COSMOLOGY is the name of the subject that deals with the large scale properties of the universe as a whole. At first sight it may seem surprising that it should be at all possible to deal with such a subject in a scientific manner. For the essence of science is the possibility of observational disproof and it might be argued that no observational knowledge of the entire universe can be at our disposal for a long time to come, if, indeed, ever. The main purpose of this article is to correct this attitude, to show that cosmology can be treated scientifically and to indicate the main lines of thought now current in the subject.
Apart from some valuable considerations due to Newton, the first serious step in scientific cosmology was taken by the Hamburg astronomer Olbers about 130 years ago. In many ways Olbers' argument is the basis of all modern cosmology and it will accordingly be presented fully.
Olbers contemplated the fact that one saw in the sky a few really bright stars, a larger number of medium bright ones, and great numbers of faint ones. He argued that persumabIy, in general, the brightest stars were close to us, explaining thereby both their appearance of brightness and their small number, since there is relatively little space close to us. Similarly, he supposed the medium bright stars to be somewhat further away, accounting both for their smaller luminosity and their greater number. Finally, the faint stars would be really far away and hence be faint and numerous. But what about yet more distant regions of space? Should one not expect them to appear to be populated with exceedingly numerous but individually extremely faint stars? Olbers Mught that this was so and accordingly he expected these immensely distant regions to contribute a faint background brightness to the night sky. He expected stars in the depths of space to provide an almost uniform glow in. the sky, individual stars being too faint to be visible but so numerous as to provide, ia the aggregate, such a glow.
Olbers was not content with this thought, but proceeded to calculate the background brightness to be expected. In this he followed the established scientific procedure of working out the observable consequences of hypotheses so as to be able to check them observationally. Since the individual distant stars were supposed to he too faint to be seen, Olbers could not rely on astronomical knowledge of the distant regions of space but had to make assumptions about them, assumptions that would enable him to infer the background fight of the night sky and so to check the correctness of his assumptions. The assumptions Olbers made concerning the constitution of the distant parts of the universe were as follows:
- The distant regions are essentially like our astronomical neighbourhood. The average distance between stars and the average luminosity of each star are more or less the same throughout the universe. In other words, the universe is homogeneous when viewed on a large scale.
- The general character of the universe is not only the same at all places but also at all times. (This assumption. is needed since, owing to the finite velocity of light, we see distant regions not as what they are now, but what they were like a long time ago.) In other words the universe is unchanging in time when viewed on a large scale.
- On an average the relative velocity of any two stars vanishes, so that there are no major systematic motions in the universe.
- The laws of physics as derived from our terrestrial experience apply throughout the universe.
These assumptions seemed to Olbers, as they seem now, to be the first and most obvious ones to come to mind. They are sufficient to deduce the corresponding background brightness of the sky. The actual derivation requires a simple and brief mathematical argument.
Imagine spheres to be drawn with the earth at the centre and of radius a, a + h, a+2h,
a + 3h and so on, where a is much greater than h and h is a very large
distance. The choice of h and a is determined by the need for every one of the
spherical shells bounded by two successive spheres to he so large that it
contains large numbers of stars (or, more correctly in the light of present
knowledge, numerous galaxies). The number should be so large that average
properties of luminosity and spacings can be used without serious error. Since
the thickness of each shell is the same, the volume of each shell will be
proportional to r2, where r is the radius of the shell. (It is
irrelevant whether the inner or outer radius is used since the thickness h is
far smaller than r.) Accordingly, the number of stars in each shell is
proportional to r2 and so is the total rate at which stars in each
shell emit light, since the average spacing and luminosity of stars have been
assumed to be the same everywhere at all times. How much of this light reaches
us? All the stars in the shell of radius r are at approximately the same
distance r from us. Accordingly, the intensity of light received from any one
of these stars is its rate of sending out light, divided by 4
r2. Therefore the intensity of
light received from all stars in a shell is the rate at which all stars in the
shell emit light, divided by 4
r2. Since this rate
is proportional to r2, it follows that the light received from a
shell is independent of its radius (and does not vanish). Each shell
contributes the same finite amount of light here. Since shells can be added
without limit, the total amount of light received from all shells is infinite.
