Towards a Unified Cosmology

27.1: The Problem
The conclusion was reached in Part Three that a cosmological model based on Symmetrical Impermanence would contain spiral nebulae. In this respect it would resemble actuality. But it did not seem to do so in another respect, for no reason could be found why the nebulae should contain discrete stars. It seemed that they must consist only of a more or less diffuse gas.

For many years this conclusion led me to doubt the validity of Symmetrical Impermanence. It seemed to lead to a false model. But it will be shown below that what was at fault was not Symmetrical Impermanence but the traditional theory of gravitation. If one adopts the new theory that has been presented in Chapter 25, one arrives at a model in which the nebulae do contain discrete stars.

The difficulty of arriving at the correct model with the traditional theory is, it will be remembered, that, according to this theory, the gravitational pull on particles of gas in a cosmic cloud would always be towards the centre of gravity of the whole cloud. But stars would not form if movement were exclusively towards the common centre. The result would be one single, compact mass. For stars to separate out there must be movement towards local centres; some particles must move outwards, away from the centre of gravity of the whole cloud and towards the centres of the incipient stars. So star formation would require the setting up of parochial fields of force strong enough to compete successfully with the gravitational field common to the whole cloud.

Of course one could save the traditional theory of gravitation by inventing additional hypotheses. Perhaps, one might say, some other kind of force operates to cause stars to condense out of a cloud of gas. Perhaps the stars have not condensed out of a cloud of gas at all but have beer assembled by some quite different and unknown process. Perhaps the Cosmic Statute Book contains a law to say that particles shall congregate to form stars and they obediently do so. But 'perhaps' as the basis of an explanation is a word that should be avoided in physics whenever possible, An hypothesis that cannot be inferred from the Principle of Minimum Assumption has, I should like to insist once again, no place in physics. But it will be shown below that no ad hoc hypothesis is needed to explain the formation of stars.

27.2: In a Tenuous Cloud Gravitational Pulses are Intermittent
The explanation of star formation lies in the simple fact that the gravitational force is, like light, intermittent. Around any appreciable concentration of matter the discontinuity is no more observable than the discontinuity in a beam of radiation, which, nevertheless, consists of a bundle of discrete photons. But when the quantity of mass in a given place is quite small, there must be a significant interval of time between successive gravitational pulses.

In a gas so diffuse that scattered atoms are well separated from each other the sites for extinctions must be few and far between. According to the new theory of gravitation, it has to be remembered, these isolated atoms do not exercise any gravitational effect at all so long as they continue to exist. It is only when, here and there, an atom becomes extinct that a gravitational pulse is emitted. The effect of such intermittent extinctions is very different from a steady pull in any one direction.

After there has been an extinction in one particular place there may not be another in the vicinity for an appreciable time. The next nearest extinction may be a great distance away if the gas is very diffuse. Such infrequent extinctions will impart spasmodic jerks to all matter that comes under their influence. During the intervals of time between them there will be no forces at all except those that arise from still more remote extinctions; and as the pulses diminish in intensity according to the inverse square law the more remote sources of quanta of gravitation will have a relatively feeble effect.

In such conditions it is rather meaningless to speak of a centre of gravity for the whole cloud. There is a geometric centre, but the gravitational pull is by no means always and everywhere directed towards it. The pulls are random; they arise from scattered sources and operate in all directions. At most one can say that there are, on the average, more pulls in the direction where there is most mass, namely towards the geometric centre, than away from it.

27.3: Incipient Concentrations
Let us consider in the light of the above remarks what must happen to particles in the cloud that has begun to form around an astronomical summit. The density of such a cloud, it has to be remembered, is by terrestrial standards very low. A gramme occupies a vast region.

Let us first consider extinctions. These produce pulses of gravitation. So long as such a passing pulse of gravitation lasts, all particles in the cloud that are reached by it experience an acceleration towards the site. When the pulse is over there is no more acceleration, but the particles have acquired a finite velocity and are therefore converging from all directions on to the site. Origins have an opposite effect. As these are distributed almost uniformly in space, the dispersals occasioned by them are on the average as much away from as towards any particular direction. They must create a little turbulence in the gas, but do not have any lasting effect on the distribution of its particles. They may, however, break up concentrations that are beginning to form. For after an extinction has caused particles to converge on to the site, a subsequent origin in the same place will send the particles back to where they came from. This will prevent every extinction from leading to a lasting concentration. But one can infer that some of the incipient concentrations will not be dispersed before they have established themselves. The establishing of at least some follows from statistical considerations.

The probability of an extinction anywhere is directly proportional to the gas density there. When, therefore, the particles have begun to crowd together around the site of a recent extinction, it becomes a little more probable that another extinction will occur near the previous one. When this does happen the converging particles will receive an additional acceleration in roughly the same direction in which they are moving already. They will then not be so easily scattered as before.

The second extinction will cause the crowd to thicken and make a third extinction there yet more probable. If this occurs, the crowd of particles will be rendered still more dispersal-proof. So it must go on. After a concentration has got well underway it must steadily increase.

The process just described is of the kind that can be achieved in engineering with the help of devices that provide what is called 'positive feedback'. But no such devices are needed to maintain the process of forming concentrations in extragalactic space. The laws of probability suffice to explain what happens. When the process has continued for long enough, the result is a very big and massive concentration. We call it a star. Here, incidentally, is an example of a process that tends not to a stable equilibrium, as with negative feedback, but to increase its cause.

27.4: Incipient Stars have an Irregular Structure
Probability considerations lead one to expect an increase in the number of extinctions around the geometric centre of an incipient star during the very earliest stage of its formation; but these extinctions may be near to or far from the geometric centre. Each will form its own incipient concentration so that the structure of the incipient star must be far from homogeneous. Within this structure there must be numerous parochial concentrations. But as the star becomes more dense and pulses of gravitation within it more frequent, conditions must gradually change so that the general effect is as though all the pulses emanated from the common centre. The intervals between pulses will become so short that particles will never have time to move far towards the parochial centre before they are accelerated away from it towards the centre of gravity of the whole star.

Before this happens the incipient star must have a quite irregular shape. But as extinctions within it become numerous enough to be practically continuous, it will be gradually pulled together into the shape of a homogeneous sphere.

27.5. Double and Multiple Stars
As the thickening of the gas extends to a substantial distance from the incipient star, there must be many occasions when an extinction at a substantial distance forms the beginning of a second star. If this happens while pulses from the original incipient star are still significantly intermittent, the second star will be able to form, competing for hydrogen successfully with its slightly more developed neighbour. More than one star may thus form at a certain distance from the first star. The consequence will be one of the double or multiple stars that are rather numerous.

It should be noted that the components of double or multiple stars must, according to the new theory, all begin at about the same time. If one of them had become well-established it would be so massive that it would attract all surrounding particles to itself; a later incipient concentration would not stand a chance of surviving.

The component stars must also be of approximately the same size during their period of growth. For if any one of them were much less massive than its neighbours it would be absorbed by them. Small differences in mass need not, however, prevent double or multiple stars from growing side by side during the time while they remain very tenuous.

Later, however, when the difference between gain by capture and loss by extinction becomes very narrow a small reduction in income from capture can lead to a change from growing to dwindling. One should therefore expect the two components of a double star to have unequal later histories. When both have reached the size at which income and loss balance one should expect the slightly larger one to maintain, even somewhat increase, its mass while the smaller one would lose mass at an ever increasing rate. In other words, neighbouring stars of the size at which income and loss nearly balance are in competition for new matter and the smaller ones lose the battle. The consequence of this will be discussed in Appendix D.

27.6: At What Gas Density do Stars Form?
The gas density at which stars can form would seem to be a quantity of some significance in cosmology. Knowledge of it might help us to estimate the stage in the evolution of a spiral nebula at which star formation occurs. But at present it is only possible to say that there must be an upper and a lower limit.

That there is a lower limit is obvious, for no stars can form where the density is zero. The density must be at least such that the conditions for the effective crowding together of particles are met. These conditions are that the particles are able to acquire a significant average velocity from one single quantum of gravitation and that there is a significant number of such particles. But the velocity cannot be significant if the nearest particles to the site of an extinction are a long way off. The pulse of gravitation can only produce such a velocity if it has not become too weak; and its effect diminishes with the square of distance.

Hence the pulse can only significantly affect the movement of particles within a limited range. If the number of particles within this range is small, the effect on the local density will be negligible.

It has to be remembered that the scattering effect produced by origins is independent of density. There are as many quanta of anti-gravitation per unit volume in a high vacuum as in a dense medium. But a large number of particles moving at a high velocity are not so easily dispersed by a single quantum of anti-gravitation as a small number moving slowly. For this reason the chance of becoming dispersal-proof increases up to some limit as the density increases.

The upper density limit is reached when particles are so close together that extinctions in the near vicinity follow each other in close succession, The particles will then be accelerated towards the region of the greatest number of extinctions, which means towards the geometric centre of the system. The effect of the whole mass predominates at a certain density over the parochial effect of nearby particles.

Once star formation has become established in a cloud it must become increasingly difficult for new stars to begin. The competition of the established ones must be too great. One should therefore expect most of the stars in the core of a spiral nebula to begin at about the same time. The possibility, however, of the occasional formation of new stars on astronomical summits within a spiral nebula ought not to be disregarded.

The history of the stars in the spiral arms may be a little different. The density at which the original population of stars begins must be very low; so one should not preclude the possibility that stars may begin to form while the spokes of the cloud are still lying on the astronomical shoulders and long before these have poured into the rotating core to form the spiral arms. Indeed, there are considerations that point in this direction.

After the pouring has occurred there must be considerable turbulence, The spokes have entered the core from an enormous height and must stir things up considerably as they splash into the core. I have already suggested in Chapter 20 that this turbulence ought to be picked up by a radio-telescope. Now it is not easy to believe that the little crowds of particles that are assembled around the site of a recent extinction could ever survive such a bufieting. From this I am inclined to conclude that the crowds have become fairly massive in the calm atmosphere of the spokes as these rest sluggishly on the astronomical shoulders. They must be large and compact enough to be the sites of concentrated extinctions. Only so can they be dispersal-proof, even from the violence of the agitated gas in which they find themselves after the pouring process.

On the other hand, the concentrations can hardly yet approach the massiveness of stars before the pouring process. If they did, they would be only slightly delayed in their fall by impact with the gas of the core. They would all fall deep into the interior and one should not expect to observe any stars in the spiral arms.

The tangential effect of the gas in the core would, moreover, be no greater than the radial effect. Not only would massive stars fail to stay near the surface, if they did they would not be entrained.

Thus we are led to the conclusion that star formation probably begins in the central core at an early date and later also in the spokes, far out beyond the limits of the future nebula. Formation of these stars is completed in the spiral arms.

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