Gravitational waves D. G. Blair

In the July 1961 issue of Endeavour Herman Bondi wrote ‘Gravitational waves are not only unfamiliar, even by name, but are distinctly unlikely to be observed’. Thirty years later gravitational waves are becoming more familiar. Two decades of intense effort have not yet yielded direct observation but a binary pulsar system has allowed their existence to be demonstrated. Today a large body of physicists consider the detection of gravitational waves,to be inevitable, perhaps in the next decade.

Gravitational wave astronomy will allow us to observe vibrational modes of black holes, coalescing neutron stars and gravitationally collapsing stellar cores in supernova explosions, and possibly even primordial gravitational waves from the big bang itself. In this paper I shall first describe the concept of gravitational waves, and then look at binary pulsars, which both prove their existence, and provide the best predict- able sources of terrestrial detectors. Then I shall consider the range of astrophysical sources expected, and the various instruments which have been designed to detect them and the fun- damental restrictions which limit sensi- tivity. Finally, in examining the instru- ments, I will look at the exciting prog- ress in technology which has in part been driven by the demands of gravita- tional wave detectors.

What are gravitational waves? Gravitational waves are as natural a consequence of Einstein’s field equa- tions in general relativity, as electro- magnetic waves are a natural consequ- ence of Maxwell’s equations of electro- magnetism. In spite of this, the reality of gravitational waves was somewhat masked by the mathematical complexity of general relativity, and it was not until the early 1950s that F.A. Pirani showed that gravitational waves can impart real energy to a physical system.

Einstein’s explanation of gravity is that it arises because matter causes

David Blair, Ph.D.

After graduating at the University of Western Australia, he did postgraduate research in low temperature physics at the University of East Anglia. For the last fifteen years he has worked on gravitational radiation detection at the Uni- versity of Western Australia, and on the de- velopment of ultrastable frequency standards using sapphire technology.

space-time to become curved. The curv- ature of space-time causes all trajector- ies to become curved, so that planets move in orbits around the Sun. The Sun acts as a gravitational lens. Purely by virtue of its mass it creates a distortion of space which appears to refract light, causing the positions of stars to be distorted more and more the closer their line of sight is to the limb of the sun. Figure 1 shows how the deflection of light beams past a massive object is analogous to that which one would obtain from a cusp-shaped lens. Gravi- tational lensing is now a very familiar fact of astronomy. Gravitationally dis- torted views of distant objects in the universe emphasize that the curvature of space-time is a real phenomena.

But why should this process of deflec- tion of light be interpreted as a distor- tion of space, rather than a distortion of the trajectory of the light itself. The reason is that we have no better way of defining a straight line than by a light beam. In general relativity the physics of free-falling objects, whether photons or planets, is always simple: no forces act, the objects simply follow the shor- test trajectory in space-time. The trajectories are straight, the space is curved. This leads to a beautifully ele- gant self consistent view of the motion of all objects.

In Newtonian physics space is an in- finitely rigid conceptual grid: it is the framework in which all things move. In contrast, general relativity has given us the view of space-time as a flexible dynamical medium. The curvature is described by the Einstein curvature ten- sor G. The curvature arises from the stress energy T which describes all the mass, energy and momentum of a sys- tem. Einstein’s equation, which relate G to T can be expressed as an equation of elasticity

Enduvour, New Serias, Vdume 16, No. 1,166Z. a166-6227I62 66.00 + 0.00. 0 1662. Psrgsmon Pmss pk. Printed in Great Britain.

This resembles Hooke’s Law F = k.x for the deflection of a spring under a force F. Space is curved by an amount G, due to the applied energy density or

pressure T. The spring constant (k) is C4

GE where c is the speed of light and

G is the constant of gravitation (note that G has a quite different meaning from G). This spring constant is an enormous number, about 1043. While telling us that space is flexible and can curve, this also tells us that space is enormously rigid, the stiffest material in the universe! All flexible media can sustain waves. Stiff materials (such as blocks of steel) can have large energy densities with very small amplitudes. (Imagine hitting a block of steel with a sledge-hammer.) Materials with low stiffness (such as the surface of a bal- loon) have much larger amplitudes for the same energy density. It should be no surprise at all that gravitational waves should exist once we understand space to be flexible. The enormous stiffness tells us immediately that the amplitude of gravitational waves will be very small, even if the energy density is enormous.

