Just Six Numbers: the deep forces that shape the universe, by Martin Rees. ISBN 0-75381-022-0.
The laws of nature seem to have too many arbitrary constants in them; numbers for whose values we can see no explanation; numbers that, for all we can tell, were chosen at random by whatever gods there may be. One interesting thing about these numbers (which has led some people to think that those gods shouldn't be taken too metaphorically) is that it seems that some of them couldn't be very different from what they are without making life as we know it impossible. In other words, we seem to have been very lucky that there was a universe fit for us to live in.
In this book, Martin Rees discusses six of them:
- The relative strengths of gravity and the other fundamental forces. If gravity were too strong, then stars wouldn't live long enough for the likes of us to evolve. (No very awful consequences seem to ensue if gravity is too weak; so perhaps this one isn't really so very finely tuned.)
- The ratio of the binding energy of a helium nucleus to the rest mass of its constituents. This is determined by the strength of the strong nuclear force, and it determines the amount of energy released by nuclear fusion of hydrogen to form helium. If this were much smaller than it is, stars wouldn't burn and elements heavier than hydrogen wouldn't form. If it were much greater, there'd be no hydrogen left and (for instance) water couldn't form.
- The density of the universe, relative to the "critical" density at which it just barely escapes a Big Crunch. Supposedly, if this wasn't incredibly close to 1 when the universe was very young, it would now have to be either very close to 0 or terribly large, and neither option produces a universe hospitable to life.
- The cosmological constant. This seems to be very small but not 0; if it weren't very small, then the early universe would have expanded too fast for the formation of galaxies.
- The nonuniformity of the distribution of matter in the universe. If this were much smoother, galaxies and stars and the like wouldn't form; if it were much rougher, the universe would be all black holes and very tightly grouped clusters of stars.
- The number of macroscopic dimensions. Too few dimensions and connecting up brains is too hard; too many and there are no stable orbits.
I find myself unconvinced by several of these (but, note, I am not a cosmologist or even a physicist, so maybe I'm missing important things); the obvious hole in claims of fine tuning is that there may be a big difference between life as we know it and life simpliciter.
Anyway, the discussion of these six numbers gives Rees a chance to digress on black holes, antimatter, nucleosynthesis, inflation, dark matter, and all the other usual suspects of popular cosmology. He does so very competently.
Finally, Rees addresses the question of how come these constants are (allegedly) so finely tuned. He doesn't think much of the prospects for a theory that makes their values inevitable; he prefers, like most people at present, a "multiverse" theory (in which there are many "universes" with different values for the constants) plus the anthropic principle. (I was surprised to see no mention of Smolin's evolutionary variation on this theme.) He dismisses the possibility that the tuning is a one-off coincidence, and passes over the theistic (or deistic) explanation almost without comment.
Rees does a good workmanlike job of explaining this material for a lay audience.