The Science of Discworld IV

set of constants where all hell breaks loose.
    Stenger gives an instructive example of the fallacy of varying parameters one at a time. He works with just two: nuclear efficiency and the fine structure constant.
    Nuclear efficiency is the fraction of the mass of a helium atom that is greater than the combined masses of two protons and two neutrons. This is important because the helium nucleus consists of just that combination. Add two electrons, and you’re done. In our universe, this parameter has the value 0.007. It can be interpretedas how sticky the glue that holds the nucleus together is, so its value affects whether helium (and other small atoms like hydrogen and deuterium) can exist. Without any of these atoms, stars could not be powered by nuclear fusion, so this is a vital parameter for life. Calculations that vary only this parameter, keeping all others fixed, show that it has to lie between 0.006 and 0.008 for fusion-powered stars to be feasible. If it is less than 0.006, deuterium’s two positively charged protons can push each other apart despite the glue. If it is more than 0.008, protons stick together, so there would be no free protons. Since a free proton is the nucleus of hydrogen, that means no hydrogen.
    The fine structure constant determines the strength of electromagnetic forces. Its value in our universe is 0.007. Similar calculations show that it has to lie in the range from 0.006 to 0.008. (It seems to be coincidence that these values are essentially the same as those for nuclear efficiency. They’re not
exactly
equal.)
    Does this mean that in any universe with fusion-powered stars, both the nuclear efficiency and the fine structure constant must lie in the range from 0.006 to 0.008? Not at all. Changes to the fine structure constant can compensate for the changes to the nuclear efficiency. If their ratio is approximately 1, that is, if they have similar values, then the required atoms can exist and are stable. We can make the nuclear efficiency much larger, well outside the tiny range from 0.006 to 0.008, provided we also make the fine structure constant larger. The same goes if we make one of them much smaller.
    With more than two constants, this effect becomes more pronounced, not less. Numerous examples are analysed at length in Stenger’s book. You can compensate for a change to several constants by making suitable changes to several others. It’s just like the car example. Changing any one feature of a car, even by a small amount, stops it working – but the mistake is to change just that one feature. There are thousands of makes of car, all different. When the engineers change the size of the nuts, they also change the size ofthe bolts. When they change the diameter of the wheel, they use a different tyre.
    Cars are not finely tuned to a single design, and neither are universes.
    Of course, the equations for universes might run contrary to everything that mathematicians have ever seen before. If anyone believes that, we’ve got a lot of money tied up in an offshore bank and we’d be delighted to share it with them if they will just send us their credit card details and PIN. But there are more specific reasons to think that the equations for universes are entirely normal in this respect.
    About twenty years ago, Stenger wrote some computer software, which he called MonkeyGod. It lets you choose a few fundamental constants and discover what the resulting universe is capable of. Simulations show that combinations of parameters that would in principle permit life forms not too different from our own are extremely common, and there is absolutely no evidence that fine-tuning is needed. The values of fundamental constants do
not
have to agree with those in our current universe to one part in 10 30 . In fact, they can differ by one part in ten without having any significant effect on the universe’s suitability for life.
    More recently, Fred Adams wrote a paper for the
Journal of Cosmology and Astroparticle Physics
in 2008, which focuses on a more limited version of the question. fn3 He worked with just three constants – those that are particularly significant for the formation of stars: the gravitational constant, the fine structure constant, and a constant that governs nuclear reaction rates. The others, far from requiring fine-tuning, are irrelevant to star formation.
    Adams defines ‘star’ to mean a self-gravitating object that is stable, long-lived, and generates energy by