This result is not, however, quite correctly derived. True infinities rarely if ever arise in physical arguments. The discussion omitted to account for the finite size of stars which implies that each star not only sends out light, but intercepts the light of the stars behind it. This consideration does indeed prevent the sum becoming infinite, but, since stars send out so much light from a relatively small surface, the sum remains large. It turns out to be equal to the intensity of light on the surface of an average star which is about 40,000 times as strong as sun light when the sun is in the zenith.
This important result also follows from the consideration that, in Olbers’ system, in whichever direction one looks, one's line of sight will eventually intercept a stellar surface. We are, therefore, entirely surrounded by stellar sur. faces and so are at the same temperature and hence in the same radiation field. Alternatively, one can argue that the space between the stars forms a thermodynamic system that, by assumptions (ii) and (iii), has had time to settle down to equilibrium and hence the temperature everywhere in it is the same as that of the boundary, the surfaces of the stars.
The result derived from these assumptions is patently wrong. The earth is not immersed in a diffuse bath of light 40,000 times as strong as sunlight. Olbers' paradox, as it may be called, is in striking disagreement with observation. The derivation of the paradox is logically sound and so the assumptions cannot be valid. This is a remarkable result. The assumptions made concerning the nature of the universe have been disproved by observation. The possibility of observational disproof is the decisive characteristic of science. Olbers' paradox, in demonstrating the possibility of the observational disproof of a set of cosmological assumption, shows cosmology to be a science.
But the utility of Olbers' paradox does not end with this achievement. The set of four assumptions cannot be valid, but might some of them at least be maintained? Which of them can be spared most easily? There is no point in dropping assumption (iv) concerning the validity of the physical laws, since to throw away all our knowledge would seem to offer little hope of progress. Assumption (i) (Uniformity) has considerable direct and indirect observational evidence in its favour, so that the two assumptions remaining must be considered first. Can Olbers' paradox be resolved by dropping either of these? It is clear that this can be achieved by dropping assumption (ii). For if the universe is not unchanging, then one can postulate that the stars began to shine only a finite and not too long time ago. In this case we would not receive any light from distant shells since the stars there would not have been radiating at the time light would have had to leave them to get here now. This way of resolving the paradox may be stated briefly in the phrase 'The universe is young.'
The paradox can also be resolved if assumption (ii) is retained, but assumption (iii) is dropped. This is not quite so easy to set, though.
First, one must examine what motions exist that are compatible with assumptions (i) and (ii). It is not obvious that there are such motions, and some serious mathematics is required to find the answer. It turns out that the only motions compatible with assumption (i), i.e. the only motions of a homogeneous system preserving its homogeneity, are' those in which the relative motion of any two particles is along the line joining them, has a velocity proportional to the distance between the particles (if the velocity so derived is so large as to be comparable with the velocity of light, a more complicated formula has to be used) and is either inward or outward throughout. In the first case the entire system is contracting, in the second it is expanding. The rate of expansion (or contraction) is the ratio of velocity to distance, which is the same for all particles. If assumption (ii) (unchanging character) is made this rate must be constant, otherwise it may vary in time.
Having now found the motions that become possible by rejecting only Olbers' assumption (iii), we have to see whether either of them can resolve Olbers' paradox. Fortunately, terrestrial physics readily supplies the answer. It is known that light from a receding source appears to be redder and weaker than if the source were static, that these effects become large as the velocity of the source approaches the velocity of light, and that light from an approaching source is similarly bluer and stronger. If the universe is an expanding system, then the stars of the distant shells (in Olbers' argument) are receding from us, and the far distant shells are receding very fast. The light from these shells will therefore be considerably weaker than according to Olbers'argument,and the intensity of the background light will he less than calculated before. Accordingly, if the rate of expansion is sufficiently high the background light of the sky will be as faint as it actually is, and so Olbers' paradox will be resolved. If the universe were contracting then the light from distant shells would he enhanced and the paradox would be made worse.
It follows then that the darkness of the night sky, together with assumptions (i) and (iv), implies that the universe is either expanding or it is young or both these statements apply.
It is probably advantageous to discuss the modern observations at this stage before describing the current theories. A big telescope shows that the stars we see form an organised group, our galaxy. This is a disc-shaped object with a radius of about 40,000 light years (the average distance between stars is a few light years, which is a unit of distance equal to six million million miles) and a thickness of a few thousand light years. Looking out in the plane of the disc we see vast numbers of stars forming the phenomenon of the Milky Way. There are perhaps 100,000 million stars in our galaxy.
