Monday, February 23, 2015

Why dogs aren't enough in Many Worlds

I'm very glad some folks are finding this exchange on Many Worlds instructive. That was really all I wanted: to get a proper discussion of these issues going. The tone that Sean Carroll found “snide and aggressive” was intended as polemical: it’s just a rhetorical style, you know? What I certainly wanted to avoid (forgive me if I didn’t) was any name-calling or implications of stupidity, fraud, chicanery etc. (It doesn’t surprise me that some of the responses failed to do the same.) My experience has been that it is necessary to light a fire under the MWI in order to get a response at all. Indeed, even then it is proving very difficult to keep the feedback to the point and not get led astray by red herrings. For example, Sean made a big point of saying:
“The people who object to MWI because of all those unobservable worlds aren’t really objecting to MWI at all; they just don’t like and/or understand quantum mechanics.”
I’m genuinely unsure if this is supposed to be referring to me. Since I said in my article
“Certainly, to say that the world(s) surely can’t be that weird is no objection at all”
then I kind of assume it isn’t – so I’m not sure why he brings the point up. I even went to the trouble of trying explicitly to ward off attempts to dismiss my arguments that way:
“Many Worlders harp on about this complaint precisely because it is so easily dismissed.”

But what Sean said next seems to get (albeit obliquely) to the heart of the matter:
“Hilbert space is big, regardless of one’s personal feelings on the matter.”

Whatever these arguments are about, they are surely not about what Hilbert space looks like, since Hilbert space is a mathematical construct – that is simply true by definition, and there is no argument about it. The argument is about what ontological status we ascribe to the state vectors that appear in Hilbert space. I do see the MW reasoning here: the reality we currently experience corresponds to a state vector in Hilbert space, and so why do we have any grounds for denying reality to the other states into which it can evolve by smooth unitary transformation? The problem, of course, is that a single state in quantum mechanics can evolve into multiple states. Yet if we are going to exclude any of those from having objective reality, we surely must have some criterion for doing so. Absent that, we have the MWI. I do understand that reasoning.

So it seems that the arguments could be put like this: is it an additional axiom to say “All states in Hilbert space accessible from an initial one that describes our real world are also describing real worlds” – or is it not? To objectors, it is, and a very expensive one at that. To MWers, it is merely what we do for all theories. “Give us one good reason why it shouldn’t apply here”, they say.

It’s a fair point. One objection, which has nothing whatsoever to do with the vastness of Hilbert space, is to say, well, no one has seriously posited such a vast number of multiple and in some sense “parallel” (initially) worlds before, so it seems fair to ask you to work a bit harder, since don’t we in science say that extraordinary claims require extraordinary evidence?* Might we not ask you to work a bit harder in this particular case to establish the relationship between what the formalism says and what exists in physical reality? After all, whether or not we admit all accessible states in Hilbert space a physical reality, we seem to get identical observational consequences. So right now, the only way we can choose between them is philosophically. And we don’t usually regard philosophy as the final arbiter in science.

*For example, Sean emphasizes that the many worlds are a prediction, not a postulate of the theory. But most other theories (all others?) can tell us some specific things that they don’t predict too about what we will see happen. But I’m not clear if the MWI can rule out any particular thing actually coming to pass that is consistent with the laws of physics. For example, the Copenhagen interpretation (just to take an example) can exclude the “prediction” that human life came to an end following a nuclear conflict sparked by the Bay of Pigs incident. Correct me if I am wrong, but the MWI cannot rule out this “prediction”. It cannot rule out the “prediction” that Many Worlders were never bothered by this irritating science writer. Even if MWI does not exactly say “everything happens”, can it tell us there is anything in particular (consistent with the laws of physics) that does not?

So up to this point, I can appreciate both points of view. What makes me uncomfortable is that the MWers seem so determined to pretend that what they are telling us is actually not so remarkable after all. What’s so surprising, they ask, about the idea that you can instantly duplicate a consciousness, again and again and again? What is frustrating is the blithe insistence that we should believe this, I suspect the most extraordinary claim that science has ever made, on the basis simply of Occam’s (fallible) razor. This is not, do please note, at all the same as worrying about “too many worlds”.

Still, who cares about my discomfort, right? But I wanted to suggest that it’s not just a matter of whether we are prepared to accept this extraordinary possibility. We need to acknowledge that it is rather more complicated than coming to terms with a cute gaggle of sci-fi Doppelgängers. This is not about whether or not people are “all that different from atoms”. It is about whether what people say can be ascribed a coherent meaning. Those responses that have acknowledged this point at all have tended to say “Oh who cares about selfhood and agency? How absurd to expect the theory to deal with unplumbed mysteries like that!” To which I would say that interpretations of quantum theory that don’t have multiple physical worlds don’t even have to think about dealing with them. So perhaps even that Ocaam’s razor argument is more complicated than you think.

