gravitational physics - pubman

Physics World December 1996 2 5

features

Gravitational waves are generated by the most catastrophicand powerful events in the universe. Such waves couldtell us about black holes, supernovae explosions and

the big bang - but only if we can detect them

Gravitational physicsGERHARD SCHAFER AND BERNARD SCHUTZ

GRAVITY is truly universal. It is the force that pulls us tothe Earth, that keeps the planets and moons in theirorbits, and that causes the tides on the Earth to ebb andflow. It even keeps the Sun shining. Yet on a laboratoryscale gravity is extremely weak. TheCoulomb force between two protonsis 1039 times stronger than thegravitational force between them.Moreover, Newton's gravitationalconstant is the least accuratelyknown of the fundamental constants:it has been measured to 1 part in104, while Planck's constant, whichcharacterizes quantum mechanics, isknown to within 1 part in 106.

Gravity only dominates on anastronomical scale - large bodies areusually electrically neutral, and thestrong and weak interactions areonly important over short distances.Gravity, however, grows with thesize of the body. Gravitationalforces therefore determine thestructure of bodies that are thesize of the Moon and larger - suchbodies are round because gravitypulls with equal strength in alldirections. Astronomy is thus thelaboratory for gravitational physics.

Newton developed his theory ofgravity in the late 17th century and itis reasonably accurate within oursolar system. In 1916 Einsteinreplaced it with general relativity tomake gravitation theory compatiblewith special relativity. In Newtoniangravity, changes in a gravitationalfield - caused, for example, bymoving stars - are felt instantlyeverywhere in the universe. This isnot allowed in special relativitybecause no influence can travel faster than light. By craft-ing a relativistic theory of gravity, Einstein created a grav-itational revolution that has had profound consequencesfor physics.

Perhaps the most basic of these is that changes in a grav-itational field must propagate with the speed of light - in

other words, any change in the field generates gravita-tional waves. Less expected, but equally important, is thatgravity can create more gravity, an effect that can becomeso strong that space itself curves up and traps matter

inside black holes.Black holes have had a major

impact on our understanding ofastronomy in the last 25 years.Massive black holes have beenfound at the centre of almost everygalaxy that has been studied indetail. Black holes are also thoughtto generate the relativistic jets of gasthat power quasars and giant radiogalaxies. Smaller black holes are alsoat the centre of some of the mostpowerful X-ray sources in ourgalaxy. In the next 25 years, gravita-tional waves promise to have anequally profound impact on astron-omy.

Black holes andneutron stars

1 A source, in this case a binary star system, emitsgravitational waves that affect the positions of twotest particles (blue dots) and an observer betweenthem (0). The waves essentially carry the Newtoniangravity field of the source delayed by the travel timeof the waves. The force on the particles variesbecause the field is proportional to Mr2: the force isless when the two stars lie in the x-direction andgreater when they lie in the y-direction. Theparticles thus oscillate about a mean position.However, the observer also experiences thisoscillating acceleration. Therefore the change indistance between the observer and the particlesis very small and can only be observed in thex-direction.

A simple indication of whether thegravitational field in a system needsto be described relativistically is the"escape velocity" of the system. Fora spherical body of mass M andradius R, the escape velocity isaesc = (2GM/fl)"2. Gravity in thesystem is relativistic if this speed iscomparable to the speed of light; thekey ratio is <\> = v,,sc

2/c2 = GM/Rc2.Alternatively, $ can be thought ofas the ratio of the gravitationalpotential energy of a particle in thesystem, GmM/R, to its rest massenergy, me2, where m is the mass ofthe particle.

Gravity therefore becomes relativistic when <|) is close to1. (It never gets much larger than 1 because the body thenforms a black hole.) For the Sun's gravity in the solarsystem, § never exceeds 10~5. But § approaches unity as Rdecreases or M gets bigger. Cosmology is a case wheremass dominates: as we go further into the universe, M

2 6 Physics World December 1996

increases as R3, so (j) is proportional to R2. On the otherhand, neutron stars and black holes compress the mass ofa normal star inside a very small radius. These objects areat the heart of some of the most impressive phenomena inthe universe: quasars, radio galaxies, pulsars, supernovae,gamma-ray bursts and many intense X-ray sources. Black

o.

