This the way the world ends

The search for such an oscillating universe isn't new. Fifty years ago Richard Tolman of Caltech showed that the entropy during the universe's collapse should be slightly higher than during the preceding expansion. For our purposes we can regard entropy as a measure of the waste heat produced by most physical processes, of energy that can't be used. This is in contrast to the ''free'' energy available for consumption. In relativity theory, higher entropy implies a greater expansion (or contraction) rate. So if the universe bounced at the Big Crunch, the new Big Bang would start out with a greater rate of expansion, and the universe it would create would attain a greater radius than the universe that preceded it. Each new Bang would bring a larger and larger universe. Rather than damping the bounces, entropy would amplify them -- behavior exactly contrary to intuition. When you ride a bicycle, you must keep pedaling so that friction -- which increases entropy -- doesn't bring the bicycle to a halt. In Tolman's oscillating universe, however, entropy speeds things up.

But Tolman's model makes at least two unjustified assumptions. The first is that the Big Crunch singularity is somehow avoided; the second is that the entropy at the end of one cycle is equal to that at the start of the next. There are models of the universe that bounce without resorting to quantum gravity, but they're not very realistic in their details. To date, all reasonable models of closed universes end in singularity. Consequently, Tolman's phoenix may or may not rise from the ashes.

The question of entropy leads directly to the other possible destiny of the universe -- the open scenario, in which it continues to expand forever, or at least for a very long time. Many physicists who ponder these matters feel claustrophobic in a collapsing universe and prefer this outcome. But their optimism is tempered by the second law of thermodynamics, which says that entropy always tends to a maximum in certain types of systems. As early as 1854 the German physicist Hermann von Helmholtz realized the cosmological implications of this: the universe was using up all its free energy and would eventually run down like an unwinding clock. Stars would exhaust their available fuel and the universe would become a lifeless cinder in which entropy would reach a maximum, the temperature would reach a constant value, and all change would cease.

The Heat Death of the universe, as this fate was called, profoundly disturbed both theologians and evolutionists, who believed the universe had to progress from a lower state to a higher. In his Autobiography Darwin wrote, ''Believing as I do that man in the distant future will be a far more perfect creature than he now is, it is an intolerable thought that he and all other sentient beings aredoomed to complete annihilation after such long-continued slow progress.''

Darwin might have found solace in the fact that the second law doesn't apply to the universe as a whole. In a closed universe doomed to collapse it can't even be properly formulated; in an expanding universe there's no maximum entropy state, and the temperature never becomes constant. So modern cosmologists of the open-universe school haven't been burdened with the assumption that the final resting place of the cosmos will be a maximum-entropy graveyard.