Gravitational waves are, therefore, simply ripples in the curvature of space- time. How do you measure the ampli- tude of the curvature? One way would be to monitor the curvature of space geometrically. In flat space the sum of the angles of a triangle add up to 180”. In curved space (such as a triangle drawn on the surface of a sphere) the sum differs from 180”. One could im- agine an instrument consisting of three laser beams. The sum of the intersec- tion angles would be measured, and deviations would register the passage of a gravitational wave.

If this was the only way of detecting gravitational waves then the job for the experimentalist would be even harder than it already is. Better detection schemes follow when we consider the difference between gravity and electro- magnetism. In electromagnetism there are two charges (positive and negative), whereas in gravity there is only one. There is no such thing as antigravity: all masses attract. This leads to several differences summarized in Table I below.

In both electromagnetism and gravity the radiation occurs whenever charge is

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Figure 1 The deflection of starlight past a massive object, and the cusp- shaped lens which would produce the same deflection pattern.

accelerated (mass is the charge of gravity). In electromagnetism the accel- eration of charge gives a dipole radiation pattern. The forward motion of a posi- tive charge is equivalent to a backward motion of a negative charge. There is a time varying dipole moment, and the energy radiated is proportional to the square of the second time derivative of the dipole moment. In gravity the fact that all charges have the same sign means that one cannot have a time varying dipole moment. The lowest order radiation is quadrupole radiation, characterized by systems such as those illustrated in figure 2.

The gravitational wave luminosity LG of such a system was shown by Einstein to be proportional to the square of the third time derivative of the quadrupole moment:

1 . . .

The amplitude of a gravitational wave can now be easily defined. There is symmetry between sources and detec- tors, so a gravitational wave causes a quadrupole deformation in a ring of free masses. The amplitude is the frac- tional deformation h = AL/L, where L is the size of the system and AL is its

change in length due to the wave. The flux density FG of gravitational waves is related to the amplitude by

FG = 30 Wme2(&)‘(&)

(3) The enormous stiffness of space

means that a wave with 3 per cent of the intensity of sunlight has an amplitude of 10p2”. To detect likely signals, detectors must be able to detect motions of typic- al size 1O-20 metres, as small compared with an atom as an atom is compared to a human. Such motions are much less than the size of a nucleus, and can be measured only for macroscopic bodies for which the mean position can be well defined. We will see, however, that quantum effects still provide serious limitations to the sensitivity that can be achieved.

Binary pulsars Einstein’s quadrupole formula, equa- tion (2) tells us that all binary or multi- ple astronomical systems must experi- ence gravitational wave viscosity. Orbit- al energy will be lost from the systems in the form of gravitational radiation and the objects will slowly spiral together. For the planets of the solar system the time for this to occur will be vastly greater than the age of the universe. For typical stellar mass objects the gravita- tional wave energy loss becomes signi- ficant only if the orbital period is less than a day.

Binary pulsars, consisting of a pair of closely orbiting neutron stars, are ideal for observing this behaviour. The pulsar signal, consists of sharp regular radio pulses, typically 20 per second, which are produced as the narrow beam of emission from the magnetic poles sweeps across the sky like that of light from a lighthouse. Timing the pulses allows the system to be probed very accurately. The orbital velocity of the pulsar causes the pulse period to be doppler shifted. The pulse arrival times can be determined to an accuracy of microseconds, and a full general relati- vistic analysis of the timing measure- ments allows accurate determination of the neutron star masses, their orbital parameter, and a range of non-classical effects - including the energy loss by gravitational radiation.

M K M

la)

(b) Binary stars hot face on)

(c) Ring of test particles

Figure 2 The three systems shown here can all act as sources of gravitational waves, and the first and third provide the basis for designing detectors.

Three such systems with orbital periods of less than a day have been discovered so far. The first to be disco- vered, PSR 1913 + 16, has been moni- tored for more than a decade, and shows orbital decay in precise agree- ment with the predictions of general relativity. The orbital decay data is shown in figure 3. The neutron stars will continue to move closer together, the orbital frequency will steadily increase, and in about 3 x lo8 years the neutron stars will approach coalescence. In its last seconds the orbital frequency will evolve as shown in figure 4. Coalesc- ence will occur when the orbital fre- quency reaches about 1kHz.

