by     Reginald O. Kapp


Chapter 14 - The Average and the Equilibrium Density of the Universe

The average density within an astronomical domain is the total mass within the domain divided by the volume of the domain. It will be found to be an important quantity. To appreciate its significance one must relate it to two other densities. These are the average density of the whole unverse and a quantity that I propose to call the equilibrium density.

The meaning of the former is easy to understand. If one considers a region of space large enough to be a fair sample of the whole material universe, the average density is the total mass in this region divided by its volume. To be a fair sample the region may have to be substantially larger than the domain of any particular galaxy.

The equilibrium density is a different quantity and depends on the relative rates at which matter originates and becomes extinct. To make this clear let me recall the basic features of hypotheses (A3) and (B3).

In (A3) no assumption is made to associate the origin of a particle with anything in the existing state of affairs. There is therefore no reason why a particle should originate in one specific place rather than in any other, and the minimum assumption is that every region of space has at any given moment an equal probability of being the birthplace of a particle.

Similarly no assumption is made to associate the extinction of a particle with anything in the existing state of affairs, and so there is no reason why a given particle should become extinct at any particular moment. The minimum assumption is that every particle has at that moment an equal probability of becoming extinct. If one considers any lump of matter, a certain constant fraction of it becomes extinct every year. What- ever the lump may consist of, wherever it may be, to whatever influences it may be subjected, it will lose half of its mass by extinction during a finite, though at present unknown, number of years. On the analogy of the expression 'half-life of a radioactive substance' this must be called the half-life of mass.

From this essential aspect of Symmetrical Impermanence one can thus infer that the rate of origins is constant per unit volume and the rate of extinctions constant per unit mass. The rate of extinctions per unit volume is then proportional to the mass density.

In a perfect vacuum there can be no extinctions, for there is nothing to become extinct. In such a region the net rate of origins is equal to the gross rate. But as matter accumulates in the region a certain constant fraction of it becomes extinct and the net rate is the difference between the constant rate of origins and the density dependent rate of extinctions. There must be a specific density for which these rates balance, and the net rate of origins is zero. This is the density that I propose to call the equilibrium density.

If the whole universe were at the equilibrium density, its content and extent would be constant. It would neither expand nor contract. But the observed expansion of space proves that the average density for the whole universe is less than the equilibrium value. (This assumes that origins and extinctions of matter are coupled with the expansion and contraction of space. The assumption needs to be justified. Attempts to do so will be found in Part Four and again in Appendix H). If we knew the gross rate of origin of matter per unit volume and time, or if we knew the half-life of mass, we could calculate from McCrea's estimated net increase of 500 atoms of hydrogen per cubic kilometre per year what the equilibrium density is. But as these quantities are not known, we can only say that the equilibrium density is greater than the average density of the whole universe.

By terrestrial standards both are very low values. The average density of our galaxy must, for instance, be well above the equilibrium density. But we must not allow our sense of proportion to be too much influenced by terrestrial standards. We are considering processes in extragalactic space, in most of which the density must be well below the equilibrium value.

During the first stage of growth the cloud depends entirely on new origins for increase of mass. Should extinctions exceed origins the cloud would not grow but dwindle. It follows that the average density of the cloud must be below the equilibrium value during and right up to the end of the first stage of growth.

The central core must, of course, greatly exceed the equilibrium density and so the gas between this core and the top of the crater must be in a very tenuous condition indeed. This situation must continue after the first stage of growth has passed. The top of the crater, now grown to an astronomical ridge or reversal zone, marks the boundary between some- what steep slopes. Hydrogen must be pouring down these as fast as it forms on each side, leaving the slopes near the ridge almost depleted. The inner slope, moreover, the one towards the growing cloud, must be the steeper of the two and must therefore be the more depleted one.

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