§a)

1 1 ° 2 2g

grav

ita

10"24

compactbinaries

stochasticbackground

I

10"4

compactbinary

black hole binary coalesce0 coalescence

black hole I\ • formation 1

\ # black hole . V ^

K binarV / u o V

nee

^ LISA

1 1 1

10"2 10° 102

frequency (Hz)

supernovai collapse

1

104

2 The sensitivity of interferometers based on the ground and in space. Ground-baseddetectors can measure gravitational waves of frequencies between 1 Hz and 1 kHz, whichare generated by the coalescence of binaries and by supernova explosions. Only aspace-based detector such as LISA will be able to detect the low-frequency wavesproduced by binary systems, the formation of black holes and the big bang.

holes and neutron stars also radiate gravitational waves.A black hole can be thought of as a star where the

escape velocity equals the speed of light - it appearsblack because even light is trapped inside the star. Theedge of the hole, R = 2GM/c2, is called the event horizon,where R is about 3 km for a black hole with the samemass as the Sun. Anything that falls within the eventhorizon cannot return.

Michell and Laplace first recognized the special natureof these objects in the 18th century, and in 1917 KarlSchwarzschild theoretically discovered the fully relativi-stic black hole. However, it was not until the 1960s thatJohn Wheeler of Princeton University coined the name"black hole".

Wheeler also proposed the so-called no-hair theorem,which holds that stable black holes are uniquely describedby their mass, angular momentum and electric charge. (Inthis respect black holes resemble elementary particles.Rotating black holes even have the same ratio of magneticmoment to angular momentum as electrons.) The smoothsurface of a black hole also hides any evidence for thenumber of baryons and leptons that have fallen into it.Gravity therefore violates the conservation laws for baryonand lepton number that are central to the standard modelof particle physics. There is also a singularity inside thehorizon, where both the density and the gravitational fieldtend to infinity. A full quantum theory of gravity will beneeded to show what happens here, although many spec-ulations have already been made.

The horizon turns a black hole into a perfect blackbody that absorbs all of the radiation that falls into it.Stephen Hawking of Cambridge University in the UKhas shown that a black hole behaves as a thermodynamicobject that has entropy and that emits black-body radia-tion at a specific temperature. Black holes have othermacroscopic properties - for example, they have an effec-tive electrical resistivity of 377 Q. when they interact withexternal electromagnetic fields.

Black holes are formed when gravity overwhelms the

internal pressure in a star or gas cloud, causing it tocollapse. The object's radius decreases during the collapse,causing § to increase. If gravity becomes weakly relativistic(<)>> 0.001), the collapse cannot stop unless the total massis less than about 2M©, where MQ is the mass of the Sun.Below this mass, nuclear forces can halt the collapse once

(|) has reached about 0.4. This creates aneutron star with a density similar to that ofa normal atomic nucleus. The matter in aneutron star is so compressed that theelectrons combine with protons to formneutrons. Neutron stars are essentiallymacroscopic nuclei held together by gravity.

Fritz Zwicky and Walter Baade predictedthe existence of neutron stars in 1933,shortly after Chadwick discovered the neu-tron. But observational evidence only camein 1967, when Jocelyn Bell and AnthonyHewish of Cambridge University discoveredpulsars - spinning neutron stars with strongmagnetic fields. Pulsars emit radio wavesand other radiation in beams that sweepacross the sky like beams from a lighthouse,and so regular pulses of radiation areobserved on Earth. Most pulsars rotate a fewtimes per second, although some spin over600 times per second. Such speeds are onlypossible because the objects are heldtogether by ultrastrong gravitational fields.

Neutron stars are often formed in supernova explosions,which happen when a massive star has exhausted itsnuclear fuel. The core of the star undergoes gravitationalcollapse and the energy that is released blows off the outerparts of the star, leaving a neutron star. Striking confir-mation of this process came in 1987 with the detection ofneutrinos from a supernova in the Large MagellanicCloud. These neutrinos had energies of about 10 MeV,and were exactly like the neutrinos expected from a hot,newly formed neutron star. However, we still have nodirect evidence for a neutron star in this supernova.

Convincing evidence for black holes has also had to waituntil recent years. In the 1970s astronomers discoveredthat certain strong X-ray sources are binary systems: anordinary star dumps matter onto a companion that is socompact that the gas falling onto it releases huge amountsof energy, including X-rays. Since the energy releasedmust come from gravitational potential energy, the com-pact object must have § > 0.1 and must be either a neutronstar or a black hole. Most systems known today containneutron stars, but some - such as Cygnus X-l - containcompact objects with a mass greater than 7MQ and insome cases 15MO. These must be black holes.

These findings were not too surprising, but in the 1970sevidence began to grow for the existence of million solar-mass black holes. The stars at the centres of many galaxieshave such high random velocities that they can only beheld there by concentrations of enormous mass in regionsthat are so compact that they must be black holes. Massesranging from 106MQ to 109AfG have now been observed inalmost every galaxy that has been studied at sufficient res-olution to see the stars at its centre: the Andromeda galaxy(M31), its dwarf companion (M32), M87, NGC3115,NGC4258 (or M106), and even the Milky Way (see p20).Such supermassive holes probably form at the same timeas the galaxies. At first they appear as quasars and otherkinds of active galactic centres, but after a few billion yearsthey seem to settle down and become quieter.

