The anthropic principle [82] states that “what we can expect to observe must be restricted by the conditions necessary for our presence as observers”. It has received many interpretations among which the weak anthropic principle stating that “we must be prepared to take account of the fact that our location in the universe in necessarily privileged to the extent of being compatible with our existence as observers”, which is a restriction of the Copernican principle often used in cosmology, and the strong anthropic principle according to which “the universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage.” (see [35] for further discussions and a large bibliography on the subject).

One can then try to determine the probability that an observer measure the value of the constant (that is a random variable fluctuating in the multiverse and the density of observers depend on the local value of ). According to Bayes theorem,

This approach to the understanding of the observed values of the fundamental constants (but also of the initial conditions of our universe) by resorting to the actual existence of a multiverse populated by a different “low-energy” theory of some “mother” microscopic theory allows us to explain the observed fine-tuning by an observational selection effect. It also sets a limit to the Copernican principle stating that we do not live in a particular position in space since we have to live in a region of the multiverse where the constants are inside the anthropic bound. Such an approach is indeed not widely accepted and has been criticized in many ways [7, 182, 480, 402, 479, 511, 475].

Among the issues to be answered before such an approach becomes more rigorous, let us note: (1) what is the shape of the string landscape; (2) what constants should we scan. It is indeed important to distinguish the parameters that are actually fine-tuned in order to determine those that we should hope to explain in this way [537, 538]. Here theoretical physics is indeed important since it should determine which of the numerical coincidences are coincidences and which are expected for some unification or symmetry reasons; (3) how is the landscape populated; (4) what is the measure to be used in order and what is the correct way to compute anthropically-conditioned probabilities.

While considered as not following the standard scientific approach, this is the only existing window on some understanding of the value of the fundamental constants.

Living Rev. Relativity 14, (2011), 2
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