennium ago the introduction of decimal arithmetic caused a revolution in computing power which influenced all of science, much as personal computers today are revolutionizing our civilization.

Contemporaneous with Al-Khwarizmi were Al-Biruni and Avicenna, equally luminous for their measurements of longitudes and latitudes of locations in this region and for inventing the azimuthal equidistant and globular projections. Al-Biruni was pressed into service as a diplomat; of this he wrote, `I was compelled to participate in worldly affairs, which excited the envy of fools, but made the wise pity me'. Avicenna's treatise on medicine was a standard text for 900 years. This symposium closes the circle of scientific activity in Samarkand.

Paper, which was invented in China in the 2nd Century, was brought to Samarkand in the 8th Century and from there it travelled along the Silk Road to Arab lands in the 11th Century and thence to Fabriano in Italy in the 13th Century, its first appearance in Europe. Paper was not the first product from China to travel west on the Silk Road, silk has that distinction because it was used in Pharonic times.

I mention these examples from previous eras to remind us all to value experiments. Physics is an experimental science, an aspect emphasized by Newton, Einstein, Landau and Feynman among others.

On behalf of the participants I wish to express my gratitude to the organizations which sponsored the Samarkand symposium. These are: the United States National Science Foundation, the Abdus Salam International Centre for Theoretical Physics, Turkish Airlines, COMSTECH, Samarkand Business Centre, Samarkand State University, Samarkand Ziyolilar Saroy, Institute of Nuclear Physics (Tashkent) and the Local Organization Committee. Among the many individuals who provided much of the invisible logistical support I wish to recognize Bobomurat Ahmedov, my co-organizer, and his family for their friendship and hospitality; Umar Salikhbaev, Shahriyor Safarov and Abdullah Kuvatov of Samarkand State University, for hosting the Symposium and for the special honour conferred on Professor Pound; Bahtiyor Allayarov for the excursion to Bukhara and hotel arrangements; Mohammad Shafique for producing the conference stationery; St John Fisher College, especially the Business Office for administrative support; and Nic Marinaccio for rendering the symposium poster. Andrew Wray of the Institute of Physics Publishing deserves appreciation for his advice in preparing this special issue.

Bobomurat Ahmedov    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

L Ya Arifov    Physics Department, Simferopol State University, Ukraine

Michael Bantel    Department of Physics, University of California Irvine, USA

Paul Boynton    Department of Physics, University of Washington Seattle, USA

Sandip Chakrabarty    S N Bose National Centre for Basic Sciences, Salt Lake, Calcutta, India

Ignazio Ciofulini    Diparimento Ingeneria dell'Innovazione, University of Lecce, Italy

M Dzhumaev    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Sh Ehgamberdiev    Astronomicheskaya 33, Tashkent, Uzbekistan

Mirshod Ermamatov    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Anatoly Gafarov    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Vittorio Gorini    Dipartimento di Scienze Chimiche, Fisiche e Mathematiche, Universita' dell' Insurbia, Como, Italy

Todd Gustavson    Department of Physics, Massachusetts Institute of Technology, Cambridge, USA

William Hamilton    Department of Physics, Louisiana State University, USA

Faheem Hussain    External Affairs, Abdus Salam ICTP, Trieste, Italy

Valerio Iafolla    Istituto di Fisica dello Spazio Interplanetario, CNR Roma, Italy

Jamal N Islam    Centre for Mathematical and Physical Sciences, University of Chittagong, Bangladesh

Munawar Karim    Department of Physics, St John Fisher College, Rochester, New York, USA

Nobuki Kawashima    Department of Physics, Kinki University, Japan

Avas Khugaev    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Pierre Lemonde    BNM-LPTF, Paris, France

Enrico Lorenzini    Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USA

Jun Luo    Department of Physics, Huazhong University of Science and Technology, Wuhan, China

Michael Moore    Department of Physics, University of Washington Seattle, USA

Ismet Muzhdabaev    Samarkand State University, Uzbekistan

Nuryagdy Nazarov    Physical and Technical Institute, Turkmenistan Academy of Sciences, Ashgabat, Turkmenistan

Riley Newman    Department of Physics, University of California Irvine, USA

Anna Nobili    Departimento di Matematica, Universita' di Pisa, Italy

S Nuriddinov    Astronomicheskaya 33, Tashkent, Uzbekistan

Bruce Partridge    Department of Physics, Haverford College, Haverford, Pennsylvania, USA

Robert Pound    Department of Physics, Harvard University Cambridge, Massachusetts, USA

Asghar Qadir    Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Abdullah Quvatov    Samarkand State University, Uzbekistan

Guiseppi Ruoso    Dipartimento di Fisica `G Galilei', Universita' di Padova, Italy

Umar Salikhbaev    Samarkand State University, Uzbekistan

Alvin Sanders    Department of Physics, University of Tennessee Knoxville, USA

Dileep Sathe    2 Prerana Apts, A-40 Katsurba Society, Pune, India

Peter Saulson    Department of Physics, Syracuse University, New York, USA

Dimitri Shabanov    Samarkand State University, Uzbekistan

Mengxi Tang    Department of Physics, Zhongshan University, Guangzhou, China

A Tartaglia    Dipartimento Fisica del Politecnico, Torino, Italy

Zafar Turakolov    Institute of Nuclear Physics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Ravil Usopov    Theoretical Physics Department, Karakol State University, Bishkek, Kyrgyzstan

Leonid Verozub    Kharkov State University, Ukraine

Albert Einstein pointed out, in 1907 and 1911, that his principle of equivalence would lead to the shift of stellar spectral lines to the red when produced in more massive sources than the Earth. This became one of the `three crucial tests' of his 1917 general theory of relativity. Astronomers searched for it for several decades with rather inconclusive results. A new approach was created by the discovery of recoil-free emission and the absorption of gamma-rays, with widths basically determined by nuclear state lifetimes, announced in 1958 by Rudolph Mössbauer. Glen Rebka and I were quickly able to extend that new technique to the example of ⁵⁷Fe and to demonstrate the miniscule shift within a 23 m tower in the laboratory. By 1964, with J L Snider, I was able to reduce the uncertainty to less than 1% of the 2.5×10^-15 fractional effect predicted. In 1977 a long anticipated combination of atomic clocks and space vehicles by R F C Vessot and NASA confirmed the effect in its time-keeping aspect to better than one part in 10 000.

A cryogenic torsion pendulum for gravitational experiments is being refined at its remote operation site near Richland, Washington. Features of the apparatus include: four stages of temperature control, an angular readout of the pendulum about three orthogonal axes and a remote operation capability. Currently, we are testing the apparatus with a nominally symmetric pendulum suspended from a 25 µm diameter Al5056 fibre. Since installing the apparatus in June 1999, we have been testing and fine tuning the instruments and software. Most recently (December 1999) magnetic shielding was added, reducing the eddy current damping of the pendulum by ~10³. Magnetic contamination of the test pendulum, with a net magnetic dipole moment of ~6×10^-9 N m T^-1, served in measuring the effectiveness of the shielding.

The search for ever smaller violations of Einstein's weak equivalence principle continues to be an important experimental goal at the close of the 20th century, with string theory providing new motivations. Currently, the most sensitive laboratory and terrestrial-scale tests are carried out with instrumentation based on the 18th century concept of the torsion pendulum, but not with 18th century technology. The torsion pendulum has experienced a renaissance since the pioneering work of Robert Dicke in the early 1960s. This presentation describes a new observable associated with large-amplitude pendulum oscillations that provides measurement of extremely small torques with significant freedom from effects that may limit the traditional, non-cryogenic applications of the torsion pendulum.

Some future tests of the weak equivalence principle (WEP) with laboratory-size proof masses are likely to be conducted in freefall conditions in order to improve the test accuracy substantially. Some years ago the authors of this paper proposed to test the WEP in a vertical freefall inside a capsule released from a high-altitude balloon. The estimated accuracy in testing the WEP, with a 95% confidence level, is a few parts in 10¹⁵ in a 30 s freefall. When compared with other proposed orbital freefall experiments and ground-based tests, the vertical freefall retains some key advantages of the former without some of the disadvantages of the latter. Moreover, a two orders of magnitude increase in the accuracy of testing the WEP could be achieved with an affordable experiment that allows us to recover the detector and repeat the launches at short time intervals.

Project SEE (Satellite Energy Exchange) is an international effort to develop a space-based mission for precise measurements of gravitation. Gravity is the missing link in unification theory. Because of the unique paucity of knowledge about this, the weakest of all known forces, and because gravity must have a key role in any unification theory, many aspects of gravity need to be understood in greater depth. A SEE mission would extend our knowledge of a number of gravitational parameters and effects, which are needed to test unification theories and various modern theories of gravity.

SEE is a comprehensive gravitation experiment. A SEE mission would test for violations of the equivalence principle (EP), both by inverse-square-law (ISL) violations and by composition dependence (CD), both at ranges of the order of metres and at ranges on the order of R_E. A SEE mission would also determine the gravitational constant G, test for time variation of G, and possibly test for post-Einsteinian orbital resonances. The potential finding of a non-zero time variation of G is perhaps the most important aspect of SEE. A SEE mission will also involve a search for new particles with very low masses, since any evidence of violations of the EP would be analysed in terms of a putative new Yukawa-like particle.

Thus, SEE does not merely test for violations of general relativity (GR); SEE is a next-generation gravity mission.

`Galileo Galilei' (GG) is a proposal for a small, low-orbit satellite devoted to testing the equivalence principle (EP) of Galileo, Newton and Einstein. The GG report on the phase A study recently carried out with funding from ASI (Agenzia Spaziale Italiana) concluded that GG can test the equivalence principle to 1 part in 10<sup>17</sup> at room temperature. The main novelty is to modulate the expected differential signal of an EP violation at the spin rate of the spacecraft (2 Hz). Compared with other experiments, the modulation frequency is increased by more than a factor of 10<sup>4</sup>, thus reducing 1/f (low-frequency) electronic and mechanical noise. The challenge for an EP test in space is to improve over the sensitivity of ground-based experiments (about 1 part in 10<sup>12</sup>) by many orders of magnitude, so as to deeply probe a so far totally unexplored field; doing that with more than one pair of bodies is an unnecessary complication. For this reason GG is now proposed with a single pair of test masses. At present the best and most reliable laboratory-controlled tests of the equivalence principle have been achieved by the `Eöt-Wash' group with small test cylinders arranged on a torsion balance placed on a turntable which provides the modulation of the signal (a 1-2 h rotation period). The torsion balance is not a suitable instrument in space. We have designed and built the GGG (`GG on the Ground') prototype. It is made of coaxial test cylinders weakly coupled (via mechanical suspensions) and quickly rotating (6 Hz achieved so far); in addition, it is well suited to be flown in space - where the driving signal is about three orders of magnitude stronger and the absence of weight is very helpful - inside the coaxial, co-rotating GG cylindrical spacecraft. The GGG apparatus is now operational. Preliminary measurement data indicate that weakly coupled, fast-spinning macroscopic rotors can be a suitable instrument to detect small differential effects. Rotation (up to 6 Hz so far) is stabilized by a small passive oil damper. A finer active damper, using small capacitance sensors and actuators as in the design of the space experiment, is in preparation. The current sensitivity of the GGG system is of 10^-9 m s^-2/√Hz at about 300 s, which can be improved because horizontal seismic noise is rejected very well; perturbing effects of terrain tilts (due to microseismicity and tides) will be reduced by adding a passive cardanic suspension. As for the capacitance read-out, the current sensitivity (5 pm displacements in 1 s integration time at room temperature) is adequate to make GGG competitive with the torsion balance. Because of the stronger signal and weaker coupling of the test rotors in space, this sensitivity is also adequate for GG to reach its target accuracy (10^-17). Information, references, research papers and photographs of the apparatus are available on the Web (http://tycho.dm.unipi.it/nobili).

A precise knowledge of the Newtonian gravitational constant G has an important place in physics and is of considerable metrological interest. Although G was the first physical constant to be introduced and measured in the history of science, it is still the least well known. The 1998 CODATA recommended value for G, (6.673±0.010)×10^-11 m³ kg^-1 s^-2, has an uncertainty of 1500 parts per million (ppm), which is much larger than that of all other fundamental constants. Here we review the status of our knowledge of the absolute value of G, nine experiments for measuring the absolute values of G within the last five years, the experiments in progress and being planned, and the systematic error due to the inelasticity, the nonlinearity and the thermoelasticity of torsion fibre.

We report on our efforts to give direct limits to the existence of forces other than gravitational ones in the submillimetre range. The technique used involves looking at the expected shifts to the resonant frequency of microresonators whose motion is monitored through a fibre optic interferometer.

