February 13, 2013

The Normalizability Objection to the MWH

Filed under: Metaphysics,Natural Theology,Philosophy of Religion — camcintosh @ 12:42 pm

According to the Many Worlds Hypothesis (MWH) our universe is one among many—perhaps an infinite number—of spacetime universes (misleadingly called “worlds”). It is not clear whether the MWH should postulate a large but finite number of worlds, or an infinite number of worlds. Here are two reasons to think the MWH should postulate an infinite number as opposed to a large but finite number:

(i) Postulating an infinite number of worlds constitutes a simpler hypothesis than postulating a large but finite number. This is because the latter requires an additional explanandum—viz., why this particular number?—in the same way telling a friend to meet at 6:13 or 6:21 rather than, say, 6:00 or 6:30 does.

(ii) If the only reason for postulating a large but finite number of universes is just to meet a certain probabilistic threshold (i.e., however many universes are needed to render more probable fine-tuning), then it is extraordinarily ad hoc.

I have not looked deeply into the literature on the MWH, so I am unaware of any reasons for postulating a large but finite number of universes independent of that mentioned in (ii) (if any reader is aware of such reasons, I’d appreciate a note).

So suppose the MWH postulates an infinite number of universes. If the normalizability objection (see here for the original statement by the McGrews and Vestrup, or Here for my brief synopsis) to fine-tuning arguments (FTAs) is sound, then it is also a sound objection to the MWH. This is because the probability range postulated by the MWH would be infinite, and hence, not normalizable.

Suppose instead that the MHW postulates however many universes—from one to infinity—is needed to render more probable fine-tuning. This shows that there is no principled upper bound on the probability range postulated by the MWH. And this is precisely the problem the normalizability objection highlights. So it’s not clear that the MWH can avoid the normalizability objection even if it can get away with postulating a large but finite number of universes.

In other words, one cannot endorse both the normalizability objection and the MWH in response to FTAs. My own suspicion is that this casts serious doubt on the soundness of the normalizability objection.



  1. Actually, the MWH doesn’t postulate any universes at all. The myriad of universes are a consequence of the postulates of quantum mechanics, not the other way round. The idea behind the MWH is that the observer is also a quantum system. When an observation is performed, the observed system and the observer become entangled, that is, the states of one correlate to the states of the other. If before we had a wave-function where the electron was in the spin up and spin down state at the same time (recall that, in QM, the state of a particle is given by a wave function that contains all the possible measurement outcomes for that particle), now we still have one wave function with two parts: in one, we have an electron with spin up and an observer having measured spin up, in the other we have an electron with spin down and an observer having measured spin down.
    Because the two sides of the wave-function cannot communicate any more (we say they have “decohered”) it appears as if the universe has split in two. This happens for every single measurement-like event, thus creating the multiverse, which is in fact nothing but a huge wave function with multiple parts that cannot interact because of decoherence.
    Answering your question, this predicts an immensely large number of “parallel universes” but not an infinite number.

    Comment by David Yerle — February 14, 2013 @ 3:27 am | Reply

    • Thanks for the comment, Dave. I was unaware of the niceties of the MWH you mention. Can you direct me to a helpful, neutral overview of what you take to be an accurate statement of the MWH?

      Needless to say, if you’re right, the impression created from the bit I’ve read on the topic is certainly misleading. I’m curious, too, if what you suggest is but one quantum-interpretation of the MWH among several alternatives that aim to give the MWH a physical interpretation.

      Comment by camcintosh — February 14, 2013 @ 9:43 am | Reply

    • There is no “neutral” exposition, I’m afraid. The clearer, most meaningful expositions all come from proponents of the interpretation. The best I’ve seen is in the book “The fabric of reality” by David Deutsch. The wikipedia article on it is also pretty OK and it will probably be more neutral, though less understandable. The key concept here is “decoherence”: wikipedia also has a decent article on it. That I’m aware of, the only possible interpretation of the many-worlds interpretation (that sounded a bit convoluted) is through no-collapse of the wave function. All you do, basically, is eliminate the measurement postulate that says the wave-function collapses after a measurement. The rests just appears naturally.
      Hope that helped!

      Comment by David Yerle — February 14, 2013 @ 9:49 am | Reply

  2. Come to think of it, David, if the MWH doesn’t postulate any universes at all, then it doesn’t pose it’s intended threat to the design hypothesis as an explanation of fine-tuning. So, instead of having to choose between the MWH and the normalizability objection (because they’re incompatible), the critic of the FTA would have to put all stock into the normalizability objection alone. This is a nice result, because the normalizability objection is demonstrably dissoluble.

    Comment by camcintosh — March 14, 2013 @ 12:13 pm | Reply

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