Essentially, this is a very simple gravi- tational quadrupole system, with the dynamics quite accurately described by Einstein’s quadrupole formula. When the orbits are circular and the masses are equal the gravitational wave lumi- nosity is given by

TABLE 1 COMPARISON OF ELECTROMAGNETIC WAVES AND GRAVITATIONAL WAVES

Electromagnetism

Gravity

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Charges Lowest Order Polarisations Spin Rest Velocity Radiation Mass

2 Dipole c- l 1 0 C

1 Quadrupole 0 C

2.

0 +

-2 -

-I-

-8-

B-

-10' Y Time

Figure 3 The orbital decay of a binary pulsar PSR 1913 + 16, showing exact agreement between theory and observation, which confirms the existence of gravitational waves.

32 G Lo =--M2R4&

45 2 > (4)

where R is the orbital radius and o is the orbital angular frequency. This for- mula can be simply re-expressed in terms of the Schwartschild radius of the stars (the radius it must be reduced to to become a black hole, r, = 2GM@, and the orbital velocity v. Then it becomes

2

(5)

Notice how the tiny scaling factorG 2

in equation (4) has been converted to its 2

reciprocal: the enormous factor c The

results demonstrate that the gravita- tional wave luminosity can become enormously high, as long as black hole conditions prevail: orbital velocities near to the speed of light and size comparable to the Schwartzchild radius. In the extreme case where v approaches c and r approaches rS, LG approaches 2 _, or 10’L Watts, an energy output G comparable to the optical luminosity of the entire visible Universe.

‘ij E

P $ 102

&

i

10’ lild 103 1cr* lo-’ 1cP 10’ 102 Id

Figure 4 The last moments of neutron star binary coalescence, showing how the gravitational wave frequency (twice the orbital period) increases from 10 Hz to 1 kHz in the last 1000 seconds of the system’s life.

Gravitational wave luminosities with- in a few orders of magnitude of this value could occur if the coalescing neut- ron stars were to go on to collapse into a black hole. This is a likely occurrence since the total mass of the combined neutron star is likely to exceed the critical mass, above which it must col- lapse to a black hole. Unfortunately, the critical mass is not known exactly, and the dynamics of the coalescence is not understood. In any case, the coalescences of neutron stars represent the most extraordinary energetic events to occur in the Universe since the Big Bang. The prospect of being able to observe such coalescences, and the formation of black holes, and even the detailed vibrational signatures for the normal modes of oscillation of black holes, make gravitational wave astro- nomy among the most exciting chal- lenges of modern science. Even without black hole formation, neutron star coalescences are strong sources of grav- ity waves, detectable by planned detec- tors even at distance of 3OOMpc, a dis- tance which encompasses more than lo6 galaxies. Within this volume neutron stars should be coalescing three times a year.

Equation (5) can be applied to any non-spherically symmetric gravita- tionally collapsing system: for example, a supernova in which a core collapse forms a neutron star or a black hole. For such systems a detailed analysis is difficult, however, partly because we do not have enough information on the initial conditions of a star prior to col- lapse and partly because the general relativistic modelling of the collapse is very difficult. Present modelling cannot tell us much more than the simple analysis of equation (5). The efficiency for conversion of rest mass energy to gravitational waves can be in the range lo-“’ to lo-‘, with a pulse duration of a few milliseconds. The peak frequency components will be - 1kHz for solar mass objects.

Gravitational waves may be expected from many other sources, and are likely to form a spectrum covering the fre- quency range 10-l” Hz to lo4 Hz. There could be a broad spectrum of primordial gravitational waves from the Big Bang. (The observed isotropy of the cosmic background radiation sets some limits on this.) More speculative sources con- sist of the coalescence of massive black holes in galaxy or quasar cores, or the interaction of black hole cores in globu- lar clusters with black hole cores in galaxies. Much more certain sources of gravity waves are the combined effects of millions of binary stars in our galaxy, which will provide a background of stochastic gravitational waves at fre- quencies in the range 1O-4-1O-5 Hz.

Seismic vibration makes it very dif- ficult to consider building terrestrial

gravitational wave detectors for fre- quencies less than 1Hz. Spacecraft de- tectors are being designed and some doppler ranging experiments with inter- planetary space probes have already set weak limits on gravitational wave densi- ties at around 10-s Hz. Gravitational waves can be thought of as causing doppler shifts to an incoming radiation beam. By making precise measure- ments of the pulse period from an iso- lated millisecond pulsar, Taylor et nl. have set limits on the gravitational wave density in the universe for frequencies - 10-s Hz.

