by professor Vladimir BRAGINSKY, Dr. Sc. (Phys. & Math.), Head of the Radiophysical Department at the Physical Faculty of Moscow State University chairman of the Commission on Gravitation at the USSR Academy of Sciences

People have long come to know the physical meaning of the word "field". As a matter of fact, we live in the midst of and are influenced by all kinds of fields (nuclear, magnetic, electrical). Beyond any doubt, the most significant and palpable one is that of gravity. Whereas the other fields affect either specific materials or certain properties of materials or certain properties of matter, the gravitational field is of a universal nature, an indispensable component of life. But for gravity, there would be no bonds between matter, not only on Earth, but also in the entire Universe.

And yet though the gravitational field is all-pervading and vital to nature and man, we know much less about it than, say, about the electromagnetic field discovered and thoroughly investigated not so long ago. Why is this so? Electromagnetic waves are a very opportune and readily controlled manifestation of the electromagnetic field, which makes it easy to probe into its nature. Is it possible to explore the gravitational field in a similar manner? Do gravitational waves really exist? If so, why have they not been detected earlier? In the USSR three laboratories- of Moscow State University, the Academy's Institute of Earth Physics and the Institute of Crystallography-are jointly developing aerials to detect bursts of gravitational radiation from extraterrestrial sources.

Their existence was predicted by the great Einstein at the beginning of the century. He held, however, that they are extremely feeble and weakly interact with matter-the reason for their having escaped detection.

According to present-day concepts based on the theory of relativity, they are disturbances of the gravitational field travelling with a finite velocity in space and carrying energy in much the same way as electromagnetic disturbances. Such disturbances are of a wave nature and act on matter and physical processes as they travel from point to point.

It is assumed that, first of all, the velocity of propagation of gravitational waves in space should be the same as that of electromagnetic wave propagation, i.e., the velocity of light.

Secondly, just as electromagnetic waves they should be transverse, i.e., their action on matter should be perpendicular to the direction of their propagation. Thus, a plane wave incident on a material body will cause the latter to contract or expand along two mutually perpendicular axes. Imagine a gravitational wave directed along the axis of a cylinder. As this takes place, the cross-section of the cylinder will be seen to take the shape of an ellipse stretched in turns horizontally and vertically. When the wave travels at right angles to the axis of the cylinder, then the ends will "breathe". A fascinating trait of these waves is that the relative force of their action increases with the distance between two probe particles or bodies. When dealing with a body of certain length, the force acting on its ends will increase with the length of the body.

Basically, a gravitational radiation source can be set up in an ordinary laboratory since any accelerated motion of a massive body will lead to emanation of gravitational waves. Yet this is hardly feasible considering that the explosion of a 17-kiloton uranium bomb releases a gravitational radiation flux of only 10 ^-4 ergs per second while the total energy of gravitational radiation amounts to not more than 10 ^-12 ergs. To compare: a flashlight bulb consumes 107 ergs per second, i.e., millions of billions times more than the gravitational energy released during the explosion. In other words, the effect of terrestrial sources of gravitational radiation is so infinitely small that no reliable transmitter-receiver scheme has as yet been conceived. Therefore, laboratories working

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in this field have to rely solely on natural extraterrestrial sources for any possible information.

Events of prodigious dimensions incommensurate with any terrestrial disaster are taking place in the cosmos. In fact, they are simply tangible manifestations of the Universe's existence, its "breath". Powerful bursts of gravitational radiation are also to be anticipated, for instance, in the event of a head-on collision of stars, or their flare up. The energy released on the "scene of the event" can be up to 10 ⁵⁴ ergs, though only 10 ³ to 1 erg per sq. cm may actually reach the Earth. The collapse of stars and the absorption of matter by the mysterious black holes is liable to be accompanied by the emission of a gravitational radiation pulse producing a short-term wave flux of up to 10 ⁴ ergs per sq. cm density on the Earth's surface.

Catastrophes of this kind give rise to eruptions of only a short duration. There are, however, also sources of continuous gravitational radiation. These are above all double stars, revolving around a common centre of gravity and emitting strictly harmonious gravitational waves. Their maximum intensity is at a frequency double that of the stars revolution. The greater part of the flux is directed along the revolution axis of the stars.

Theory maintains that the density of the gravitational radiation energy to be expected at the Earth's surface is within 10 ^{- 4} to 1 erg per sq. cm. The degree of distortion of space this can produce is worth considering. Electromagnetic waves too cause a certain distortion of space, though this is "noted" only by the charged particles, say, electrons that are made to shift in a definite direction. This motion of the electron or probe particle reveals the presence of the electromagnetic wave. As for the gravitational wave, its effect is manifest from the change it brings about in the force of attraction between bodies and particles. Consequently, at least two probes are needed to detect the presence of the waves. If the probes are placed not more than 1 m apart, the wave will make them move towards or away from each other by not more than 10 ^-19 to 10 ^-17 cm. It is of course practically impossible to graphically visualize such a small quantity?

The measurements are carried out with the aid of the Weber's monoblock aerial made of a massive solid bar or cylinder. This method of measurement is based on the assumption that a gravitational wave, perpendicular to the longitudinal axis of the cylinder interacts with the body of the aerial and causes longitudinal elastic vibrations that are converted into electric signals, either directly, when the aerial itself is a piezoelectric material, or by piezoelectric transducers attached to the surface of the aerial, or any other no less sensitive electromechanical transducer. The aerial used by Weber was a 1.5 m long block of aluminium, 60 cm in diameter weighing one and a half tons, and suspended horizontally by strong threads from a special support, with the whole assembly arranged in a vacuum chamber. All the equipment was reliably isolated from seismic and other effects of the foundation and external devices. The aerial was capable of detecting gravity waves causing a displacement of about 10 ^{- 14} cm. But it was found that to be effective the sensitivity of the aerial had to be a thousand times higher.