Quasars are the brightest objects in the universe and


could be powered by black holes. General relativity pre-dicts that rotating masses and black holes produce swirlsin the gravitational field, an effect called gravitomagnetismthat was first proposed by Lense andThirring in 1918. In1977 Roger Blandford and Roman Znajek, then atCambridge, predicted that magnetic fields threadedthrough these swirls could accelerate charged particles.Such an effect could power quasars and galactic nuclei,producing huge jets of relativistic particles that can extendmillions of light-years from the central galaxy.

Quasars have also demonstrated gravitational "lensing",another prediction of general relativity (see Physics WorldMay 1993 pp26-30). In 1979 Dennis Walsh, RobertCarswell and Ray Weymann used observations made withthe Jodrell Bank radio telescopes in the UK to show thatthe "double quasar" 0957+561 is really two images of thesame quasar. Many other examples of gravitational lensesare now known, and this effect is being used to study thedistribution of mass in the universe and its expansion rate.

Gravitational waves and their sourcesGravitational waves are excitations of a gravitational field.In general relativity the gravitational field is identified withthe curvature of space-time, so gravitational waves canalso be thought of as ripples in space-time. Gravitationalwaves travel at the speed of light and are transversallypolarized with two polarization states, just like electro-magnetic waves, although the polarizations cannot bedescribed by a single direction.

There is a fundamental difficulty in detecting gravita-tional waves. The equivalence principle states that allparticles fall at the same rate in a uniform gravitationalfield, so the field of a passing wave will affect all parts ofan experimental apparatus in the same way.This means that only the non-uniform partof a wave's gravitational field can bemeasured directly, and this is achieved bymeasuring the difference in gravitationalacceleration across the apparatus. Makingthe detector larger increases the measureddifference and enhances the effect of apassing gravitational wave.

The strength of a gravitational wave isdescribed by the size of the accelerationgradient it produces. Imagine the effect ofa gravitational wave on two free particlesthat are separated by a distance L along aline perpendicular to the direction of thesource of the wave (figure l).The source isfar enough away that the wave is essentiallya plane wave when it reaches the particles.The wave can move the particles closertogether or further apart, but cannot moveone particle past the other. Thus the maxi-mum effect a wave can have is to changethe particles' separation by L. If theobserved change in separation is 5L, thenthe amplitude of the wave is h = 8L/L.

The gravitational waves that we expecton Earth are very weak. An observerlocated at a distance r from a source ofgravitational waves with mass M and typical radius R willsee a wave with h~e(GM/Rc2)(GM/rc2), where e is adimensionless number. For example, a neutron-starbinary system in the Virgo cluster - about 50 million light-years away - with an orbit of radius 50 km and a totalmass of 3MQ would produce wave amplitudes of about

10 . Such a wave will only move the particles in a detec-tor 4 km long by 4x 10"18 m, about 1% of the diameter ofa proton. And if this movement takes place at the expectedfrequency of 1 kHz, the relative acceleration of the ends ofthe detector will only be 4x 10~15& where g is the acceler-ation due to gravity on the Earth's surface.

Although these effects are tiny, a periodic source emitsgravitational waves with a typical power of (c5/G)e2<j)5.Thispower is immense - if an object emitted more power thanabout c5/G = 3.6 x 1052 W, it would have so much energy ina given volume that it would collapse into a black hole andnot emit anything. This huge intrinsic power means thatgravitational waves carry the imprint of the most cata-strophic events in astronomy, and that they can propagatethrough space almost undisturbed. This makes them avaluable source of information, provided that they can bedetected (figure 2).

Supernovae and binary systems could be the mostimportant sources of detectable gravitational waves. Asupernova emits gravitational waves when the collapse ofthe central core reaches neutron-star densities and theouter parts are blown off, as long as this so-called"bounce" happens asymmetrically. Such gravitationalwaves would shed light on the dynamics in the core nearthe point of maximum density. Numerical simulations ofaxisymmetric collapse processes (i.e. those with rotationalsymmetry about some axis) have been done in recentyears (see Physics World July pp43-48). These have pro-duced wave bursts with a frequency range of100-1000 Hz - essentially because the bounce takes1-10 ms - and amplitudes of up to 10~23 for a sourceabout 50 million light-years away. Simulations of asym-metric collapse with strong rotation will be possible withthe next generation of supercomputers, and these models