The dream of gravitational astro- nomy, however, focuses most strongly on high frequency gravitational waves due to stellar mass sources, such as supernovae and coalescing neutron stars. For such sources a tetrahedral array of four or more detectors on the surface of the Earth creates an omni- directional telescope. Wave direction is determined by measuring the amplitude and arrival time of signals which will take - 40ms to pass through the Earth. A few arc minutes directional resolution will be achievable if signal arrival times are determined to a bit less than a millisecond. Such a telescope will allow us to probe the details of supernovae, to observe the modes of oscillation of the black hole event horizon, and monitor gravitational collapse events throughout a large volume of the Universe.

Detectors for gravitational waves We saw above that the typical frequen- cy for roughly solar mass event is - 1kHz. Strong signals can be of only very short duration, hence signals will nor- mally be of broad bandwidth. There are two general ways of making detectors. One consists of carefully monitoring the distance between two free test masses using electromagnetic waves. The second consists of measuring the acous- tic energy induced in a solid bar of material. In the first case a practical means of achieving sufficient sensitivity is to let the test masses be mirrors in an L-shaped configuration, and use a Michelson interferometer to detect rela- tive motion between orthogonal direc- tions. To achieve extra sensitivity the laser beam may be reflected many times between the mirrors, but the configura- tion must always have an optical path less than half the wavelength of the gravity wave or the second half cycle will cancel the effects of the first. The second type of detector consists of a large mass of metal, or resonant bar. A gravity wave will apply a small deforma- tion to the bar, which is sensed as a very small change in acoustic vibration. For the resonant bar the length must be such that the fundamental longitudinal resonant frequency of the bar is compa- rable to the gravitational wave fre- quency.

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Thus a laser interferometer detector for 1 kHz waves can be up to - 150km long, but in practice, economics (and the curvature of the earth) has led peo- ple to consider 3 km a practical length to choose. However a resonant bar must be shorter than this by the ratio of V.&z (where V, is the velocity of sound in the bar). Thus a bar antenna should be about 3m long. A gravitational wave of amplitude 10 -*” will induce 3 x lo-*“m deflection between the ends of a bar. Both are exceedingly small quantities, but we shall show that both are measur- able in principle, although the latter is close to the quantum limit.

Fundamental restrictions. To determine the limits to the sensitivity of any of these devices we must consider the quantum mechanical restrictions on the measurements. The familiar form of the uncertainty principle A x Ap G h im- plies that the position of an object x can be measured to arbitrary precision (that is, Ax = 0) as long as the uncertainty in momentum Ap is arbitrarily large. But the uncertainty principle arises because the measurement device acts back on the system being measured, and at the very minimum quantum zero point fluctuations are imposed on the other variable. That is, in the process of measuring the position to high preci- sion, the momentum is disturbed, and clearly this means that future position measurements will be corrupted.

One does not have to measure posi- tion or momentum when monitoring a system. There is an arbitrary range of variable one can consider measuring, such as energy, velocity, acceleration, etc. Many measurements, however, use amplifiers, and special properties of am- plifiers set a limit called the standard quantum limit. Linear amplifiers (as used in hi-fi) increase the amplitude A of a signal, and, crucially, preserve the phase +. (If they didn’t, they would be horribly distorting!)

They measure two variables, normal- ly called Xi and Xz, where Xi = A sin r$ and X2 = A cos $. There is an uncer- tainty principle for these variables, AXi AX2 3 hlmw, where m is the mass and w the frequency. However, because of the symmetry between these variables, linear amplifiers impose equal uncer- tainty on each variable, AX, = AXZ. This immediately translates to the stan- dard quantum limit, which sets a limit of resolution equivalent to about 1.4 times the energy of a photon, and (applied to a position measurement) sets a limit

d h - mo

This is a standard quantum limit. However, if a phase sensitive or non- linear amplifier is used, AX, need not

equal AX*. Then in principle, one can measure arbitrarily small signals.

To people used to counting photons with photomultipliers and other energy detectors, the concept of the photon has become almost axiomatic. This is wrong. The photon’s existence depends on the use of a direct energy measure- ment scheme. In general, the uncertain- ty principle only requires a product of the form AX, AX2 to be large enough, and it is not at all unreasonable to consider a measurement system for which AX, is much smaller than AX*, using special detectors and amplifiers. Such a system is said to be squeezed: the uncertainty is squeezed into one variable only. Applied to gravity wave detectors, this means that one can mea- sure gravity wave signals that are smal- ler than the standard quantum limit. In practice squeezing is very difficult to achieve because losses always act to undo the squeezing. Thus ultra-low loss systems must be used.