We had to start from the very beginning, from the yet unborn theory of gravitational aerials. To get to the root of the problem, let's examine its technological aspect.

The natural thermal vibration of the aerial is the main hindrance in detection of the small vibrations created in it by gravitational waves. The particle acceleration due to thermal vibration (Brownian movement) is described by an equation containing the invariable parameters of the given experiment (Boltzmann's universal constant, the gravity wave fre-

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quency, etc.) and certain parameters that are at the experimentator's command. The acceleration is directly proportional to the temperature of the aerial and inversely proportional to its mass and quality factor. Hence, the precise inference: "thermal noise" is the greater the higher the temperature and the aerial has to be cooled for better performance. The second conclusion to be drawn from the equation is that the accuracy of measurement can be improved by increasing the mass of the aerial. Most experimentators are working along these lines. Thus, the Stanford University in the USA is developing a 5-ton receiver cooled down to a temperature closely approaching absolute zero.

Soviet researchers have chosen what seems to be a more promising path by concentrating their efforts on another parameter of the equation-the quality factor of the aerial. The quality factor is defined as the ratio of the energy stored by the receiver during vibration to the energy dissipated per cycle of the gravity wave frequency. In other words, it shows how well the aerial retains the impinging pulse. Quality as such is an independent and a most fascinating subject. The quality of aerials is affected by numerous and often conflicting factors, and the choice of the best compromise depends entirely on the experimentator's skill. Weber's receiver had a quality factor of 10 ⁵ . We have been able to raise the figure to 5x10 ⁹ , i.e., to make it 50 thousand times better.

The choice of material was of paramount importance and, in the long run, this proved to be monocrystallic sapphire. Vibrations dampen very slowly in such a crystal, it is said to possess low dissipation. The index describing the storing capacity of aluminium is 2x10 ² , while that of sapphire proved to be as high as 10 ¹⁶ . At such slow attenuation, the Brownian movement is stretched out in time and, as a result, short bursts become more distinct against its background. Another advantage of the sapphire aerial is that improvement in quality allows to reduce its mass and volume contributing to a more uniform and deeper cooling.

Monocrystals of the proper size and purity simply do not exist in nature and to grow them in a laboratory is no simple task. Nevertheless, the Institute of Crystallography of the USSR Academy of Sciences produced a sapphire monocrystal weighing six kg! This solved the first half of the problem-that of minimizing the effect of the Brownian movement.

However, there still remained the no less difficult task of developing a device for measuring ultrasmall vibrations of the aerial without introducing any noise. The difficulties were not only of an experimental, but also of a fundamental nature, since in trying to measure such small displacements, we were actually intruding into the field of measurements in quantum mechanics.

Quantum mechanics holds that any physical intrusion for closer examination of the properties of electrons or other elementary particles is bound to bring about an unpredictable change in their state. Moreover, this is a corollary of quantum mechanics. Thus, the interference caused by highly accurate measurement of the electron coordinate will inevitably "push" or, to be more exact, impart an unpredictable impulse to the electron. The next measurement will then yield a coordinate value quite different from that of the first measurement. Measurement of the electron impulse with the same degree of accuracy will inevitably shift its coordinate. This annoying state of affairs becomes even more annoying on closer inspection. Suffice it to recall that the problem was tackled in the 1920s and 1930s by Niels Bohr, Wemer Heisenberg, Wolfgang Pauli and other prominent scientists to realize its importance. Thus, a closer look leads to the conclusion that the unpredictable discrepancy is a direct result of registration of data pertaining to the coordinate or impulse of the particle. The discrepancy does not depend on how the data is obtained or how it is registered; be it in the mind of the experimentator or on tape. As long as the information is beyond the particle in question, all subsequent measurements will show a discrepancy to have been present. The only way to avoid this is by "returning the measuring equipment back to the initial position" and, consequently, returning the information to the particle.

The well-known Heisenberg principle of uncertainty stipulates that the coordinate of a particle and its impulse cannot be measured at the same time with the same degree of accuracy. According to this principle, the product of the error of measurement (or of accurate measurement) of the coordinate (/\x) and the error of measurement or the accurate measurement of the impulse (/\p) is a constant quantity. Hence, the error in the measurement of the impulse (/\p) will increase as the error in the measurement of the coordinate (/\x) becomes smaller, i.e., the accuracy with which we determine the position of the particle will be higher.

But to return to our problem. An elegant mathematical theory of optimal quantum filtration shows that a measurement or combination of measurements can be performed accurately Unfortunately, the theory does not explain how this can be achieved in practice. Yet the search for gravitational waves requires implementation of precisely such quantum mechanics measurements. The accuracy in the registration of the aerial's deviation is to be of the order of 10-17 cm or even less in some one thousandth of a second, corresponding to the duration of a burst of gravitational radiation. During the interval of one thousandth of a second, the massive metal body of the horizontally suspended aerial will behave as a free body or as the electron we've just discussed. In other words, the aerial obeys the laws of quantum mechanics in the same way as an electron.

So quantum mechanics has actually led us into an impasse known as the principle of uncertainty, and we will never be able to develop an aerial of satisfactory resolution. But there is a certain circumstance in our favour: the strictly harmonious nature of the expected vibration of the aerial. Of course, there is no avoiding the principle of uncertainty in continuous transmission to the macrosystem of information on the microdisplacements of the aerial.

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