Looking further into space one sees, well beyond the confines of our galaxy, other similar groups of stars, other galaxies more or less similar to our own. These galaxies frequently occur in clusters containing anything from a few to a few thousand member galaxies. The average distance between galaxies (outside clusters) is towards a million light years, about thirty times the radius of an average galaxy. With modern telescopes galaxies can he observed even at distances of many hundreds of millions of light years, and hence vast numbers of galaxies are known. Allowing for clusters, the distribution appears to be reasonably uniform and so lends support to Olbers' assumption (i). A very difficult examination of the light of distant galaxies shows that the spectral lines are shifted to the red. The only plausible inference that can be drawn is that this reddening is due to a velocity of recession. It turns out that the red shift varies between different galaxies so as to be proportional to their distances from us (as inferred by the faintness of the light received) so that the velocity of recession is proportional to the distance. It was pointed out before that expansion with such a velocity-distance law is (apart from contraction) the only possible type of motion compatible with the assumption of uniformity. The fact that the observed motion is just of this type is a strong indication that assumption (i) (uniformity) is correct. Incidentally, the velocities measured by the red shift are very large (up to one-fifth of the velocity of light).
This is the setting in which the principal current theories of cosmology must be appreciated. The first of these gives up both assumptions (ii) (unchanging aspect of the universe) and (iii) (no motion), but bases itself firmly on assumption (i) (uniformity) and (iv) (validity of the terrestrially discovered laws of nature). Since the best formulation for the behaviour of matterin-the-large is the general theory of relativity, this cosmological theory is based on it and is known as relativistic cosmology. General relativity and uniformity do not define a unique model of the universe, but a whole range of them. However, one of these, the model discovered by G. Lemaître, is generally thought to agree best with our universe. This is an evolving, changing model.
The model starts off with all the matter of the universe in a highly condensed hot nuclear state, Lemaître's 'primeval atom.' The elements are made from the primitive hydrogen in a kind of nuclear explosion that leads to violent expansion. Under the influence of gravitation the rate of expansion slows down until an almost static state is reached in which the primeval uniform distribution of matter condenses into galaxies. A repulsive force that arises naturally in relativistic cosmology finally asserts itself sufficiently to start off an accelerating period of expansion, in which we now live.
The other current theory bases itself firmly on Olbers' assumptions (i) and (ii). Because of the stress it lays on the unchanging aspect of the universe it is called the steady-state theory. The reason for this stress is found in a critical examination of assumption (iv). The laws of nature, on which relativistic cosmology is based, are a summary of our terrestrial experiences gained in what is, on the cosmical scale, an extremely small region of space and an extremely brief period of time. It is impossible, on the basis of such limited experience, to judge which features are permanent and which are only temporary, or of only local significance. In particular, if the universe varied in space or time it would he likely that some features of our physical laws (especially the so-called constants of nature) should vary with it. To put it differently, in such a varying universe there is no reason to expect our experiences to be typical, no reason to expect our summaries of these experiences, our laws of physics, to apply elsewhere. In these circumstances cosmology would be an exceptionally difficult subject in which every conceivable variation of the 'laws of nature' should be allowed for. The only possibility of avoiding these difficulties would arise if the universe were uniform in space and time, i.e. if Olbers' first two assumptions were valid. Then our experiences would not refer to any special place and time, but to typical conditions and hence would be applicable everywhere at all times. The assumption that this is so (i.e. (i) and (ii) valid) is known as the perfect cosmological principle as opposed to the so-called cosmological principle which states merely that the universe is, on the large scale, uniform in space, though not necessarily in time. It is the purpose of the steady-state theory to draw inferences from the perfect cosmological principle, inferences that can be checked observationally, so confirming or disproving the principle.
In the discussion of Olbers' paradox it was shown that if (i) and (ii) are retained, then the resolution of the paradox requires the universe to be expanding. In other words, since in the steady-state theory the aspect of the universe is unchanging, the resolution of the paradox given by the statement 'the universe is young' is inadmissible, and so the expansion follows. On the basis of the perfect cosmological principle the recession of the galaxies follows from the observation that it is dark at night, and the results of intricate astronomical work confirms this implication.
