Monday, March 9, 2015

What happens when collapse doesn't happen in collapse theories?

On collapse theories like GRW, Quantum Mechanics proceeds deterministically according to the Schroedinger Equation until a random "hitting" event occurs, when collapse occurs. There is a frequency parameter f that controls how often hitting events tend to happen. They tend to happen much more frequently when there are large amounts of matter involved than when there are small.

Nonetheless, the hitting events are random. Thus the physics of collapse theories implies that it is physically possible, with a non-zero (but presumably tiny) probability, that no hitting event happen in the universe over the next year, and hence no collapse happens over a year. Since this is physically possible, it should make sense to ask: What would it be like if this happened? Indeed, if we live in an infinite multiverse governed by a collapse theory with the same frequency everywhere, we can be confident that such no-collapse years do occur.

So what would it be like if no collapse occurred? I can think of three plausible proposals:

  • Nothing: A (nomic or metaphysical) precondition of consciousness is a brain in a pure, or at least close to pure, quantum state, so in a no-collapse year, once everybody's brain states came to have a sufficient superposition of states (from the preferred basis), nobody would be conscious. However, after that year passed, there would be a collapse, and there would be false but plausible memories corresponding to the outcome of the collapse.
  • Everett: For that no-collapse year, we would be living as if in a branching Everett-style multiverse. Either we would be experiencing different things in different branches, or we would have counterparts in different branches experiencing different things. Then with the collapse at the end of the year, all the branches but one would disappear.
  • Weird: We would be having strange superposed experiences, perhaps quite unlike anything we can imagine. We would have superposed neural memory states. Then at the end of the year, when collapse occurred, our memories would also collapse, and we would end up with an ordinary set of memories corresponding to one component of the superpositions.

Here's one curious feature of all three proposals: At the end of the year, we would be back to business as usual, seemingly with normal memories of the past year. We would have no way of telling after the fact that we had a year with no collapse. On the Nothing proposal, we would have no way of telling during the no-collapse year, either, since we wouldn't be conscious during it. On the Everett proposal, some of our counterparts or branched selves would be having strange, improbable experiences. On the Weird proposal, we would be having strange experiences, but then we would have no memory of them.

If we take the Everett proposal, then the GRW theorist does not avoid the metaphysical oddness of persons in a branching multiverse—her only special contribution is to say that this oddness is unlikely to occur. If we take the Weird proposal, then the collapse theorist still has to deal with the metaphysical and psychological oddness of Schroedinger's cat phenomena—again, her only contribution is to say that such phenomena are unlikely. If these difficulties are really serious metaphysical problems, then the GRW theorist does not avoid them. A die that turns into a square circle once it rolls a million heads is not any less metaphysically problematic than a plain and simple square circle.

I suspect the Nothing approach is the best one for the GRW theorist. For instance, Nothing combined with compact-support-collapse helps with the infamous tails problem for collapse theories (see this for a nice discussion of the tails problem; alas, my suggestion doesn't help with the relativistic problems the author points out). For maybe we are conscious only at those instants when the wavefunctions have compact support. This is good reason to opt for the Nothing proposal if one has a collapse theory.

But the Nothing approach leads to a strange sceptical hypothesis, namely that I have not been conscious over the past week, notwithstanding apparent memories from yesterday. For remember that the collapse theories have a free parameter, f, which governs the frequency of collapses. If that parameter is low enough, then collapses will be rare, say once a month in my vicinity. And what reason do I have on the Nothing proposal to suppose that f isn't that low? The apparent memories of continuous past consciousness are exactly what I would expect with a low parameter, since the apparent memories are induced by the collapse of superposed neural states. We do have some constraints on f. For instance, f had better not be so low that it's surprising why anybody is ever conscious. Maybe there are some stronger constraints than that, though this is not clear to me. But there is no reason given the Nothing proposal to deny a value of f that yields once-per-month collapses.

The Everett proposal may well lead to a sceptical worry about low values of f as well. For how do we know that we're not right now in a no-collapse period?

The Weird proposal does not lead to this sceptical worry that f might be low. For on the Weird proposal, given a low f it's surprising that my current conscious state is non-weird, and so that's evidence against Weird plus a very low value of f. But Weird is weird.

The above sceptical worries about low values of f are ameliorated if in addition to being collapse theorists we are theists. For God likely wouldn't want us to have too many misleading memories, and hence would likely make f high enough to prevent misleading memories.


wo said...

Nice! I'd go for the Everett option though. True, the GRW theorist thereby doesn't avoid the metaphysical oddness of persons in a branching multiverse, but that doesn't strike me as a serious problem. The GRW theorist could still maintain that she (a) avoids the Everettian's extreme clash with our everyday conception of the world, and (b) can explain the Born rule. I thought these are the main attractions of GRW.

Alexander R Pruss said...

It's just occurred to me that if we take the Everett way, then it's hard to resist the idea that there are conscious beings at the tails of the wavefunction. For once we've admitted that conscious states can be superposed, then why can't low probability ones be superposed as well.
Not a very rigorous argument, though.