There have been some good comments on last week's post about the Many-Worlds Interpretation, which I find a little surprising, as it was thrown together very quickly and kind of rant-y on my part, because I was annoyed by the tone of the original Phillip Ball article. (His follow-up hasn't helped that...) But then maybe that's why it succeeded in generating good comments. Tough call.
Anyway, I let these slide for a while because of day-job stuff, so I'm going to promote this to a new post, and try to address some of these. Because, apparently, we are never out of universes in which I'm writing about Many-Worlds.
The biggest is a pair of comments from RM, one of which (#3) I responded to already:
If cats are too “squishy”, how about a slightly more “physicsy” scenario: You have a particle which you’ve prepared in a 50/50 superposition of up/down spin. You pass the particle through an apparatus with a magnetic field such that a spin up particle will curve right, and a spin down particle will curve left. At the appropriate location on the other side of the apparatus you have two identical detectors, each with sensitivity such that a single non-superimposed particle is sufficient to trigger it. Each detector is linked to a separate LED, which turns on when the detector is triggered. You pass a single superimposed particle through the apparatus, and the right detector’s LED turns on. How is that event interpreted in you preferred version of the many worlds hypothesis? Or is there something about this scenario that’s subtly nonsensical?
My response, to save you clicking through, was:
Each LED is in a superposition of on and off states, entangled with the state of the electron, which is in a superposition of “curved left” and “curved right,” entangled with the spin. Nothing happens to the original spin superposition, it just becomes embedded in a much larger entangled state, which includes whatever apparatus you’re using to measure the state.
Now, you’re free to choose to consider only a subset of that ever-expanding entangled superposition state, for the sake of convenience when trying to calculate stuff. So, you can calculate the probability of ending up in the particular piece where the LED on the right is lit, and continue the calculation using just that piece. But that’s no different than, say, calculating the energy levels of an isolated hydrogen atom without worrying about the fact that, (if you’ll forgive a detour through Brian Cox territory) the electron in any real hydrogen atom technically needs to be in an antisymmetric state with every other electron in the universe. While technically true, that doesn’t have any measurable consequences, so you can safely ignore it for the sake of being able to get things done.
to which RM replied:
I’m total okay with having the entire apparatus be in a single wave function, with the two LEDs being in an entangled state, superimposed in an anticorrelated on/off superposition. Raises no eyebrows from me.
However, all of the accumulated experience from these sorts of experiments indicates that 1) it’s possible to talk about the result of a single run with a single particle and 2) for that single particle run, when the experimenter observes the LEDs, they will see only a single LED lit, rather than observing a superposition of states (whatever that would mean). That’s what I’m really asking: what happens with the MWI that makes the equally probable superpositon of spin states resolve itself into that recognition of the single lit LED in the experimenter head, followed by them shouting down the hall “Hey, Chad, the right one lit up!”
As I understand the MWI, we keep extending the range of the superimposed/entangled states. So the superimposed light from the LEDs result in superimposed states on the experimenter’s retina, which result in superimposed neuronal signals, which result in superimposed vocal cord and sound waves and ear drums and neuronal signals in Chad. So now, theoretically, you have two versions of Chad, one in which he heard “left”, and one in which he heard “right”, and the wavefunction for each keeps evolving independantly. But experience and experiment tells us we only ever observe one. Why? One you get into mental states of physicist, you go past “computational convenience”. Obsevation is the cornerstone of experimental science, and if we throw that into the woodchipper, we might as well take up banking.
I think there are two subtle but related problems going on here, and I'm not quite sure which is the real issue. One of these is a belief that somebody ought to be able to see the existence of both branches of the wavefunction, the other is a kind of privileging of "mental states." Neither of these objections strikes me as particularly convincing.
The idea that somebody ought to see both branches is implicit in calling out the fact that we only see one outcome as strange. But as I said in the original post, I think this is mostly a matter of not thinking carefully enough about what it means to measure things. Seeing multiple branches of the wavefunction would require somebody to be standing outside those branches, and the whole point of the interpretation is that there's no "outside" to the universe. Everything is part of the same ginormous wavefunction, and if you're going to talk about "seeing" something, it has to be in terms of a measurement you can in principle make within that wavefunction.