It’s been instructive to see that the MWI is something of a hydra: there are several versions, or at least several views on it. Some say that the “worlds” bit is itself a red herring, a bit of gratuitous sci-fi that we could do without. Others insist that the worlds must be actual: Sean says that people must be copied, and that only makes any kind of sense if the world is copied around them. Some say that invoking problems with personhood is irrelevant since Many Worlds would be true anyway even without people in it. (The inconvenience with this argument is that there are people in it.) Sean, interestingly, says that copying people is not only real but essential, “for deriving the Born rule” in MWI. This is a pointer to his fascinating paper on “self-locating uncertainty”. Here he and Charles Sebens points out that, in the MWI where branch states are rendered distinct and non-interacting by decoherence, the finite time required for an observer to register which branch she is on means that there is a tiny but inescapable interval during which she exists as two identical copies but doesn’t know which one she is. In this case, Carool and Sebens argue, the rational way to “apportion credence to the different possibilities” is to use the Born rule, which allows us to calculate from the wavefunction the likelihood of finding a particular result when we make a measurement. This, they say, is why probability seems to come into the situation at all, given that the MWI says that everything that can happen does happen with 100% probability.

This sounds completely bizarre: a rule of quantum physics works because of us? But I think I can see how it makes sense. The universe doesn’t care about the Born rule: it’s not forever calculating “probabilities”. Rather, the Born rule is only needed in our mathematical theory of quantum phenomena – and this argument offers an explanation of why it works when it is put there. Now, there is a bit of heavy pulling still to do in order to get from a “rational way to make predictions while we are caught in that brief instant after the universe has split but before we have been able to determine which branch we are in” and a component of the theory that we use routinely even while we are not agreed that this situation arises in the first place. I’m still not clear how that bit works. Neither is it fully clear to me how we are ever really in that limbo between the universe splitting and us knowing which branch we took, given that, in one view of the Many Worlds at least, the universe has split countless times again during that interval. Maybe the answer would be that all those subsequent split produce versions that are identical with respect to the initial “experiment”, unless they involve processes that interact with the “experiment” and so are part of it anyway. I don’t know.

I do think I can see the answer to my question to Sean (not meant flippantly) of whether it has to be humans who split in order to get the Born rule, and not merely dogs. The answer, I think, is that dogs won’t do because dogs don’t do quantum mechanics. What seems weird is that we’re then left with an aspect of quantum theory that, in this argument, is the way it is not because of some fundamental underlying physical reason so much as because we asked the question in the first place. It feels a bit like Einstein’s moon: was the Born rule true before we invented quantum theory? Or to put it another way, how is consciousness having this agency without appearing explicitly anywhere in the theory? I’m not advancing these as critiques, just saying it seems odd. I’m happy to believe that, within the MWI, the logic of this derivation of the Born rule is sound.

But doesn’t that mean that deriving the Born rule, a longstanding problem in QM, is evidence for the MWI? Sadly not. There are purported derivations within the other interpretations too. None is universally accepted.

The wider point is that, if this is Sean’s reason for insisting we include dividing people in MWI, then the questions about identity raised in my article stand. You know, perhaps they really are trivial? But no one seems to want to say why. This refusal to confront the apparent logical absurdities and contradictions of a theory which predicts that “everything” really happens is curious. It feels as though the MWers find something improper about it – as though this is not quite the respectable business for a physicist who should be contemplating rates of decoherence and the emergence of pointer states and so on. But if you insist on a theory like this, you’re stuck with all its implications – unless, that is, you have some means of “disappearing worlds” that scramble the ability to make meaningful statements about anything.


John C. Beach said...

This discussion is very fascinating, and I regret that I have such a limited education on the topics. I could never hope to grasp even a respectable inkling of the full implications of what you are discussing, so I am just trying to understand this within the context of a book I have just read, Feynman’s “QED, The Strange Theory of Light and Matter.” I was really floored by the idea that a positron is an electron traveling backward in time. How does this fit into the MWI discussion?

It seems that there is some disagreement about whether or not our current reality continuously branches into realized (but inaccessible) futures. But if a positron is just an electron in reverse-time, and it follows the reverse of the behaviors expected of an electron traveling forward in time, does that mean it will reverse the double-slit interference experiment of an electron? From our perspective of moving forward in time would we witness an interference pattern that can travel through a double-slit and produce a single positron for the detector on the other side? Would that mean that our “now” is a cinch point? (i.e. a convergence and then divergence of possibilities rather than just a forward-splitting?)

Thanks for any insights,

John Beach

John C. Beach said...

Just for grins, I carried this thought a little further and considered sources of positrons. I was wondering how the experiment I described could be constructed, and it occurred to me that perhaps it has already been invented. In the famous Curie-Joliot experiment of 1934, does the transmutation from Phosphorous-30 to Silicon-30 (by a proton changing to a neutron and the emission of a positron) mean that P-30 is some kind of superposition of states? By bombarding Aluminum with an alpha particle, did they create a compact all-in-one-package in P-30 that included both the interference pattern AND the equivalent of a double-slit, and as it emitted a positron the P-30 transmuted to Silicon?

John Beach

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