Many Worlds Are Never Exhausted

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.