So, the reason we see only one outcome of a single-particle measurement is that we're part of the wavefunction. Before the measurement, the particle is in a superposition state that has a "left" piece and a "right" piece, two unlit LEDs, and a bored physicist waiting for a result. In quasi-equation form:
Ψ = (bored physicist)(unlit left)(unlit right)[(electron left) + (electron right)]
The "weird quantum" part of this is inside the square brackets, bolded to make it more obvious.
once one of the LEDs lights, this changes to:
Ψ = (bored physicist)[(left lit)(unlit right)(electron left) + (unlit left)(right lit)(electron right)]
After the machine goes "ping," we expand again:
Ψ = [(left physicist)(left lit)(unlit right)(electron left) + (right physicist)(unlit left)(right lit)(electron right)]
which is to say, our big entangled state now includes a state where the physicist seeing the left LED lit is entangled with the left LED being lit is entangled with the electron going left, and the complementary state with the physicist seeing the right LED lit, etc.. The physicist sees only one outcome because the seeing of outcomes is part of the wavefunction.
Which brings in the second objection, namely that there's something fishy about including the "mental states of physicists" in things. But I don't see how you can justify drawing a line between the measurement apparatus with the LED's and the mental states of physicists, and saying that one of these is permissible and the other is not.
Ultimately, the mental state of a physicist is a consequence of a particular arrangement of the real measurable particles making up the body and brain of that physicist. We don't know exactly how that works, because that's a truly enormous number of particles put together in complicated ways, but the only alternative is to subscribe to some sort of mystical Cartesian division between mind and body, and I don't see any reason to go there.
And if you can accept measuring apparatus containing LEDs as part of the superposition, I see no reason why mental states of physicists can't also be in there. After all, having an LED in a superposition of "lit" and "unlit" already involves a macroscopic number of electrons within solid objects being in superpositions of moving and not-moving. Scaling that up to the physical brain of a physicist is a difference of degree, not kind.
Now, this may seem to contradict my objections to Ball's original article, but that's mostly because I was a little peeved, and didn't phrase those properly. My problem with his article isn't the inclusion of mental states of physicists at all, but the attempt to use subjective experiences as an argument against Many-Worlds on what are essentially aesthetic grounds. The notion of wavefunction branches including observers who see particular things (or don't see particular things) is not a problem; indeed, it's an inescapable consequence of the interpretation. The thing I have a problem with is talking about fuzzy, ill-defined issues with those mental states as if they prove something about the foundation of the interpretation. If you want to talk philosophical foundations in a meaningful way, you need to talk about stuff you can actually measure and how you can actually measure it, otherwise you're just blowing smoke.
The other thing I wanted to highlight was this analogy from "ppnl":
Usually when I hear about many worlds I hear talk about the universe splitting on each measurement. This brings to mind a tree like structure of worlds. I think this confuses things.
Instead think of a vast space or continuum of worlds. What we know about our world locates us in that space and probabilistically determines our path through that space. But we can’t ever fully exist at a point in that space and so there are interference effects from near by spaces.
But does that mean all those other spaces exist? Well what do you mean “exist”? In the sense that those other worlds have interference effects they exist. It can be useful to think of them existing. Beyond that you will have to define exactly what you mean by “exist” to get a meaningful answer.
Does the past exist? Does the future exist? Relativity encourages us to thing of the past and future as an existing geometric structure. But is it or is this just a useful stance? Again you will have to pick a definition of exist that allows a meaningful answer.
I like the analogy between other "worlds" and past events, because it's true that the specific outcome of a specific measurement depends on the presence of those other wavefunction branches, in the same way that the specific situation you find yourself in today are contingent on lots of things that happened in the past. And I think that carries over nicely in that the influence of many of those past events are unknowable, in the same way that the random and unmeasured influence of a larger environment plays an essential role in decoherence.
