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
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
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
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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