Probability of Fine-Tuning

#63

June 29, 2008

Probability of Fine-Tuning

How does one determine the probability of fine-tuning for a life-supporting universe such as ours? Dr. Craig has argued that the universe’s fundamental constants are set so precisely for life that it would be absurd to assume they would randomly be such. In this article, he demonstrates how one would go about finding just how improbable such well-tuned constants would be.

Dear Dr. Craig,

I had a question about the argument from fine-tuning, specifically regarding the values of certain constants. I’m in the middle of an undergrad program in Physics, and so I’m familiar with many fundamental constants of the universe, but not exactly with the extent of their ‘tuning.’

My question is, how is it possible to calculate the probability of a constant being such that it leads to a life-supporting universe?

For example, let’s say that we have constants A, B, and C. Let’s say that in order for a life supporting universe to result, A must equal 4, B = 6, and C = 2. It would seem to me that we could calculate the probability of A being four if we knew that A had to be a number between 1 and 10. But if A must be between 1 and 10 (lets call this range R), then that range itself must be finely tuned.

That is, R has to be such that it contains the number four in its subset. The smaller the value R, the less likely it is the R contains the number four. The larger the value R, the less likely it is that A will become four. Additionally, since R could be any number from 0 to infinity, it would seem as though the probability of it containing four would be some constant k in infinity, and a constant over infinity is, of course, zero.

As I’m sure you’re well aware, many scientists respond to the fine tuning argument by invoking a multiverse (which is ironic, since this is a non-scientific claim) and anthropic principal argument. They would make the claim that in each universe the values of A, B, and C are different, so if each constant has a 1/10 probability of supporting life, then with 1000 universes there is a 62.3% chance of life existing in at least one.

But why must A, B, and C exist? Doesn’t this suggest that there is yet another governing law ABOVE the multiverse that says each universe within it must have values A, B, and C, and that each value must then be different? Is there some mistake in my reasoning? It seems this should be more obvious otherwise.

Thanks,

Ken

- country not specified

Probability of fine tuning

I think your intuitions on this matter are basically correct, Ken. I’d commend to you the work of Robin Collins, who is probably the best thinker working on these questions. I’ll include a list of references at the end of this answer. In order to calculate the probability of a constant’s being such that it leads to a life-supporting universe, we need to calculate the ratio between the range of life-permitting values and the range of values it might have, whether life-permitting or not. We can assess the range of life-permitting values by holding the laws of nature constant while altering the value of the constant which plays a role in that law. So, for example, we can figure out what would happen if we decrease or increase the force of gravity, and we discover that alterations beyond a certain range would result either in large-scale objects’ ceasing to stick together or else collapsing. That will give us an idea of the range of strength of the gravitational force that is compatible with physical life forms.

Then we compare that range with the range of values that the constant could have assumed. This is trickier, but a simple rule of thumb is to take the range to be as wide as we can see that such values are possible. There may be values that a constant could have which lie outside our ken, but so long as the range that we can see is large in comparison to the life-permitting range, then that constant’s having the value it does is improbable. For some of the constants, like the cosmological constant, the range of life permitting values is incomprehensibly tiny in comparison with the range of values we see that it could have, so that the chances of the constant’s having the value it does is virtually next to impossible.

The range itself is not fine-tuned. Rather it is the individual constant that is fine-tuned, that is to say, in order for the universe to be life-permitting the constant must fall into a very narrow life-permitting range in comparison to the range of values it could have assumed.

Probability of fine tuning – The creation of multiple universes requires fine-tuning

You’re right that detractors of design have been forced to resort to the extraordinary Many Worlds Hypothesis in an effort to explain away fine-tuning. If there is a World Ensemble of universes which are infinite in number and varying randomly in their constants and initial conditions, then by chance alone a life-permitting universe will appear in the ensemble, indeed, it will appear an infinite number of times.

Now this recourse to the World Ensemble will be in vain if it turns out that the mechanism that generates the World Ensemble must itself be fine-tuned, for then one has only kicked the problem upstairs. And, indeed, that does seem to be the case. The most popular candidate for a World Ensemble today, the inflationary multiverse, does appear to require fine-tuning. For example, M-theory, the theory which supposedly governs the multiverse, works only if there are exactly eleven dimensions—but it does nothing to explain why precisely that number of dimensions should exist.

So when your teachers or classmates pull the multiverse out of the bag, just ask them, “Isn’t the multiverse itself describable by specific physical laws? Don’t those laws themselves include constants and boundary conditions which must be fine-tuned in order for the multiverse to exist?’” It will be interesting to hear their reply!


Further Reading

Collins, Robin. (2002). “God, Design, and Fine-Tuning.” In God Matters: Readings in the Philosophy of Religion, Raymond Martin and Christopher Bernard, eds. New York: Longman Press.

Collins, Robin. (2003). “Evidence for Fine-tuning.” In God and Design: The Teleological Argument and Modern Science, Neil Manson, ed. London: Routledge, pp. 178-199.

Collins, Robin. (2005). “Hume, Fine-Tuning and the ‘Who Designed God?’ Objection,” in In Defense of Natural Theology: A Post-Humean Assessment, James Sennett and Douglas Groothius, eds., pp. 175-199.

Collins, Robin. (2005). “How to Rigorously Define Fine-tuning.” Philosophia Christi 7 (December, 2005): 382-407.

Collins, Robin. (2007). “The Teleological Argument.” In Philosophy of Religion: Contemporary Issues, Paul Copan and Chad V. Meister, eds. Oxford: Wiley-Blackwell.