5 x 106 km

; relative orbit; of spacecraft

3 The planned LISA detector will be a space-based interferometer that has three arms toextract two independent gravitational signals. The baseline is five times the Sun's diameter,about 5x 106 km, and the orbit of the instrument is shown by the dashed lines. LISA will beable to observe waves at mHz frequencies and is due to be launched in 2015.

could predict the production of much more radiation.Binaries consisting of neutron stars and/or black holes

lose their orbital energy as gravitational waves before theyeventually spiral together and coalesce. The frequency ofthe waves is twice the orbital frequency of the binary,which gradually increases as the orbit decays. Most detec-


tors start to measure these waves once their frequency isabove 10 Hz. By the time the stars coalesce, the frequencyis about 1 kHz for neutron stars and a few hundred Hz forthe more massive black holes.

Coalescing binaries happen very rarely - about 10"4

times less frequently than supernovae, which occur aboutonce per galaxy per 50 years - but the signal can bedetected from a great distance. Indeed, the predicteddetection rate of at least one per year is higher than thatfor supernovae.

Gravitational waves of frequencies between 1CT4 and10~' Hz should be picked up by the most sensitive space-based detectors. Many types of binary systems in our

galaxy radiate at these frequencies, as will the most spec-tacular event we expect to see in the universe: the mergingof two supermassive black holes in the centre of a verydistant galaxy. Rare as such an event may be, a detector inspace could see it anywhere in the universe.

Rotating neutron stars could be another importantsource of gravitational waves. In 1970 the lateSubrahmanyan Chandrasekhar of the University ofChicago discovered that gravitational waves emitted by arotating star can carry away angular momentum so effec-tively that they amplify themselves, leading to a runawayspin-down of the star. In 1978 John Friedman at theUniversity of Wisconsin at Milwaukee and one of us (BS)

On the lookout for gravitational wavesAlbert Michelson invented the interferometer inthe 1870s to perform the Michelson-Morley exper-iment, which showed that the speed of light is thesame in all directions. This work laid the experi-mental foundations of special relativity. Advancedversions of the same instrument are now takingrelativity another step forward: these interferome-ters will be able to detect gravitational waves andwill open up an entirely newbranch of astronomy.

In an interferometer, lightfrom a coherent source isdivided at a beamsplitter andsent down two perpendiculararms (see figure). The light isthen reflected back and isagain divided by the beam-splitter. One path leads to aphotodetector, which meas-ures a coherent superpositionof light from both arms. Theintensity depends on the rela-tive length of the arms: maxi-mum intensity is measuredwhen they are the same lengthor differ by a multiple of the wavelength of light,and zero intensity is measured when they differ byan odd number of half-wavelengths. An interfer-ometer can therefore sense changes in the differ-ence in length between the two arms through thechange in the intensity at the photodetector.

A gravitational wave can generate such changes- for example, if it is travelling perpendicular tothe plane of the interferometer, one arm isstretched and the other is compressed. The expan-sion/compression oscillates as the wave passes, sothe photodetector measures a time-dependentoscillation in the intensity that can be used tomeasure the strength of the gravitational wave.However, a single detector cannot determinewhere a wave has come from. This is one reasonwhy such detectors are being built in the US,Europe and Japan.

It has taken decades of development to convertthese principles into practical instruments. Even ifthe arms are 4 km long, the relative change inlength between the arms will only be about4xlO"18 m, so it is crucial to prevent any distur-bance. Ground vibration is eliminated bysuspending the mirrors on wires hanging from

mirror 1

photodetector

vibration-absorbing stacks. This mirror "pendu-lum" typically has a natural period of about 1 s,which prevents ground vibrations above a fre-quency of about 1 Hz from moving the mirror. Thependulum also allows the mirrors to move freelywhen a gravitational wave passes through. Thiseffectiveness of this isolation system sets a lowerlimit on the observing frequency - the first instru-

ments will go down to about100 Hz and we hope to see10 Hz in a few years' time.

Detectors must operate inhigh vacuum, about 10"8 Torr,to prevent pressure fluctua-tions that could affect thespeed of light in one part ofthe instrument. Observationsmust also be made away fromthe resonant frequencies inthe detector - the naturalfrequency of the suspensionis typically about 1 Hz,and the mirrors have funda-mental vibration modes above10 kHz. But the upper fre-

quency limit for observations is likely to be about100-200 Hz because of thermal vibrations. Thesecan be minimized by choosing suitable materialsand mirror sizes and shapes, but the behaviour ofthermal noise as a function of frequency is not yetwell understood.

However, an intrinsic source of noise - a quan-tum effect called photon shot noise - is likely to setthe sensitivity limit over most of the observingrange. A light intensity of up to a megawatt wouldbe needed for the signal from a gravitational waveto overcome quantum fluctuations, but laserscannot produce this kind of power continuously. Anumber of clever tricks have been developed toovercome this problem. For example, the powerrequirement could be reduced to 20 VV by boun-cing the light up and down the arms about 500times, which would accumulate the effect of thewave on the light.

Even better is an idea called power recycling,which was invented in 1983 by Ron Drever atGlasgow University, and independently by RolandSchilling of the Max Planck Institute for QuantumOptics in Munich. This trick basically involvesreflecting the light that exits the interferometer


showed that this could affect all neutron stars, no matterhow slowly they are rotating. This so-called CFS instabi-lity is a gravitational version of the Kelvin-Helmholzinstability, which describes how the wind excites waves onthe surface of the ocean. This effect could be observed ingravitational waves from neutron stars, particularly thosethat are accreting mass and angular momentum from acompanion in a binary system.

Gravitational waves were also generated in the big bang.These now form a random sea of radiation called the sto-chastic background that, like the cosmic microwave radia-tion, carries information about the very early universe. Butwhile the microwave background was created when the

towards the laser back into the instrument withthe same phase as the incoming laser light. Thistechnique reduces the laser power requirementto 0.2 W, and means that detector builders areoptimistic about measuring amplitudes of 10~21.

However, astrophysicists want to measureamplitudes of 1O~22, which raises the powerrequirement by about 100. Continuous solid-state Nd-YAG lasers, now being developed,should deliver the extra power. But with thismuch power in the system other things can gowrong. For example, the beamsplitter couldabsorb enough light to heat up, which wouldchange its refractive index and destroy the inter-ference effect. This thermal lensing problemcould be solved by a technique called signal re-cycling, which was devised by the late BrianMeers of Glasgow University.

In signal recycling, a partly silvered mirror isplaced between the beamsplitter and the photo-detector, which creates a cavity for the lightbeam between the mirrors at the ends of thearms and the extra mirror (see figure). If thelight has the right wavelength to fit inside thecavity, it will form a standing wave pattern thatbecomes stronger with time. Any motion ofthe mirrors alters the frequency of the lightsupported by the cavity, so a gravitational wavesplits the single-frequency input light into twofrequencies that are equal to the laser frequencyplus or minus the frequency of the gravitationalwave. The aim is to place the mirror such thata standing-wave pattern will form for one ofthese frequencies.

Signal recycling therefore tunes the detector toa narrow signal bandwidth. The more reflectivethe mirror is, the narrower the bandwidth andthe greater the gain at the selected frequency.The selected frequency can be altered by movingthe signal-recycling mirror - this movementis only about 0.004 |am for a detector with4 km arms, which is quite easy to achieve.Alternatively, a wide bandwidth can be achievedby choosing a mirror with high transmissivity,which can be useful for "cleaning" the beam andremoving some of the effects of thermal lensing.

The GEO600 detector will be the first to imple-ment signal recycling. The initial aim is to cleanthe beam and to produce good sensitivity over afairly wide bandwidth. But later observationswill use a narrow-band mode to look for specificsources, including rotating neutron stars. D

universe was about 3xl0 5 years old, primordial gravita-tional waves were generated in the first microsecond afterthe big bang. Unfortunately, we cannot predict how muchof this radiation exists because we do not yet understandthe physics of the very early universe. But the detection ofthese waves would provide fundamental insights into howthe forces of nature might unify at high energies.

Wave detectors

Many gravitational-wave detectors are now being devel-oped, particularly resonant-mass detectors and laser inter-ferometers on the ground and in space. Waves can also bedetected by precisely timing ultrastable pulsars and bytracking the position of interplanetary spacecraft.

Resonant-mass, or cylindrical bar, detectors were firstbuilt in the 1960s by Joseph Weber at the University ofMaryland, and many groups are now building andimproving these detectors. Modern instruments candetect waves with amplitudes down to 10~19, but they aresensitive only to frequencies over a range of about 1 Hznear 1 kHz; at other frequencies they are "blind". Newtechnology is being developed to cool the bars to below100 mK and to build massive spherical solid detectors,and should allow amplitudes of 10~21 to be measured overbandwidths of 100 Hz.

