AMERICAN SCIENTIST

A QUARTERLY PUBLICATION OF THE SOCIETY OF THE SIGMA XI DEVOTED TO

THE PROMOTION OF RESEARCH IN SCIENCE

VOL. 30 APRIL, 1942 NO. 2

THE PROBLEM OF THE EXPANDING

UNIVERSE

By EDWIN HUBBLE

Mt. Wilson Observatory

I PROPOSE to discuss the problem of the expanding universe from the observational point of view. The fact that such a venture is permissible is emphatic evidence that empirical research has definitely entered the field of cosmology. The exploration of space has swept outward in successive waves, first, through the system of the planets, then, through the stellar system, and, finally, into the realm of the nebulae. Today we study a region of space so vast and so homogeneous that it may well be a fair sample of the universe. At any rate, we are justified in adopting the assumption as a working hypothesis and attempting to infer the nature of the universe from the observed characteristics of the sample. One phase of this ambitious project is the observational test of the current theory of the expanding universes of general relativity.

I shall briefly describe the observable region of space as revealed by preliminary reconnaissance with large telescopes, then sketch the theory in outline, and, finally, discuss the recent more accurate observations that were designed to clarify and test the theory.

THE OBSERVABLE REGION

The sun,as you know, is a star, one of several thousand million stars which together form the stellar system. This system is a great swarm of stars isolated in space. It drifts through the universe as a swarm of bees moves through the summer air, From our position near the sun we look out through the swarm of stars, past the borders, and into the universe beyond.

Until recently those outer regions lay in the realm of speculation. Today we explore them with confidence. They are empty for the most part, vast stretches of empty space. But here and there, separated by immense intervals, other stellar systems are found, comparable with our own. We find them thinly scattered through space out as far as telescopes can reach. They are so distant that, in general, they appear as small faint clouds mingled among the stars, and many of them have long been known by the name “nebulae”. Their identification as great stellar systems, the true inhabitants of the universe, was a recent achievement of great telescopes.

On photographs made with such instruments, these nebulae, the stellar systems, appear in many forms. Nevertheless they fall naturally into an ordered sequence ranging from compact globular masses through flattening ellipsoids into a line of unwinding spirals. The array exhibits the progressive development of a single basic pattern, and is known as the sequence of classification. It may represent the life history of stellar systems. At any rate, it emphasizes the common features of bodies that belong to a single family.

Consistent with this interpretation is the fact that these stellar systems, regardless of their structural forms, are all of the same general order of intrinsic luminosity ; that is, of candlepower. They average about 100 million suns and most of them fall within the narrow range from one-half to twice this average value. Giants and dwarfs are known, 10 to 20 times brighter or fainter than average, but their numbers appear to be relatively small. This conclusion is definitely established in the case of giants, which can be readily observed throughout an immense volume of space, but is still speculative in the case of dwarfs which can be studied only in our immediate vicinity.

The limited range in luminosity is important because it offers a convenient measure of distance. As a first approximation, we may assume that the nebulae are all equally luminous, and, consequently, that their apparent faintness indicates their distance. The procedure is not reliable in the case of a single object because the particular nebula might happen to be a giant or a dwarf rather than a normal stellar system. But for statistical purposes, where large numbers of nebulae are involved, the relatively few giants and dwarfs should average out, and the mean distances of large groups may be accurately determined. It is by this method that the more remote regions of space, near the limits of the telescope, may be explored with confidence.

Throughout the observable region the nebulae are found scattered singly, in pairs, and in groups up to great compact clusters or even clouds. The small scale distribution is irregular, and is dominated by a tendency towards clustering. Yet when larger and larger volumes of space are compared, the minor irregularities tend to average out, and the samples grow more and more uniform. If the observable region were divided into a hundred or even a thousand equal parts, the contents would probably be nearly identical. Therefore, the large scale distribution of nebulae is said to be uniform ; the observable region is homogeneous, very much the same everywhere and in all directions.

We may now present a rough sketch of our sample of the universe. The faintest nebulae that can be detected with the largest telescope in operation (the 100-inch reflector on Mount Wilson) are about two million times fainter than the faintest star that can be see with the naked eye. Since we know the average candle power of these nebulae, we can estimate their average distance – 500 million light years. A sphere with this radius defines the observable region of space. Throughout the sphere are scattered about 100 million nebulae, at various stages of their evolutional development. These nebulae average about 100 million times brighter than the sun and several thousand million times more massive. Our own stellar system is a giant nebula, and is presumably a well-developed, open spiral. The nebulae are found, as has been said, singly, in groups and in clusters but, on the grand scale, these local irregularities average out and the observable region as a whole is approximately homogeneous. The average interval between neighboring nebulae is about two million light years, and the internebular space is sensibly transparent.

THE LAW OF RED SHIFTS

Another general characteristic of the observable region has been found in the law of red shifts, sometimes called the velocity-distance relation. This feature introduces the subject of spectrum analysis. It is well known that, in general, light from any source is a composite of many individual colors or wavelengths. When the composite beam passes through a glass prism or other suitable device, the individual colors are separated out in an ordered rainbow sequence, known as a spectrum. The prism bends the light waves according to the wavelength. The deflections are least for the long waves of the red and are greatest for the short waves of the violet. Hence position in the spectrum indicates the wavelength of the light falling at any particular place in the sequence.

Incandescent solids, and certain other sources, radiate light of all possible wavelengths, and their spectra, called emission spectra, consist of various isolated colors separated by blank spaces. The patterns are well known, hence gases in a distance light source can be identified by their spectra.

The sun presents a third kind of spectrum, known as an absorption spectrum. The main body of the sun furnishes a continuous spectrum. The heavy atmosphere surrounding the main body is gaseous and would normally exhibit an emission spectrum. Actually, the atmosphere, because it is cooler than the main body, absorbs from the continuous background those colors it would otherwise emit. Therefore the solar spectrum is a continuous spectrum on which is superposed a pattern of dark gaps or lines. These dark lines identify the gases in the solar atmosphere and indicate the physical conditions under which they exist.

The nebulae are stellar systems, and their spectra resemble that of the sun. Dark lines due to calcium, hydrogen, iron and other elements in the atmospheres of the component stars are identified with complete confidence. In the case of the nearer nebulae, these lines are close to their normal positions as determined in the laboratory or in the sun. In general, however, accurate measures disclose slight displacements, either to the red or to the violet side of the exact normal positions.

Such small displacements are familiar features in the spectra of stars and are known to be introduced by rapid motion in the line of sight. If a star is rapidly approaching the observer, the light waves are crowded together and shortened, and all the spectral lines appear slightly to the violet side of the normal positions. Conversely, rapid recession of a star drags out and lengthens the light waves, and the spectral lines are seen to the red of their normal positions.

The amount of these displacements (they are called Doppler shifts) indicate the velocities of the stars in the line of sight. If the wavelengths are altered by a certain fraction of the normal wavelengths, the star is moving at a velocity which is that same faction of the velocity of light. In this way it has been found that the stars are drifting about at average speeds of 10 to 30 miles per second, and, indeed, that the stellar system, our own nebula, is rotating about its center at the majestic rate of one revolution in perhaps 200 millions years.

Similarly, the nebulae are found to be drifting about in space at average speeds of the order of 150 miles per second. Such speeds, of course, are minute factions of the velocities of light, and the corresponding Doppler shifts, which may be either to the violet or the red, and barely perceptible.

But the spectra of distant nebulae show another effect as conspicuous as it is remarkable. The dark absorption lines are found far to the red of their normal positions. Superposed on the small red or violet shifts representing individual motions, is a systematic shift to the red which increases directly with the distances of the nebulae observed. If one nebula is twice as far away as another, the red shift will be twice as large; if n times as far away, the red shift will be n times as large. This relation is known as the law of red shifts ; it appears to be a quite general feature of the observable region of space.

If these systematic red shifts are interpreted as the familiar Doppler shifts, it follows that the nebulae are receding from us in all directions at velocities that increase directly with the momentary distances. The rate of increase is about 100 miles per second per million light years of distance, and the observations have been carried out to nearly 250 million light years where the red shifts correspond to velocities of recession of nearly 25,000 miles per second or 1/7 the velocity of light.