I think this analogy dovetails nicely with stuff I wrote in my quantum book. There are other bits I'm not so sure of, but I'll try to think more about this and explore it in a bit more detail later. But for the moment, it's worth highlighting as a comment I thought was really interesting.
And that's it for now, at least in this branch of the ever-expanding superposition in which we live in.
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Perhaps somewhat OT, but "some sort of mystical Cartesian division" is surely just a placeholder for a model that includes Mind DoFs at human scales. Mind is a complex low energy phenomenon that we may not be able to probe using highly focused high energy apparatus. For a given effective field theory we have to use a measurement apparatus that is sensitive to the DoFs of the EFT. Identifying useful DoFs for a complex system is difficult and requires artfulness, in this case perhaps in the extreme, but I think you're using "mystical" in an excessively derogatory way here. People do understand other people, modeling them and the effective interactions between them, and such models could be said to be EFTs as we now understand them (unless generalization is not allowed).
To return to MW, an EFT approach to physics is subversive for any interpretation that takes a particular technical feature of a model at a given scale absolutely seriously. In the MWI case there's not much of a sense of humor, scale, or proportion about the wave function [scales of action being as or more important than length scales, needless to say for physicists and well-educated dogs].
This is an excellent explanation of something that seems to cause far more confusion than it really should! The Mind Projection Fallacy in one of its most pernicious guises. Why do you never see a superposition of two states? Because to have observed is to have become entangled, and as such you'd never expect to 'stand outside' and see multiple branches.
I think that the objection that you are responding to (Ball's that is) is indeed off-base. However, there are deeper issues with many-worlds that are not so easily overlooked. For example, if I have a particle that is initially in a pure state that looks like a superposition
a |up> + b |down>
and I have an apparatus set to make an up/down measurement, then quantum mechanics tells me that I'll see up with probability |a|^2 and down with |b|^2. However, the naive language used to describe the splitting into many worlds suggests that there are two worlds, an up-world and a down-world, so why aren't the probabilities always 50/50 in such a scenario?
Yes, you can add further postulates to try to rectify the problem---in fact you absolutely have to. But in that case, the notion that many-worlds rests on two simple postulates and all the rest is derived is false. You have added more postulates. Perhaps they are phenomenological ones, but you can't make any progress connecting many worlds to the actual use of quantum mechanics without these postulates.
Furthermore, there are deep questions about the interpretation of probability itself that get inextricably entangled with the many worlds approach. Who chooses which version of "you" is the one you're experiencing? Could your awareness actually be flitting around the various branches? (you wouldn't know because all your memories would be shifting around too). What is the meaning of probability in this many worlds scenario?
Also, why is the basis in which states like the experimenter being bored or not the preferred one? A state vector in an enormous Hilbert space can be decomposed in a huge number of ways. In fact, what allows us to distinguish between the basis you gave in your example versus a basis very close to it (but not quite it). Those are two different descriptions of the world and yet, intuitively, they shouldn't be all that different. Many worlds does not tell us how to think about such issues however, at least as it is usually expressed. In order to do so, it would need more postulates.
In fact, the preferred basis conflicts with claims that many worlds maintains a manifest form of locality. If you set up an entangled system in the usual Bell-state example, then if indeed there is only one branch before a measurement occurs, then there is a sudden splitting into multiple branches and an instantaneous correlation is created between the spins of the two particles that wasn't there before. That seems like non-local action. If you want to get around this, you could argue that there were two branches all along, but then you run into trouble if an experimenter decides to change the orientation of their spin detector.
Finally, the assumption of a universal wave function is itself quite suspect. At every observable scale we find no exactly pure states (how could we, the moment the system is observed it has been opened by the observer). As scales get larger, the level of entanglement with other system only grows. If a scenario like eternal inflation is correct, then it seems that there may not be any largest closed system in any constructive sense of the term. So there may be no sensible universal quantum system to assign a pure state to.
These are among the much deeper issues that one might raise with many worlds.