However, the most promising detectors are the inter-ferometers, which measure the effect of a gravitationalwave on light travelling in two perpendicular arms (seebox). Several prototype interferometers with arm-lengthsof tens of metres have been shown to detect waves ofamplitude 10~19 at bandwidths above 100 Hz, and thevery large interferometers needed for realistic detectionare now being built. The Laser InterferometerGravitational-wave Observatory (LIGO) in the US is apair of 4 km interferometer systems, one in Hanford,Washington and the other in Livingston County,Louisiana; the French-Italian detector VIRGO has 3 kmarms and is being built near Pisa in Italy; and theBritish-German detector GEO600 is a 600 m instrumentthat is under construction near Hannover in Germany.All of these instruments should be able to detect ampli-tudes of 10~21 over bandwidths of a few hundred Hz bythe end of this century, and the sensitivities of the longerinstruments could be improved further.

The most ambitious project is the Laser InterferometerSpace Antenna (LISA), a space-based laser interferometerthat is planned as a cornerstone mission by the EuropeanSpace Agency. Consisting of free-flying spacecraft thatcommunicate by lasers over distances of a few millionkilometres, LISA comes close to the ideal gravitationalwave sensor (figure 3). It will be able to detect the gravi-tational waves from ordinary binaries and from super-massive black-hole systems that have frequencies oflO^-lO"1 Hz and amplitudes of as low as 10 . This is along-term project that might not be launched until after2015, but such timescales do not discourage scientists inthis field. After all, they have been developing ground-based techniques for the last 35 years and expect to waitanother 3-5 years to see the first detection.

Binary pulsars

The motion of astronomical binary systems has been thetest bed for gravity from Newton's time. The nearby solar-system binaries — Moon-Earth, Mercury-Sun and others— first helped to establish Newton's laws, and laterrevealed the anomalous perihelion advance of Mercury.


This was a crucial test of general relativity, which has beentested further by studies of the equivalence principle inthe Moon-Earth system, the relativistic precession of theMoon-Earth system, and time dilation effects in the solarsystem. These tests have all confirmed that general relati-vity is highly accurate, but they only explored the weakgravitational fields of non-relativistic bodies that moveslowly enough for the fields to be independent of time.

The main problem with general relativity is that it isincompatible with quantum mechanics. Tensor-scalartheories of gravity take account of the effects that arisefrom a quantum theory that unifies gravity with otherinteractions, but they only deviate from general relativitywhen the bodies have strong internal gravitational fields.

A means of testing strong, dynamical gravity was prov-ided by the discovery of a binary pulsar in 1974 byRussell Hulse and Joseph Taylor, then at the University ofMassachusetts. This pulsar, PSR 1913+16, and its com-panion are neutron stars with strong internal fields((t> = 0.2), and they reach a maximum speed of about400 kms"1 in dieir highly eccentric 7V4 hour orbits. Thearrival times of the radio pulses at the Earth vary accor-ding to the position of the pulsar in its orbit, and theirregularity makes them ideal for tracking the star. Thearrival times are influenced by several relativistic effects:the precessional motion of the pulsar's orbit, known asthe periastron advance; the variable speed of the pulsar asit moves through the companion's gravitational field,which leads to time dilation and gravitational red shift;and the loss of gravitational waves that causes the orbitalperiod to shrink.

All of these effects can be isolated in the measuredarrival times. The first two have been used to determinethe orbital parameters and the masses with unprecedentedaccuracy - the pulsar's mass is 1.4411MO and the com-panion's mass is 1.3874MO. These values can be used ingeneral relativity to predict the change in orbital period,and the prediction agrees with the observed value towithin measurement errors, about 0.35%. This is the besttest we have of general relativity for strong gravitationalfields, and it earned Hulse and Taylor the Nobel Prize forPhysics in 1993.

Of the 700 or so pulsars known today, only 44 are inbinary systems. Most of these have white dwarf compan-ions, but five appear to be in a binary system with aneutron star. All of these show relativistic effects, and animportant binary for general relativity is PSR 1534+12,which was discovered in 1990 by Alexander Wolszczan,then at Cornell University. Although the orbital period isstill fairly stable, this system allows an effect that is toosmall to be observed in the Hulse-Taylor system to bemeasured. This Shapiro time-delay is caused when theradio signals from the pulsar pass so close to the compan-ion that gravitational lensing introduces an extra delayinto their arrival times. This independent strong-field testof gravitation theory is not dynamical, but it agrees withgeneral relativity to within 1.5%.

Binary pulsars with white-dwarf companions also playan important role in testing gravity theories. For example,tensor-scalar theories predict that the binary system ofPSR 0655+64 should radiate dipolar scalar waves and thatother binaries should experience dipolar forces in thedirection of the galactic centre. This would be a violationof the equivalence principle that would effectively polarizethe orbits. None of these effects have been detected so far,which constrains possible scalar gravitational fields.

