I think I missed this the first time around, but this weekend, I watched the bloggingheads conversation about quantum mechanics between Sean Carroll and David Albert. In it, David makes an extended argument against the Many-Worlds Interpretation of quantum mechanics (starting about 40:00 into the conversation).
The problem is, I can’t quite figure out what the problem is supposed to be.
The argument has something to do with a thought experiment in which you take a million particles, prepared in a state such that a measurement of their spin will give an equal probability of measuring “up” or “down.” The most likely outcome will be for roughly half of the spins to be up, and roughly half of the spins to be down.
There will be one branch of the wavefunction, though, in which every single spin will be up, and one branch in which every spin will be down. The odds against this are astronomical, as a matter of normal probability, but it can happen, so there must be a part of the wavefunction that describes that hugely unlikely event.
Albert seems to think that this poses some sort of insuperable problem for the Many-Worlds Interpretation. I can’t really figure out why, though.
It’s certainly true that any observer seeing such an outcome will be surprised, and for good reason, it’s a one-in-two-to-the-million event. It’s also true that this outcome must be represented somewhere in the wavefunction of the universe. Albert seems to take this as meaning that it’s somehow unreasonable for that observer to be surprised by that result, and that this somehow poses an enormous problem for quantum mechanics.
The thing is, though, this isn’t a problem that’s specific to quantum mechanics. This is just the infinite-number-of-monkeys problem from regular probability. Given a large enough sample of random events, you will eventually find anything you like– a large enough number of monkeys banging on typewriters will eventually produce the Skindhead Hamelt. If you flip a coin often enough, you will eventually get a run of a million heads in a row.
It’s highly unlikely that any set of a million coin-flips will all come up heads, and you’d be absolutely right to suspect something funny was going on. Even with perfectly fair coins flipped in a perfectly random manner, though, somebody, somewhere is going to see a run of a million heads.
So I really don’t see how this is a killer argument against Many-Worlds. Or, more precisely, I don’t see how it’s a killer argument against Many-Worlds specifically, as opposed to a killer argument against probability theory generally. But then, down that road lies madness, in the Zeno’s Paradox sort of vein, in which you manage to philosophize yourself into believing that things that are manifestly true can’t possibly be true (happily, you’ll never make it all the way to the end of the road, because first you have to get halfway to madness, and then half of the remaining half, and…).
There are interesting questions to be asked about probability in Many-Worlds– Sean brings up the most obvious, namely, “How do you recover the Born rule for probabilities from a system in which all outcomes happen somewhere?” That doesn’t seem to be what David is talking about, though, because he declines to follow up on that aspect when Sean brings it up. Instead, he goes off on this weird thing about people being surprised by improbable events, and I’m not sure why.
I hope there’s something deep and subtle going on here, but I honestly don’t see what it’s supposed to be. Which is probably why I’m an experimentalist, not a theorist or a philosopher.