I’ve been rereading Max Tegmark’s 1997 paper on the Many Worlds Interpretation of quantum mechanics, written in response to an informal poll taken that year at a quantum workshop. There, the MWI was the second most popular interpretation adduced by the attendees, after the Copenhagen Interpretation (which is here undefined). What, Tegmark asks, can account for the robust, even increasing, popularity of the MWI even after it has been so heavily criticized?
He gives various possible reasons, among them the idea that the emerging understanding of decoherence in the 1970s and 1980s removed the apparently serious objection “why don’t we perceive superpositions then?” Perhaps that’s true. Tegmark also says that enough experimental evidence had accumulated by then that quantum mechanics really is weird (quantum nonlocality, molecular superpositions etc) that maybe experimentalists (apparently a more skeptical bunch than theorists) were concluding, “hell, why not?” Again, perhaps so. Perhaps they really did think that “weirdness” here justified weirdness “there”. Perhaps they had become more ready to embrace quantum explanations of homeopathy and telepathy too.
But honestly, some of the stuff here. It’s delightful to see Tegmark actually write down for once the wave vector for an observer, since I’ve always wondered what that looked like. This particular observer makes a measurement on the spin state of a silver atom, and is happy with an up result but unhappy with a down result. In the former case, her state looks like this: |☺>. The latter case? Oh, you got there before me: |☹>. These two states are then combined as tensor products with the corresponding spin states. These equations are identified by numbers, rather as you do when you’re doing science.
Well, but what then of the objection that the very notion of probability is problematic when one is dealing with the MWI, given that everything that can happen does happen with certainty? This issue has been much debated, and certainly it is subtle. Subtler, I think, than the resolution Tegmark proposes. Let’s suppose, he says, that the observer is sleeping in bed when the spin measurement is made, and is placed in one or other of two identical rooms depending on the outcome. Yes, I can see you asking in what sense she is then an observer, and invoking Wigner’s friend and so on, but stay with me. You could at least imagine some apparatus designed to do this, right? So then she wakes up and wonders which room she is in. And she can then meaningfully calculate the probabilities – 50% for each. And, says Tegmark, these probabilities “could have been computed in advance of the experiment, used as gambling odds, etc., before the orthodox linguist would allow us to call them probabilities.”
Did you spot the flaw? She went to sleep – perhaps having realized that she’d have a 50% chance of waking up in either room – and then when she woke up she could find out which. But hang on – she? The “she” who went to sleep is not the “she” who woke up in one of the rooms. According to this view of the MWI, that first she is a superposition of the two shes who woke up. All that first she can say is that with 100% certainty, two future shes will occupy both rooms. At that point, the “probability” that “she” will wake up in room A or room B is a meaningless concept. “She”, or some other observer, could still place a bet on it, though, right, knowing that there will be one outcome or the other? Not really – rational betters would know that it makes no difference, if the MWI holds true. They’ll win and lose either way, with certainty. I wonder if Max, who I think truly does believe the MWI, would place a bet?
The point, I think, is that a linguist would be less bothered by the definition of “probability” here than by the definition of the observer. Posing the issue this way involves the usual refusal to admit that we lack any coherent way to relate the experiences of an individual before a quantum event (on which their life history is contingent) to the whole notion of that “same” individual afterwards. Still, we have the maths: |☺> + |☹> (pardon me for not normalizing) becomes |☺> and |☹> afterwards. And in Tegmark’s universe, it’s the maths that counts.
Oh, and I didn’t even ask what happens when the probability of the spin measurements is not 50:50 but 70:30. Another day, perhaps.