On this interpretation the present distribution of nebulae could be accounted for by the assumption that all the nebulae were once jammed together in a very small volume of space. Then, at a certain instant, some 1800 million years ago, the jam exploded, the nebulae rushed outward in all directions with all possible velocities, and they have maintained these velocities to the present day. Thus the nebulae have now receded to various distances, depending upon their initial velocities, and our observations necessarily uncover the law of red shifts.

This pattern of history seems so remarkable that some observers view it with pardonable reserve, and try to imagine alternative explanations for the law of red shifts. Up to the present, they have failed. Other ways are known by which red shifts might be produced, but all of them introduce additional effects that should be conspicuous and actually are not found. Red shifts represent Doppler effects, physical recession of the nebulae, or the action of some hitherto unrecognized principle in nature.

COSMOLOGICAL THEORY

The preliminary sketch of the observable region was completed about ten years ago. It was not necessarily a finished picture, but it furnished a rough framework within which precise, detailed investigations could be planned with a proper understanding of their relation to the general scheme. Such new investigations, of course, were guided when practical by current theory. Let me explain the significance of this procedure.

Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list still further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and behavior of the physical universe.

The relation is evident in the history of cosmology. The study at first was pure speculation. But the exploration of space moved outward until finally a vast region, possibly a fair sample of the universe, was opened for inspection. Then theory was revitalized ; it now had a sure base from which to venture forth.

Current theory starts with two fundamental principles : general relativity and the cosmological principle. General relativity states that the geometry of space is determined by the contents of space, and formulates the nature of the relation. Crudely put, the principle states that space is curved in the vicinity of matter, and that the amount of curvature depends upon the amount of matter. Because of the irregular distribution of matter in our world, the small scale structure of space is highly complex. However, if the universe is sufficiently homogeneous on the large scale, we may adopt a general curvature for the universe, or for the observable region as a whole, just as we speak of the general curvature of the earth's surface, disregarding the mountains and ocean basins. The nature of the spatial curvature, whether it is positive or negative, and the numerical value, is a subject for empirical investigation.

The second, or cosmological principle is a pure assumption – the very simple postulate that, on the grand scale, the universe will appear much the same from whatever position it may be explored. In other words, there is no favored position in the universe, no center, no boundaries. If we, on the earth, see the universe expanding in all directions, then any other observer, no matter where he is located, will also see the universe expanding in the same manner. The postulate, it may be added, implies that, on the grand scale, the universe is homogeneous and isotropic – very much the same everywhere and in all directions.

Modern cosmological theory attempts to describe the types of universes that are compatible with the two principles, general relativity and the cosmological principle. Profound analysis of the problem leads to the following conclusions. Such universes are unstable. They might be momentarily in equilibrium, but the slightest internal disturbance would destroy the balance, and disturbances must occur. Therefore, these possible worlds are not stationary. They are, in general, either contracting or expanding, although theory in its present form does not indicate either the direction of change or the rate of change. At this point, the theorist turned to the reports of the observers. The empirical law of red shifts was accepted as visible evidence that the universe is expanding in a particular manner and at a known rate. This arose the conception of homogeneous expanding universe of general relativity.

In such universes, the spatial curvature is steadily diminishing as the expansion progresses. Furthermore, the nature of the expansion is such that gravitational assemblages maintain their identities. In other words, material bodies or groups and clusters of nebulae do not themselves expand but maintain their permanent dimensions as their neighbors recede from the in all directions.

Several types of expanding universes are possible, and some of them can be further specified by the nature of the curvature, whether it is positive or negative. In fact, the particular universe we inhabit could be identified if we had sufficiently precise information on three measurable quantities, namely, the rate of expansion, the mean density of matter in space, and the spatial curvature at the present epoch. Recent empirical investigations have been directed toward these problems, and the results will be briefly described in the remaining section of this discussion.

COMPARISON OF THEORY AND OBSERVATIONS

We may begin with two results which are thoroughly content with the theory. The first result concerns the assumption of homogeneity ; the second, the conclusion that groups maintain their dimensions as the universe expands.