The "There are two branches, the probability should be 50/50" thing always reminds me of the brilliant Daily show segment where John Oliver visits a kook who thinks the LHC is going to destroy the world. He asks the kook "What are the chances?" and the reply is "50/50: either it will destroy the world, or it won't." to which Oliver says "Oh, Walter. I don't think probability works that way."
I'm not especially bothered by the idea of adding the Born rule for getting probability from the wavefunction as a separate axiom. But if you don't like that, there are a lot of people who think they're making progress on ways of deriving the Born rule within the context of Many-Worlds-- Sean Carroll talks a bit about this in his post.
I don't find any of the other problems all that upsetting either, but it's late, and I'm tired, so I'm not going to attempt detailed answers now. I had meant to mention Sean's Born rule stuff in the original post this morning, though, but didn't because it was getting too long, so I thought I should throw a plug in here.
On the issue of what it is like to be in a superposition, I think Everett already proposed a good answer to that. Suppose the state after a measurement is
|spin up>|Experimenter has seen spin up> + |spin down>|Experimenter has seen spin down>,
where I am leaving out all the messy detector and environment stuff (just assume it is absorbed into the experimenter states). What will happen if you ask the experimenter if she saw a definite outcome? Well, it had better be the case that if the state were:
|spin up>|Experimenter has seen spin up>
then the experimenter would say that she had seen a definite outcome, i.e. the state would evolve to
|spin up>|Experimenter has seen spin up>|Experimenter says she saw a definite outcome>.
Similarly, if the state were
|spin down>|Experimenter has seen spin down>
then this would evolve to
|spin down>|Experimenter has seen spin down>|Experimenter says she saw a definite outcome>
Now, because of the linearity of quantum theory, we can simply compute what would happen in the superposition case. Namely it would evolve to:
(|spin up>|Experimenter has seen spin up> + |spin down>|Experimenter has seen spin down>)|Experimenter says she saw a definite outcome>
So, if systems always evolve according to the linear Schroedinger equation, then there can be no question of the experimenter believing anything other than that she has seen a definite outcome, provided we accept the reliability of her reports. Thus, if a universally Schroedinger evolving wavefunction describes reality, and there is nothing to be added to that description, then there is no question of it feeling any different to be in a superposition than it does to not be in a superposition.
Since your interests in this are basically refuting bad arguments against many worlds, rather than making the case *for* many worlds, I can completely understand your feelings regarding the problems I raise. However, let me just briefly try to clarify what I was saying.
Regarding the "Daily Show" argument: the point wasn't that you could naively look at many worlds as saying everything is 50/50, but rather to highlight that the two postulates that are taken as basic fail to tell us what to do with the amplitudes associated to branches. As a result, you need at least one further postulate (such as the Born rule) though probably you need more than that if you think about it carefully. Approaches like Sean Caroll's clearly add more axiomatic content to the interpretation, so it's wrong to say that it's as simple as two basic postulates and then some derivations.
Basically, many worlds is not as axiomatically simple as many of its proponents claim. This is the main point of the other problems that I raised as well.
The question of a universal wavefunction is, I think, even more pressing if you want to be more careful from a philosophical perspective. That's because this is a postulate about something utterly untestable (unlike say, the postulate of Schrodinger evolution for an isolated, closed quantum system). Not only is it untestable, but insofar as you might try to look around at the world to justify it, it flies in the face of the pattern that we *do* see, which is that the larger the scale the more significant the entanglements.
Anyway, as I said, I see where you're coming from---shooting down some bad arguments against MWI. I was trying to raise some of the actual problems with the approach.
Why is it called the Multiple World Interpretation?
It sounds like there is just one world full of superpositioned states. The electron/LED example can obviously be extended backwards as well as forwards in time, so the apparatus that generates the 50/50 electron itself is in a superpositioned state and the generator pumping out its electrons and the guy that invented the generator's grandmother's hair comb are also part of the superposition and so on.
Are we supposed to think of each multiplied out term of superposition as a different world? Does the passage of time actually correspond with the multiplication process as in the example? Is this vanilla multiplication or something more interesting, perhaps non-commutative?
I'd think an interpretation where there is some kind of finality or closure in the measurement process would be more multiple world-y.