In general relativity a current of mass-energy, such as a spinning body, gives rise to peculiar phenomena on bodies, particles and clocks in its vicinity, which are not predicted by the Newtonian gravitational theory; one of these phenomena is the Lense-Thirring effect on particles orbiting a spinning central body. In this paper we first review the method used to measure the Lense-Thirring effect, by analysing the orbits of the two laser-ranged satellites LAGEOS and LAGEOS II, that has provided a direct measurements of this effect; we then report on these detections of the Lense-Thirring effect, obtained by analysing the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II with the orbital programs GEODYN-SOLVE, using the Earth gravitational models JGM-3 and EGM-96 and this new method. The first detection was obtained in 1995, the most accurate measurements were obtained in 1998 using EGM-96, with about 20-30% accuracy. Finally, we briefly review the proposed LARES experiment to measure the Lense-Thirring effect with an accuracy of about 2-3% and to provide other basic tests of general relativity and gravitation.

Some new results and quantitative estimates of the effect of the angular momentum of a spinning mass are elaborated, especially for the gravitomagnetic clock effect, i.e. for the difference in proper times shown by two counter-rotating identical clocks orbiting the central spinning mass. Such time differences even around the Earth appear to be measurable and stimulate the need for a feasibility study of actual experiments.

We reports improvements to our Sagnac effect matter-wave interferometer gyroscope. This device now has a short-term rotation-rate sensitivity of 6×10^-10 rad s^-1 over 1 s of integration, which is the best publicly reported value to date. Stimulated Raman transitions are used to coherently manipulate atoms from counterpropagating thermal beams, forming two interferometers with opposite rotation phase shifts, allowing rotation to be distinguished from acceleration and laser arbitrary phase. Furthermore, electronically compensating the rotation-induced Doppler shifts of the Raman lasers allows operation at an effective zero rotation rate, improving sensitivity and facilitating sensitive lock-in detection readout techniques. Long-term stability is promising but not yet fully characterized. Potential applications include inertial navigation, geophysical studies and tests of general relativity.

The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-½ particle polarized vertically up and down near the surface of a rotating body is ℏΩsin θ. Here θ is the latitude and Ω = 2GJ/(c²R³), where J and R are, respectively, the angular momentum and radius of the body. It seems that this relativistic quantum gravitational effect could be measurable in the foreseeable future.

Classic tests of the cosmological parameters such as Hubble's constant or the density of the Universe, ρ₀, are designed to explore the spacetime geometry of the Universe. They have sometimes been ineffective because of the evolution of the galaxies used as test objects. Over the last decade, a range of new possibilities for determining the cosmological parameters has opened up. I will begin by describing recent, more precise, measurements of Hubble's constant (the expansion rate of the Universe). I will then turn to measurements employing supernovae in distant galaxies to determine the acceleration or deceleration rate of the Universe. Interestingly, the current data suggest that the Universe is being accelerated by a cosmological constant term - an addition to standard general relativity. Next, I will describe how present and future measurements of fluctuations in the cosmic microwave background will give us very precise measurements of a number of cosmological parameters. Interestingly, the combination of microwave background and supernovae results will be much more precise in defining the cosmological parameters than either technique used separately. In describing both the supernovae results and observations of the microwave background, I will spend a little time discussing observational techniques and sources of possible systematic error.

Since black holes are `black', methods for their identification must necessarily be indirect. Due to the very special boundary conditions on the horizon, the advective flow behaves in a particular way, which includes the formation of a centrifugal-pressure-dominated boundary layer or CENBOL where much of the infall energy is released and outflows are generated. The observational aspects of black holes must depend on the steady and time-dependent properties of this boundary layer. Several observational results are written down in this review which seem to support the predictions of thought experiments based on this advective accretion/outflow model. In future, when gravitational waves are detected, some other predictions of this model could be tested as well.

Detection of gravitational waves involves technological challenges that appear almost insurmountable. I list the chief obstacles, and briefly explain how they are being overcome.

Under the action of an incident plane gravitational wave, electromagnetic waves travelling around a circular waveguide are modulated. The energy flux density of the electromagnetic waves will give rise to new components. When some special relation between the frequency of the electromagnetic wave, the frequency of the gravitational wave and the cyclical frequency of the electromagnetic wave around the waveguide is satisfied, a mechanism, similar to resonance, will cause that energy flux density to become greater than the dimensionless amplitude of the incident gravitational wave in order.

A space-based superconducting gravitational low-frequency wave detector is considered. The sensitivity of the detector is sufficient to use the detector as a partner of other contemporary low-frequency detectors such as LIGO and LISA. This device can also be very useful for experimental study of other effects predicted by theories of gravitation.

We propose an experiment to measure the Casimir force in the Schwarzschild metric of the galactic centre. The method of calculation is summarized, magnitudes are calculated and the measuring apparatus is described.