The distribution of nebulae has been studied in two ways. The first information came from sampling surveys at Mount Wilson and at the Lick Observatory. Small areas, systematically scattered over the sky, were studied with large telescopes. This the nebulae that were counted lay in narrow cones penetrating to vast distances. These surveys established large scale homogeneity over the three-quarters of the sky that could be studied from the northern latitudes of the observatories involved.

Later, the Harvard College Observatory, with the help of its southern station, has furnished counts of nebulae extending over large areas but made with moderate size telescopes. In other words, these nebulae are scattered thoroug wide cones penetrating to moderate distances. Shapley, in his reports, has stressed or perhaps over-stressed, the familiar, small scale irregularities of distribution, but analysis of such published data as are adequately calibrated agrees with the earlier conclusion. In fact, the mean study results from the two quite different methods of study are sensibly the same. This fact re-emphasizes the large scale homogeneity of the observable region.

The second result is derived from a study of the Local Group. Our own stellar system is one of a dozen nebulae that forms a loose group, more or less isolated in the general field. These neighboring systems furnished the first clues to the nature of the nebulae and the scale of internebular distances. They are so near that their brightest stars could be recognized and compared with similar stars in our own system. Radial velocities of the members of the Local Group, listed in Table I, suggest that the law of red shifts probably does not operate within the group. This conclusion is positive evidence supporting the validity of the theory. If the universe is expanding, the group maintains its dimensions as the theory requires.

The remainder of the recently accumulated information is not favorable to the theory. It is so damaging, in fact, that the theory, in its present form, can be saved only by assuming that the observational results include hidden systematic errors. The latter possibility will naturally persist until the investigations can be repeated and improved. Nevertheless, a careful re-examination of the data now available suggests no adequate explanation of the discrepancies.

TABLE I – RADIAL VELOCITIES IN THE LOCAL GROUP

The observed velocities (second column) represent a more reasonable distribution than the velocities corrected for red shifts (fifth column). The latter are all large and negative with the exception of the first two, for which the red shifts are insignificant. This fact suggests that the law of red shifts does not operate within the Local Group.

* A spectrum of an object in IC 1613, obtained by Baade, shows a definitely negative velocity. The numerical value of the velocity is rather uncertain, and, for this reason is not included in the table. However, the negative sign indicates that IC 1613 is consistent with the other members of the local group.

THE INTERPRETATION OF THE REDSHIFTS

The investigations were designed to determine whether or not red shifts represent actual recessions. In principle, the problem can be solved ; a rapidly receding light source arrears fainter than a similar but stationary source at the same momentary distance. The explanation of this well-known effect is quite simple when a beam of light is pictured as a stream of discrete quanta. Rapid recession thins out the stream of quanta, hence fewer quanta reach the eye per second, and the intensity, or rate of impact, is necessarily reduced by a fraction that is merely the velocity of recession divided by the velocity of light – in other words, the red shift expressed as a faction of the normal wavelengths of the light in question. Recession at one-tenth the velocity of light reduces the apparent brightness by 10 per cent ; at one-quarter the velocity of light, by 25 per cent.

For velocities of a few miles of a few hundred miles per second, the dimming factor is negligible. But for the extremely distant nebulae, where the apparent recessions reach tens of thousands of miles per second, the effects are large enough to be readily observed and measured. Hence, if the distances of nebulae were known quite accurately we could measure their apparent faintness and tell at once whether or not they are receding at the rates indicated by the red shifts.

Unfortunately, the problem is not so simple. The only general criterion of great distances is the very apparent faintness of the nebulae which we wish to test. Therefore, the proposed test involves a vicious circle, and the dimming factor merely leads to an error in distance. However, a possible escape from the vicious circle is found in the following procedure. Since the intrinsic luminosities of nebulae are known, the apparent faintness furnishes two scales of distances, depending upon whether we assume the nebulae to be stationary or receding. If, then, we analyze our data, if we map the observable region, using first one scale and then the other, we may find that the wrong scale leads to contradictions or at least to grave difficulties. Such attempts have been made and one scale does lead to trouble. It is the scale which includes the dimming factors of recession, which assumes that the universe is expanding.