The fundamental nature of quantum mechanics therefore reveals itself when considering precision measurements on tons of metal! We are forced to recog- nize that quanta (such as photons and phonons) are quanta only when the measurement imposes that particle like nature on them. Two thousand five hundred years ago Demo&us said:

‘We are accustomed to speak of heat, of cold, of light.

In reality there are atoms and space’.

Today we could well paraphrase this:

‘We are accustomed to speak of photons, of phonons, of electrons.

In reality there are wavefunctions and fields’.

Even more explicitly, we may ask the question:

‘When is a photon not a photon? The answer is:

‘A photon is a photon when we mea- sure its energy. A photon is almost a photon if we measure its amplitude and phase. A photon is not a photon when we squeeze it!’

To date, squeezing technology has not been applied to either resonant bars or laser interferometer gravity wave de- tectors. For bars, squeezing can allow the sensitivity to be brought below the standard quantum limit and in principle could allow bars to be significantly im- proved. For laser interferometers the main advantage of squeezing is to change the photon statistics so that photon shot noise which arises due to fluctuations in photon density are re- duced. This can allow higher sensitivity to be achieved at lower laser power.

A peculiarity of gravitational waves is that the strain h does not necessarily return to zero after a burst. A burst of

gravitational waves transfers rest mass and angular momentum from inside a spherical volume to the outside. The burst can create a stepwise change in h. Some people have interpreted this as being extremely significant, because a resonant bar, for example, is per- manently charged in length by a passing event. The problem is that this DC change is utterly unmeasurable. Only AC measurements are possible at the 1O-20 level.

Resonant bar detectors. While fun- damental physics limits the achievable sensitivity of gravitational wave detec- tors, enormous ingenuity is required to reach this level of sensitivity in a prac- tical device.

The technology of resonant bars is most mature in this regard. A develop- ment programme of almost two decades has solved very difficult problems of vibration isolation, thermal noise and ultrasensitive vibration measurement. Figure 5 shows the construction of a typical antenna. A massive metal bar made from a low acoustic loss material - aluminium or niobium - is supported by a complex set of vibration isolation components which are designed to re- duce ambient acoustic and seismic noise - typically - 10-l’ metres amplitude in a few Hertz bandwidth around 8OOHz - to less than lo-” metres amplitude. The bar is enclosed by a massive cryoge- nic system, which cools the bar to 4.2K, to reduce the intrinsic Brownian motion of the antenna, and also to allow super- conductivity to be used to create ultrasensitive vibration transducers. The transducers, which must be able to resolve 10-19-10-20 metre changes in the vibration of the antenna, use either superconducting quantum interference device (SQUID) amplifiers, or micro- wave superconducting cavity sensors. In either case, the motion of the antenna modulates a superconducting capacitor or inductor, and this is registered as a small current amplified by the SQUID, or a change in microwave phase am- plified by a cryogenic transistor am- plifier.

Vibration isolation, low tempera- tures, and sensitive measuring devices are not enough. The Brownian motion is still too large unless the acoustic losses of the antenna are very small. Low acoustic losses force the Brownian motion (which has amplitude - lo-l5 metres) to take on very pure sinusoidal motion. A gravity wave causes a devia- tion in this motion, and this is what is measured. Niobium, as used in the Perth antenna, has such a low acoustic loss that when struck it will ring like a bell for many days!

During the 1990s four detectors, at Louisiana, Rome, Stanford, and Perth should be operating in coincidence with sensitivity sufficient to see any intense

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Main antenna support beams

Experimental chamber

- 30K shield n

77K shield

Catherine wheel and cantilever 11 Suspension for niobium bar

Figure 5 Cross-section of cryostat, with side view of antenna.

gravitational wave event occurring in our galaxy. Currently two of these de- tectors, at Louisiana and Rome, are operating as sensitivities h - 7 X 10-19. The other two should join them in 1992. A four-detector coincidence by this array would be very difficult to attribute to anything but gravitational waves.

Unfortunately, the strong gravita- tional wave events in our galaxy are likely to occur at most a few times every 10 years, and at worst once in 100 years. Long term observations will provide strong constraints on our knowledge of gravitational collapse, and the missing mass in our galaxy, but it may not yield signals!