Apart from binary pulsars, spacecraft and artificialsatellites are useful tools for testing gravity theories. The

first such test was in 1976, when a Scout rocket took amaser clock to an altitude of 10 000 km. Robert Vessotand collaborators from Harvard University comparedthe rate of the clock with that of an identical clock onEarth, and measured the gravitational red shift to aprecision of 0.02%.The test is now known as the GravityProbe A experiment.

Gravity Probe B, also known as the RelativityGyroscope Experiment, is now being built at StanfordUniversity by a team led by Francis Everitt, and it is dueto be launched in 1999. This probe will provide the firstdirect observation of gravitomagnetism - the eddies in agravitational field generated by rotating masses - by meas-uring the gravitomagnetic field of the Earth from a lowpolar orbit.

The STEP (Satellite Test of the Equivalence Principle)experiment is another idea from Stanford, which is cur-rently being considered by space agencies in Europe andthe US. This space-based experiment will test the ideathat gravity has the same effect on identical particles to aprecision that is some 105 times greater than can beachieved with Earth-based techniques. The plan is tomeasure the difference in acceleration between twobodies of different composition to an accuracy of onepart in 1017.This could unveil a composition-dependentforce that could prove important for theories attemptingto quantize gravity.

A gravitational revolution

In the long term, LISA is likely to provide the most fun-damental tests of strong-field general relativity. Thisspace-based interferometer will measure the radiationemitted by merging black holes and by neutron starsfalling into massive black holes. It will thus explore thestrongest possible gravitational fields and will test manyaspects of gravity, including the no-hair theorem, gravito-magnetism and the equivalence principle. It might alsoprovide measurements of the cosmological deceleration,and hence of the total mass of the universe, to an accuracyof better than 1%. The use of gravity to test gravity - byusing gravitational waves to tell us about the strongestgravitational fields in the universe - will mark the maturityof general relativity and the fulfilment of Einstein's gravi-tational revolution.

Further readingM Begelman and M J Rees 1996 Gravity's Fatal Attraction: BlackHoles in The Universe (Freeman)D G Blair (ed) 1991 The Detection of Gravitational Waves(Cambridge University Press)S W Hawking and W Israel (eds) 1987 300 Years of Gravitation(Cambridge University Press)B F Schutz and C M Will 1993 Gravitation and GeneralRelativity Encyclopedia of Applied PhysicsVoL 1 pp303-340 (VCHPublishers)S L Shapiro and S ATeukolsky 1983 Black Holes, White Dwarfs,and Neutron Stars (Wiley, New York)K S Thome 1994 Black Holes and Time Warps (Norton, London)C M Will 1993 Theory and Experiment in Gravitational Physics(Cambridge University Press)C M Will 1995 Was Einstein Right? (Oxford University Press)

Gerhard Schlfer is in the Gravitational Theory Group at theFriedrich Schiller University, D-07743 Jena, Germany.Bernard Schutz is at the Albert Einstein Insiitute. D-14473Potsdam, Germany


The Art of Richard P. FeynmanImages by a Curious Character

Compiled by Michelle Feynman

This book brings together, for the first time, a large collection of the artwork of Richard P. Feynman, scientistextraordinaire and winner of the Nobel Prize for Physics in 1965.

Beginning with his earliest attempts at drawing the human figure in 1962, the selected artwork displaysFeynman's fascinating development of a personal artistic sensitivity to line, form and the mood of hissubjects, as well as his experimentation with various styles and media.

The book includes approximately 100 works produced over a twenty-five year period until 1987, the yearbefore his death. They mainly consist of black and white drawings (his favorite medium) as well as asmaller number of color pieces, carefully chosen and photographed by his daughter Michelle.

Also included are a number of warm-hearted and humorous anecdotal stories from close colleagues, artteachers and friends.

1995 • 176pp, 7 colour plates, 92 black & white • Cloth • ISBN: 2-88449-047-7 • US$65 / £40 / ECU52 • Gordon and Breach Arts International

For further information, or to order, please contact the relevant address below:Biblios Publishers' Distribution Services Ltd., Star Road, Partridge Green, West Sussex, RH13 8LD, UK • Tel: +44 (0) 1403 710971 • Fax: 444 (0) 1403 711143

orUniversity of Toronto Press, 250 Sonwil Drive, Buffalo, NY 14225, USA • Tel: +1 (800) 565-9523 • Fax: +1 (800) 221-9985

G+B Arts InternationalA member of The Gordon and Breach Publishing Group

INSERT 5 ON REPLY CARD

Electronic Instrumentationfor Cryogenic Systems

The best for less!

Helium Depth Indicatorswith control, serial port and high current options.Superconducting Magnet Controllers1EEE/RS232 interface, fail-safe, air cooled units. 80-600Amodels and now up to 20V charging for some versions.Multi-Sensor Monitorsfor simultaneous display of temperature, magnetic fieldand resistance.Helium Level ProbesRigid, flexible and semi-flexible designs for all purposes.Nitrogen Level Probesoperated directly by the Helium Depth Indicator.Rhodium Iron Sensorscylindrical or flat geometries, 3 calibration options.Magnet Protection Systems

For commitment to the highest standards of quality,reliability and versatility, contact:

TwickenhamScientific Instruments

71 Elers Road, London W13 9QB.Telephone 0181 567 8005 Fax 0181 892 7436

For all your requirements of

SCIENTIFIC EQUIPMENT& MATERIALS

Call

CAMLONEquipment of your choice from leading manufacturers

*

TEL: (01223) 32 90 20FAX: (01223) 30 28 62(International dialling code for Cambridge +44 1223)

* * * *Camion House, Richmond Road, P. O. Box 43,Cambridge CB4 3TN, England.


De Martini, F./Denardo, G./Shih, Y. (Eds.)

Quantum InterferometryProceedings of an Adriatico Workshop,Tireste, March 1996

1996. XXI, 544 pages withca. 164 figures. Hardcover.Ca. £ 95,-/$ 160.-/DM 228,-.ISBN 3-527-29447-3(VCH, Weinheim)

This book collects the texts of lecturesgiven by foremost experts concerningthe various modern aspects of 'Quan-tum Interferometry' at an AdriaticoConference held, with the same title, inTrieste in March 1996.

Schleich, W.P./Mayr, E./Krahmer, D.

Quantum Optics in PhaseSpaceSpring 1997. Ca. XII, 350 pages withca. 150 figures. Hardcover.Ca. £41,-/$68,-/DM 98,-. ,ISBN 3-527-29435-X ^ e > N '(VCH, Weinheim)

Based on a two-semester graduatecourse given at the University of Ulm,this book provides a compact intro-duction to the theory. It gives a goodpreparation for research and caneither be used alone or with otherbooks.

Vogel, WVWelsch, D.-G.

Lectures on Quantum Optics1994. X, 442 pages with 63 figures.Hardcover. £ 39,-/$ 60.-/DM 98,-.ISBN 3-05-501387-5(Akademie Verlag, Berlin)

In this book, the fundamentals ofquantum optics are introduced in asufficient depth for their practicalapplication and for an understandingand treatment of specialized problemsarising in recent research. On thebasis of a general quantum-field-theoretical approach, the topics arepresented in a unified manner.

Optics from VCHn

Kreis, T.

Holographic InterferometryPrinciples and Methods

1996. 351 pages with 163 figures and8 tables. Hardcover.£ 60,-/$ 95.-/DM 148,-. ^ISBN 3-05-501644-0(Akademie Verlag, Berlin)

The book presents the principles andmethods of holographic interferometryin deformation and stress analysis,determination of refractive-indexdistributions, or applied to non-destructive testing. Emphasis of thebook is on the quantitative computer-aided evaluation of holographicinterferograms.

Fuzessy, Z./Jiiptner, WV \\&NX-Osten, W. (Eds.)

Simulation and Experiment inLaser MetrologyProceedings of the InternationalSymposium on Laesr Applications inPrecision Measurements, held inBalatonfured/Hungary, June 3-6, 1996

1996. 342 pages with 254 figures and5 tables. Hardcover.£ 41,-/$ 75.-/DM 98,-.ISBN 3-05-501762-5(Akademie Verlag, Berlin)

Over the last few years, opticalmeasurement techniques such asstructured illumination, holographicinterferometry and tomography havebeen applied more and more incombination with CAE-tools such asCAD and FEM. This combination hasfound a world of new applications.The contributors to the proceedingsvolume document the latestachievements in this advancing field.

Also of interest:

Henneberger, F./Schmitt-Flink, S./Gobel, E.O. (Eds.)

Optics of SemiconductorNanostructures1993. 589 pages with 232 figures.Hardcover.£ 92,-/$ 145.-/DM 224,-.ISBN 3-05-501544-4(Akademie Verlag, Berlin)

Wei3, C.O./Vilaseca, R.

Dynamics of LasersSeries: Nonlinear Systems

1991. XIII, 276 pages with 235 figuresand 3 tables. Hardcover.£ 40,-/$ 60.-/DM 99,-.ISBN 3-527-26586-4(VCH, Weinheim)

To order please contact yourbookseller or:

VCH, P.O. Box 10 11 61,D-69451 Weinheim,Telefax (0) 62 01 - 60 61 84

VCHA Wiley company


— For further information, visit our Physics home page at http://www.vchgroup.de/physics/

gravitational physics - pubman

Documents