ALTERNATIVE FORMS OF THE LAW OF RED SHIFTS

The project was carried out by the precise formulation of (a) the laws of red shifts, and (b) the large scale distribution of nebulae. The form of the law of red shifts is most readily derived from the study of the brightest nebulae in the great clusters. These nebulae, as a class, are the most luminous bodies in the universe, and their spectra can be recorded out to the maximum distances. Furthermore, the clusters are so similar that the apparent faintness of the five or ten brightest members furnish reliable relative distances. The observations now extend out to about 240 million light years where the red shift is about 13 per cent of the normal wavelengths of the incoming light. Since the corresponding velocity of recession is the same fraction of the velocity of light, the nebulae in the most distance cluster observed, if they are actually receding, will appear 13 per cent fainter than they would appear if they were stationary. The difference is small but, fortunately, the measures can be made with fair accuracy.

The results may be stated simply. If the nebulae are stationary, the law of red shifts is sensibly linear ; red shifts are a constant multiple of distances. In other words, each unit of light path contributes the same amount of red shift.

(Insert Fig.1 and Fig.2 graphs here)

On the other hand, if the nebulae are receding, and the dimming factors are applied, the scale of distances is altered, and the law of red shifts is no longer linear. The rate of expansion increases more and more rapidly with distance. The significance of this result becomes clear when the picture is reversed. Light that reaches us today left the distant nebulae far back in the dim past – hundreds of millions of years ago. When we say that the rate of expansion increases with distance, we are saying that long ago, the universe was expanding much faster than it is today ; that, for the last several million years at least, the rate of expansion has been slowing down. Therefore, the so-called “age of the universe,” the time interval since the expansion began, is much shorter than the 1800 million years suggested by a linear law of red shifts. If the measures are reliable, the interval would be less than 1000 million years – a fraction of the age of the earth and comparable with the history of life on the earth. The nature of the expansion is permissible and, in fact, specifies certain types of possible worlds. But the time scale is probably not acceptable. Either the measures are unreliable or red shifts do not represent expansion of the universe.

THE LARGE SCALE DISTRIBUTION OF NEBULAE

If the new formulation of the law of red shifts were unsupported by other evidence, the implications would probably be disregarded. But similar discrepancies are met in quite independent studies of large scale distribution. Five sampling surveys (four at Mount Wilson and one at Mount Hamilton) made with large reflectors, furnish the numbers of nebulae per unit area in the sky, to successive limits of apparent faintness. The results furnish the numbers of nebulae per unit volume in five spheres whose radii range from about 155 to 420 million light years on the stationary distance scale, or about 145 to 365 million light years for the expanding distance scale.

On the assumption that red shifts do not represent actual recession, the large scale distribution is sensibly homogeneous – the average number of nebulae per unit volume of space is much the same for each of the spheres. Further confirmation is found in some of the recent Harvard counts of nebulae which fall within the area of the sky covered by the deep surveys, and which are based on the same scale of apparent faintness. Sufficient data can be extracted from the reports to determine a mean density over large areas extending out to perhaps 100 million light years, and the result is substantial agreement with those of the earlier investigations. All of these data lead to the very simple conception of a sensibly infinite, homogeneous universe of which the observable region is an insignificant sample.

The inclusion of dimming corrections for recession, because they alter the scale of distance in a non-linear way, necessarily destroys the homogeneity. The number of nebulae per unit volume now appears to increase systematically with distance in all directions. The result violates the cosmological principle of no favored position and, consequently, is referred to some neglected factor in the calculations. If the density appeared to diminish outward, we would at once suspect the presence of internebular obscuration, or, perhaps, the existence of a super-system of nebulae. But an apparently increasing density offers a much more serious problem. About the only known, permissible interpretation is found in positive spatial curvature, which, by a sort of optical foreshortening, would crowd the observed nebulae into apparently smaller and smaller volumes of space as the distance increased.

