Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

infinity of universes 225of the initial conditions of the universe. 15 “The physical laws ‘laid down’ in the bigbang seem to apply everywhere we can now observe. But though they are unchanging(or almost so), they seem rather specially adjusted” (Rees 1998, p. 250). This couldbe either a coincidence or an “intelligent design.” To avoid this conclusion, one couldadopt the following argument: “There may be other universes – uncountable many ofthem – of which ours is just one. In the others, the laws and constants are different. Butours is not randomly selected. It belongs to the unusual subset that allows complexityand consciousness to develop. Once we accept this, the seemingly ‘designed’ or ‘finetuned’features of our universe need occasion no surprise” (Rees 1998, p. 250).Many people support the multiverse idea because of some conclusions followingfrom the chaotic scenario of inflationary cosmology and from cosmological modelsbased on the superstring theory and the so-called M-theory, which they have independentreasons for believing. The details of these highly hypothetical models neednot concern us here. 16 For our present point of view, the important fact is that almostall considerations regarding the multiverse are based on probabilistic arguments. Weclaim that some physical properties are randomly distributed in the multiverse, thatour position in the multiverse is not random, and so forth. At the same time, at leastin some formulations, the multiverse is claimed to be an infinite – and perhaps evenuncountably infinite – collection of universes. The point is that we do not know whetherthe concept of probability can legitimately be defined on such a collection. Mathematicallyspeaking, we do not know whether there is a probability measure on it (or evenwhether this collection is a set), and if such a measure does not exist, any probabilisticutterance about the multiverse is meaningless. If we want to improve the situation, wemust impose quite demanding constraints on our understanding of multiverse. However,even if this is the case, the problem is utterly difficult (see Ellis 2007). Tegmarkhas put this bluntly: “As multiverse theories gain credence, the sticky issue of howto compute probabilities in physics is growing from a minor nuisance into a majorembarrassment” (Tegmark 2003).I do not claim that we should stop talking about the multiverse (even the mostaudacious speculations can have positive influence on science), but rather that weshould be aware of our conceptual and linguistic constraints. Unfortunately, this isnot always the case. Especially, when infinity and probability are combined together,unexpected situations are ready to be born. The same Tegmark (2003) does not hesitateto write the following: “If space is infinite and the distribution of matter is sufficientlyuniform on large scales, then even the most unlikely events must take place somewhere.In particular, there are infinitely many other inhabited planets, including not just one butinfinitely many with people with the same appearance, name and memories as you.” 17He claims that, according to his “extremely conservative estimate,” in the infiniteuniverse “the closest identical copy of you is about 10 1029 m away” (Tegmark 2003).15 For a debate concerning the multiverse idea see Carr (2007).16 See the corresponding chapters in Carr (2007).17 Tegmark justifies his conclusion by quoting the ergodic theorem (which, in its essence, is a probabilistictheorem). To be more precise, Tegmark, based on this theorem, claims that the probability distribution ofoutcomes in a given volume in the multiverse is the same as the probability distribution of outcomes indifferent volumes in a single universe, provided that each universe within the multiverse evolves from randominitial conditions.