It is feasible to scale up resonant bar detectors to at least 10 times greater mass, bringing the attainable sensitivity to h s lo- *r The large scale engineer- . ing makes this rather a daunting task. More promising, perhaps is the applica- tion of quantum squeezing, to squeeze more sensitivity out of the existing de- tectors.

Laser interferometer detectors. To be certain of seeing signals a gravitational wave detector must have sensitivity h s lo-**. The most promising way of achieving this, is by laser interferomet- ry. The concept is shown in figure 6. A Michelson interferometer measures the

relative displacement between two mir- rors and a beam splitter. The mirrors hang as pendulums, and above the pen- dulum frequency, they respond like free test masses. A gravitational wave stretches one arm and shrinks the other: this is detected by a change in the interference fringes.

sary to use a high laser intensity, so that the statistical fluctuations of photon arrival times (that is, shot noise) is reduced. The beauty of a laser inter- ferometer is that it can be scaled up. A practical size is on earth - 3km. Low- frequency detectors in space could be millions of kilometres long. For a 3km

To achieve high sensitivity it is neces- detector, sensitivity can be increased if

Figure 6 A laser Michelson interferometer for detecting gravitational waves.

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Test masses on pendulum suspensions

VI Detector

Figure 7 A laser interferometer with extra mirrors to create optical delay lines to increase the sensitivity. (Courtesy of New Scient., 1 September 1990.)

the laser beam is allowed to reflect many times back and forth in each arm. This can be achieved by adding two extra mirrors, as shown in figure 7.

Prototype detectors from 10 to 40 metres in length have been developed at Glasgow, Munich, Caltech and ISAS (Japan). They have achieved impressive sensitivity: h - 3 x lo-” in a 1kHz bandwidth.

All the groups, plus groups in Austra- lia, Italy, and France, plan to build large-scale detectors. To do this repre- sents an exciting technological chal- lenge. Optical components must be accurate to the nanometer level. Optic- al losses must be at the parts per million level. The diffraction limit means that the optical beam sizes are relatively large, so that the vacuum pipes for this system (l-l Sm diameter) represent the largest volume of vacuum ever created on Earth. Laser power must be high, typically lOOW, and the laser itself must be stabilized so that its frequency is controlled to about 1 millihertz accura- cy. Up to now argon ion lasers have

been used, but most groups plan to use super efficient laser diode pumped neodymium-YAG lasers. These are amongst the most efficient, compact light sources ever created, with an enor- mous range of potential applications from projection laser television to frighteningly dangerous ray guns. At their projected sensitivity, these detec- tors could see neutron stars coalescing out to distances of 1OOMpc. Assuming that ours is a typical galaxy, such events should occur at least three times a year, and should certainly be observed.

In addition, enormously more fre- quent supernovae, and other forms of neutron star and black hole births, means that we should be able to see that space-time is alive with ripples. From these we will be able to map out an otherwise hidden Universe. A corre- lated array of four or more detectors on earth will create a telescope with a few minutes of arc resolving power. The detectors can be easily optimized for different frequency bands, and different types of signals. Thus one can search for

bursts, chirrups (the rising frequency of coalescence), weak continuous signals, or random stochastic background. The latter are predicted to have been gener- ated and amplified in the earliest mo- ments of the Big Bang. If these could be detected, it would give us a glimpse of the Universe when it was 20 orders of magnitude younger than it was when the cosmic microwave background sig- nal was released.

Conclusion Efforts at gravitational wave detection have already spawned new technologies and new physics outside the direct areas of relevance. These include improved SQUIDS now used for non-contact monitoring of the brain; sapphire clock technology; new transducers for gra- vimetry on earth and in space; and the understanding of quantum squeezing. Gravitational wave detection epito- mises the way fundamental science can drive innovation and create mostly un- predictable spin-offs. When the dream of gravitational wave detection, fol- lowed by gravitational astronomy, is realised it will be a landmark in human achievement, and it will open up a whole new window to the Universe.

Bibliography This paper is based on an enormous body of research by workers in the U.S.A., Europe, U.S.S.R., Australia and Japan. The reader is referred to the following books for further information and references. 1. Blair, D. G. (ed.), ‘The Detection of

Gravitational Waves’, Cambridge Uni- versity Press, 1991.

2. Durelle, N. and Piran, T. (eds), ‘Gravita- tional Radiation’, North Holland, 1982.

3. McClelland. D. and Bachor. H. A. feds), ‘Gravitational Astronomy: Instrcment Design and Astrophysical Prospects’, World Scientific, 1991.

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