Spatial curvature is an expected feature of an expanding universe, and, together with the precise form of the law of red shifts, further specifies a particular type of possible world. Thus, if the measures were reliable, we might conclude that the initial cosmological problem had been solved ; that now we knew the nature of the universe we inhabit. But the situation is not so simple. Just as the departures from linearity in the law of red shifts indicate a universe that is strangely young, so the apparent departures from homogeneity indicate a universe that is strangely small and dense.

The sign of the curvature required to restore homogeneity is positive, hence the universe is “closed” ; it has a finite volume although, of course, there are no boundaries. The amount of curvature indicates the volume of the universe: about four times the volume of the observable region. Such a universe would contain perhaps 400 million nebulae. The total mass, however, would be far greater than that which can be attributed to the nebulae alone.

CONCLUSION

Thus the use of dimming corrections leads to a particular kind of universe, but one which most students are likely to reject as highly improbable. Furthermore, the strange features of this universe are merely the dimming corrections expressed in different terms. Omit the dimming factors, and the oddities vanish. We are left with the simple, even familiar concept of a sensibly infinite universe. All the difficulties are transferred to the interpretation of red shifts which cannot then be the familiar velocity shifts.

Two further points may be mentioned. In the first place, the reference of red shifts to some hitherto unknown principle does not in any way destroy the validity of the theory of expanding universes. It merely removes the theory from immediate contact with observations. We may still suppose that the universe is either expanding or contracting, but at a rate so slow that it cannot now be disentangled from the gross effects of the superposed red shifts.

Secondly, the conclusions drawn from the empirical investigations involve the assumptions that the measures are reliable and the data are representative. These questions have been carefully re-examined during the past few years. Various minor revisions have been made, but the end-results remain substantially unchanged. By the usual criteria of probable errors, the data seem to be sufficiently consistent for their purpose. Nevertheless, the operations are delicate, and the most significant data are found near the limits of the greatest telescopes. Under such conditions, it is always possible that the results may be affected by hidden systematic errors. Although no suggestion of such errors has been found, the possibility will persist until the investigations can be repeated with improved techniques and more powerful telescopes. Ultimately, the problem should be settled beyond question by the 200-inch reflector destined for Palomar. The range of that telescope, and the corresponding ranges of the dimming corrections, should be about twice those examined in the present investigations. Factors of 25 percent in the apparent brightness of nebulae at the limits of the spectrograph, and 40 to 50 per cent at the limits of direct photography should be unmistakable if they really exist.

Meanwhile, on the basis of the evidence now available, apparent discrepancies between theory and observation must be recognized. A choice is presented, as once before in the days of Copernicus, between a strangely small, finite universe and a sensibly infinite universe plus a new principle of nature.

REFERENCES

No extensive bibliography is furnished, because the list would be largely a repetition of the carefully selected bibliography compiled by H. P. Robertson as an appendix to his discussion of “The Expanding Universe,” published in Science in Progress, Second Series, 1940. Robertson's contribution to the series is the clearest non-technical presentation of the fundamental problem of cosmology that has yet appeared.

A few papers, subsequent to Robertson's bibliography, are listed below.

Hubble, Edwin. The motion of the Galactic System among the Nebulae. Journal of the Franklin Institute, 228, 131, 1939. Cites evidence suggesting that the law of red shifts does not operate within the Local Group.

Eddington, Sir Arthur. The Speed of Recession of the Extragalactic Nebulae. Festschrift für Elis Strömgren, Copenhagen, 1940. Derives the rates of expansion as an apriori datum, and finds a numerical value agreeing with the observed value within the uncertainties of the data.

Shapley, Harlow. Various discussions of counts of nebulae, and their bearing on the problem of the general distribution. The papers are found in vols. 23, 24, 25 and 26 of the Proceedings of the National Academy of Sciences, 1938-1941. Emphasis is placed on small scale irregularities of distribution and the rôle played by the great cloud of nebulae in Centaures.

Transcribed by Ritchie Annand from an old copy of American Scientist in the hopes of keeping Edwin Hubble's lesser-known thoughts in general circulation. Many thanks to Vincent Sauvé for sourcing a copy of the original paper for me.