When anthropic reasoning won’t work

If you want to use anthropic arguments to get rid of “why” questions in physics, then these work quite well when you’re dealing with integer-valued questions – “why does space have three dimensions and not two or four?”. They work less well in other cases.

Take the Fine Structure Constant, for example. This is usually written as 1/α²=137.0359 (or thereabouts) and there is a respectable body of work showing that a change of even a few percentage points in this value would make intelligent-life-as-we-know-it impossible.

Let’s leave to one side all the begged questions about intelligent-life-as-we-don’t-know-it and consider: can anthropic considerations explain the value of 1/α²?

Let’s concede (what is not necessarily true) that a change of 5% in 1/α² would make life impossible. What about a change of 0.5%? What about a change of 0.00000005%?

At some point in this scale of values of 1/α² ever closer to the real one, there must come a value that is not the real value but is so close to it as to be indistinguishable in its anthropic implications. The question to be answered is then: why does not 1/α² have that value instead of the value it actually has?

There is, in other words, an “anthropic range” for any constant of physics – a range within which that constant must fall (other things being equal) in order for us to be here and observe it. But that range is a range, it is not a single value. Whatever reasons there may be for the value that constant has, those reasons cannot be simple ones of the kind “if it were different, we shouldn’t be here to see it”.

To take a parallel: doorways tend to be a bit over six feet in height. Lower, and too many people would bang their heads; higher, and materials would be wasted. So far, so good. But now suppose that an archaeologist excavates a ruined city and finds that every door was precisely 6’3½” high. Anthropic arguments would no longer suffice: the archaeologist would have to think of other reasons for the figure.

So it is with the fine structure constant, the cosmological constant, and others. Anthropic arguments give us a range: within that range there are uncountably many possible values. Why does the constant have the particular value that it has?

There is one way out, if you really want to use anthropic arguments here. Suppose that the value of 1/α² is not just within the range required for intelligent life (of our particular kind) but is in some sense the best possible value for intelligent life. An optimum value can be a single value (and usually is), so that sort of argument could, in theory, work – but it would be untestable, and a pretty weird kind of world-view would result.

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