Sunday, January 16, 2011

Maximising E[Habitable Earth-Like Planets]

Fascinating e-correspondence (now about 23 emails) with Don Page and two other cosmologists, one immensely distinguished, around Don Page's paper suggested by the remark in Questions of Truth. I hope to discuss this with one of them tomorrow so things may become clearer.

Although Don’s paper is (of course) interesting I don't think it establishes the conclusion he seeks. Arguably the data he presents shows that the observed value of Λ is well within ε of the value that would be maximal for (the probability of intelligent) life developing, where ε is our margin of uncertainty about where such a maximal value might be. But the other hand I think that the idea could be developed into a potentially powerful, testable and tractable hypothesis.

We don’t remotely know enough about the overall possibilities of intelligent life. But we do know that life like ours requires the existence of what we might call a Habitable Earth-Like Planet (HELP). It’s hard to be sure exactly what characteristics of a HELP are vital, but we might try:

  1. stable average temperatures* somewhere between say 280-350K
  2. not too much ionising radiation or
  3. bombardment by large meteors
  4. M/MEarth >0.1 and <>stability for at least (say) 2bnYr, and
  5. an abundance of key elements (esp H,O,C,N) within a factor of 2 of their observed values.
We could then formulate an in-principle-testable hypothesis (MaxHELP) that the fundamental constants of nature locally maximise E[HELP] the expected number of HELPs in the universe. In particular that, within experimental error and the uncertainly of our calculations, ∂E[HELP]/∂y = 0 for any fundamental constant y. There is a weak statistical argument in favour of MaxHELP (if the only thing we can be sure about is that there exists at least one HELP, and we think all other astronomical observations may be corrigible in the long run) and a methodological argument that if it turned out to be true it would provide an interesting insight into why the fundamental constants had the values they do. It also seems to go with the grain of much of the work on exoplanets.
My basic problem with Don’s current paper is that, even assuming life is made of baryons, the quantity we are trying to maximise (let's call it L and work in logs) is presumably B + F + P where

  • B = ln(number of baryons produced during a time where the universe could form life)
  • F = ln(fraction of such baryons that become structures large enough for suitable living observers)
  • P = ln(average number of such living observers formed per baryon in such structures).

Don observes that in his ref [11] ∂F/∂Λ < 0 for the observed value of Λ and infers that ∂L/∂Λ < 0. But of course ∂L/∂y = ∂B/∂y + ∂F/∂y + ∂P/∂y, and without upper bounds on the other terms, the inference doesn’t follow. It seems most improbable that we can currently calculate an “optimal” value of Λ to better than 1E-121 so all that we can say is that the rough hypothesis Don derives from QoT is within Margin of Error.

However the more modelling there is of planetary formation, the easier it will be to test MaxHELP. At least this theist “would not be surprised” if it were true, though equally unsurprised if it turned out to be only approximate. But it seems worth discussing and then perhaps publishing in collaboration.

* by which of course I mean not just that the average of the temperatures over the surface of the planet is about this, but that for a large fraction of the planet's surface temperatures are in this range almost all the time. A situation like that of Mercury wouldn't do.

No comments: