I was delighted to hear from John Cramer today. He was on the physics faculty at Wheaton College when I was a Freshman and Sophomore and I hadn't had communication with him since then. He is now emeritus professor of physics at Oglethorpe U in Atlanta.
John offered the following critique of multiverse theories and he gave me permission to post it. I will give all of you time to think it over and comment if you wish. In a day or two I'll submit my response to him and his response to me and perhaps we can keep the conversation going.
Thesis: Multiverse theories do not explain the fine tuning of our universe.
1) Suppose at first that our universe, U0, has only one finely tuned constant, κ. That is, the value of κ in U0 lies in a small range of values, R, that permit intelligent life to exist in U0.
2) Suppose also that U0 is only one of many extant universes, Ui, in which the values of κi can range over all real numbers. That is, a multiverse exists.
3) Since the universes of the multiverse are countable, their cardinality is the countable infinity, א0.
4) The upper bound of κi values in any multiverse is no less than the cardinality of real numbers, א1.
5) As Cantor showed long ago, א1 >> א0.
6) Therefore, a multiverse can never contain all possible values of κi.
Multiverse theories contain, as a standard feature, the implicit assumption that values of κ will be randomly selected from all possible real values and distributed among the universes. The U0 value of κ “must” somehow appear in one of the universes. This is an unwarranted belief. The probability that a multiverse contains U0 is not 1 but zero (א0/א1, with apologies to mathematical purists).
True enough, א0 universes may contain as many as א0 values of κ, but it is crucial to specify which values. The set of all integers is a countable infinity but it has א0 gaps (ranges like 0 to 1, etc.) in it, each with א1 missing values of κ. All multiverse theories necessarily have such gaps. Therefore, to explain the fine tuning of κ, a multiverse theory must be able to show that R is a likely range of values of κ in some universe (which will then be presumed to be U0). Thus, even a countable infinity of universes cannot, by itself, explain the fine tuning of κ.
Additionally, there are many more than one “fine tuned” quantities in U0. Consequently, it is incumbent on proponents of multiverse explanations to show that their choice of multiverse actually generates values of each κ in its proper R and that at least one of the universes of the multiverse has all κ values in the proper U0 ranges. Although I do not know this cannot be done, I very much doubt it can. Anyone undertaking such a project is to be commended; advancing a serious multiverse theory will be a prodigious undertaking. In fact, multiverse theories need to be theories of everything.