Self-gravitating systems

The observed existence of structures such as galaxies might lead one to think that any large number of objects subject to mutual gravitational attraction might not follow the Second Law and become randomized, but might instead always form orderly clumps. It is difficult to know, however, what an idealized self-gravitating system would do. For in practice, issues such as the limited size of a galaxy, its overall rotation, and the details of stellar collisions all seem to have major effects on the results obtained. (And it is presumably not feasible to do a small-scale experiment, say in Earth orbit.) There are known to be various instabilities that lead in the direction of clumping and core collapse, but how these weigh against effects such as the transfer of energy into tight binding of small groups of stars is not clear. Small galaxies such as globular clusters that contain less than a million stars seem to exhibit a certain uniformity which suggests a kind of equilibrium. Larger galaxies such as our own that contain perhaps 100 billion stars often have intricate spiral or other structure, whose origin may be associated with gravitational effects, or may be a consequence of detailed processes of star formation and explosion. (There is some evidence that older galaxies of a given size tend to develop more regularities in their structure.) Current theories of the early universe tend to assume that galaxies originally began to form as a result of density fluctuations of non-gravitational origin (and reflected in the cosmic microwave background). But there is evidence that a widespread fractal structure develops—with a correlation function of the form r^-1.8—in the distribution of stars in our galaxy, galaxies in clusters and clusters in superclusters, perhaps suggesting the existence of general overall laws for self-gravitating systems. (See also page 973.)

As mentioned on page 880, it so happens that my original interest in cellular automata around 1981 developed in part from trying to model the growth of structure in self-gravitating systems. At first I attempted to merge and generalize ideas from traditional areas of mathematical physics, such as kinetic theory, statistical mechanics and field theory. But then, particularly as I began to think about doing explicit computer simulations, I decided to take a different tack and instead to look for the most idealized possible models. And in doing this I quickly came up with cellular automata. But when I started to investigate cellular automata, I discovered some very remarkable phenomena, and I was soon led away from self-gravitating systems, and into the process of developing the much more general science in this book. Over the years, I have occasionally come back to the problem of self-gravitating systems, but I have never succeeded in developing what I consider to be a satisfactory approach to them.