The next point is a little more difficult. If the universe is unchanging in the large, then all its large-scale physical characteristics (such as the density of matter) must be constant. But if the galaxies are receding then the intergalactic distances are increasing, matter is moving away from matter and so it would appear, by the law of conservation of matter, that the average density must be diminishing. This is in clear-cut contradiction to the perfect cosmological principle. The only way out of the contradiction is to suppose the law of conservation of matter to be incorrect to the extent that matter is being continually created. Although this may sound outrageous and contrary to experience, it is necessary to ask what the rate of this creation process is before ruling out this possibility. Now the mean density of matter in the universe is so low and the time scale of the expansion so large, that on calculation the mean rate of creation required to compensate for the effects of the expansion turns out to be one atom of hydrogen (or an equivalent mass) per quart volume every few thousand million years. This rate is obviously too small by many orders of magnitude to conflict with the experience on which the law of conservation of matter is based. There is therefore no need whatever to reject the idea of continual creation on the grounds that it disagrees with known evidence. It only disagrees with a mathematical extrapolation from evidence. Changing this may be inconvenient, but there is no reason to suppose the world to be arranged to suit the convenience of mathematicians.
In what form is this new matter created? This question is closely concerned with the problem of evolution. Every closed system is known to go through irreversible changes. Cosmically the most important of these is probably the conversion of hydrogen into helium, which takes place in every star, the excess energy being radiated away into space. Each system, each galaxy, is therefore ageing. How can the overall aspect of the universe remain unchanging, if every galaxy is evolving irreversibly? Only if new galaxies are being born, and old ones drift out of the range of telescopes through the expansion of the universe. The newly created matter must therefore stand at the beginning of the evolutionary chain, and, according to current astrophysics, this is cold diffuse hydrogen. The creation process must therefore imply the (presumably random) creation of hydrogen atoms of low velocity at a uniform rate.
The universe of the steady-state theory may be compared with a stationary human population. Each individual is born, grows up, ages and dies, but the overall aspect of the population is unchanging. This requires not only that new individuals arise to take the place of the ones who have died, but that these new individuals should be babies, so as to stand at the beginning of the evolution of the individual. Similarly, the model of the universe is inhabited by galaxies drifting apart and ageing. In the growing spaces between the galaxies, continual creation leads to the existence of vast clouds of gas that condenseinto new galaxies which in turn age and drift away. All the large-scale average properties (density, distance between galaxies, size of galaxies, etc.) stay constant, though each member passes through irreversible changes.
The general description of the model of the steady-state theory leads up to the essential purpose of the theory, the discovery of crucial observations. There are several of these, but only a few can be discussed here.
(i) The light that reaches us now from distant galaxies left them a long time ago. If, as in Lemaître's model, all galaxies were formed at more or less the same time, then these distant galaxies must (on an average) have been younger when they sent out the light now received than near galaxies. On the steady-state theory, however, time does not matter. The average age of galaxies a long time ago was just the same as it is now.
The observations in question consist therefore in seeing whether there are any systematic changes in the characteristics of galaxies (intrinsic colour, shape, size, etc.) with distance. If there are any such changes, the steady-state theory will have been disproved; if there are none, it will be strengthened and relativistic cosmology will he weakened.
It is not easy to separate the effects of the red shift and of the faintness from changes of intrinsic characteristics. This difficulty does not allow definite conclusions to be drawn from existing observations. There is good reason to believe that further observational work will lead to a conclusive answer in a few years.
(ii) In the example of the human population it is clear that if the population is to remain stationary, the age distribution must follow a definite pattern. Correspondingly, the age distribution of galaxies must follow a certain pattern (with young galaxies predominating) if the steady-state theory applies. In Lemaître's model, on the other hand, the range of ages is quite limited, with no galaxy less than a certain age. Once it becomes possible to judge the age of a galaxy from its appearance, this test should be powerful. This possibility should arise before long.
(iii) and (iv) Tests relating to the origin of galaxies and of heavy elements. These will he discussed in D. W. Sciarria's article.
Whatever may be thought of current theories, it is clear that they are not idle speculations, but serious attempts to discern crucial observational tests. The discovery of the cosmological significance of the darkness of the night sky made cosmology a science. Current theories, in asking for more intricate but entirely possible observations, are continuing this scientific path.