What happens if the branch “you” are in gets cancelled with another branch?
One doesn’t invoke the term “different branches” unless they are macroscopically different, and if they’re ever macroscopically different, then they will remain macroscopically different forever, thanks to entropy (and the related fact that macroscopic events leave countless little persistent traces in the environment). Even moreso if we’re talking about human observers, who form memories of what they’ve seen in the form of changes to the structure of their brains. Macroscopically different branches can’t “cancel” and more generally macroscopically different branches can’t interfere in a way that has any measurable effect.
(For any quantum observable O that’s relevant in practice, ⟨ψ|O|ϕ⟩≈0 if |ψ⟩ and |ϕ⟩ are macroscopically different—e.g. the geiger counter loudly clicked in |ψ⟩ but not |ϕ⟩.)
Solomonoff inductors are a bit of an odd case because they don’t & can’t exist in the universe. But leaving that aside (let’s say we’re implementing AIXItl or whatever):
Every time the computer makes an observation, we learn some stuff about the universe, and we also learn some indexical information about where we-in-particular are sitting within the universe. This has always been true, but it’s especially true about MWI because we will never stop getting indexical updates (unlike a deterministic universe where you can learn that you’re in a particular room on earth and then there’s no more indexical information to learn). In MWI, if we observe that a pixel is bright, then we have learned that we are in a branch of the wavefunction wherein the pixel is bright. There might or might not be other branches wherein the pixel is dark, but if there are, we now know that those branches are “not where I have found myself”, and we can ignore those branches accordingly. You can still have hypotheses, but they will incorporate born-rule indexical uncertainty about which branch I will find myself in in the future, on top of whatever other indexical uncertainty you have for other reasons.
Even moreso if we’re talking about human observers, who form memories of what they’ve seen in the form of changes to the structure of their brains. Macroscopically different branches can’t “cancel” and more generally macroscopically different branches can’t interfere in a way that has any measurable effect.
Ah, but that’s the crux of the issue. They can. How should Wigner’s friend be performing inference?
Scott’s analysis seems fine to me, unless I missed something. He writes “Many-Worlders will yawn at this question” [in reference to Wigner’s friend]. Yes. I yawn. If Wigner is right outside the lab door, then Wigner is in fact in one of the branches (the same branch as his friend) even if Wigner happens to not yet know which one of them. If Wigner is on Alpha Centauri, then he is not yet in one of those two branches, and his friend is, and I don’t see any problem with that. And then a few years later he gets a message from his friend, and by that point Wigner is in one of those two branches, and when he reads the message he’ll know which one.
I’m reluctant to engage with extraordinarily contrived scenarios in which magical 2nd-law-of-thermodynamics-violating contraptions cause “branches” to interfere. But if we are going to engage with those scenarios anyway, then we should never have referred to them as “branches” in the first place, and also we should be extremely wary of applying normal intuitions in situations where the magical contraption is “scrambling people’s brains” as Scott puts it.
As a meta point, I might drop out of this conversation at any point (including maybe right now), gotta get back to work. :)
I’m reluctant to engage with extraordinarily contrived scenarios in which magical 2nd-law-of-thermodynamics-violating contraptions cause “branches” to interfere.
Agreed. Roland Omnes tries to calculate how big the measurement apparatus of Wigner needs to be in order to measure his friend and gets 10 to the power of 10E18 degrees of freedom (“The Interpretation of Quantum Mechanics”, section 7.8).
But if we are going to engage with those scenarios anyway, then we should never have referred to them as “branches” in the first place, …
Well, that’s one of the problems of the MWI: how do we know when we should speak of branches? Decoherence works very well for all practical purposes but it is a continuous process so there isn’t a point in time where a single branch actually splits into two. How can we claim ontology here?
Thanks, I see we already had a similar argument in the past.
I think there’s a bit of motte and bailey going on with the MWI. The controversy and philosophical questions are about multiple branches / worlds / versions of persons being ontological units. When we try to make things rigorous, only the wave function of the universe remains as a coherent ontological concept. But if we don’t have a clear way from the latter to the former, we can’t really say clear things about the parts which are philosophically interesting.
So much the worse for the controversy and philosophical questions. If anything, the name is the problem. People get wrong ideas from it, and so I prefer to talk in terms of decoherence rather than “many worlds”. There’s only one world, it’s just more complex than it appears and decoherence gives part of an explanation for why it appears simpler than it is.
Unfortunately, what I would call the bailey is quite common on Lesswrong. It doesn’t take much digging to find quotes like this in the Sequences and beyond:
This is a shocking notion; it implies that all our twins in the other worlds— all the different versions of ourselves that are constantly split off, [...]
One doesn’t invoke the term “different branches” unless they are macroscopically different, and if they’re ever macroscopically different, then they will remain macroscopically different forever, thanks to entropy (and the related fact that macroscopic events leave countless little persistent traces in the environment). Even moreso if we’re talking about human observers, who form memories of what they’ve seen in the form of changes to the structure of their brains. Macroscopically different branches can’t “cancel” and more generally macroscopically different branches can’t interfere in a way that has any measurable effect.
(For any quantum observable O that’s relevant in practice, ⟨ψ|O|ϕ⟩≈0 if |ψ⟩ and |ϕ⟩ are macroscopically different—e.g. the geiger counter loudly clicked in |ψ⟩ but not |ϕ⟩.)
Solomonoff inductors are a bit of an odd case because they don’t & can’t exist in the universe. But leaving that aside (let’s say we’re implementing AIXItl or whatever):
Every time the computer makes an observation, we learn some stuff about the universe, and we also learn some indexical information about where we-in-particular are sitting within the universe. This has always been true, but it’s especially true about MWI because we will never stop getting indexical updates (unlike a deterministic universe where you can learn that you’re in a particular room on earth and then there’s no more indexical information to learn). In MWI, if we observe that a pixel is bright, then we have learned that we are in a branch of the wavefunction wherein the pixel is bright. There might or might not be other branches wherein the pixel is dark, but if there are, we now know that those branches are “not where I have found myself”, and we can ignore those branches accordingly. You can still have hypotheses, but they will incorporate born-rule indexical uncertainty about which branch I will find myself in in the future, on top of whatever other indexical uncertainty you have for other reasons.
Ah, but that’s the crux of the issue. They can. How should Wigner’s friend be performing inference?
Scott’s analysis seems fine to me, unless I missed something. He writes “Many-Worlders will yawn at this question” [in reference to Wigner’s friend]. Yes. I yawn. If Wigner is right outside the lab door, then Wigner is in fact in one of the branches (the same branch as his friend) even if Wigner happens to not yet know which one of them. If Wigner is on Alpha Centauri, then he is not yet in one of those two branches, and his friend is, and I don’t see any problem with that. And then a few years later he gets a message from his friend, and by that point Wigner is in one of those two branches, and when he reads the message he’ll know which one.
I’m reluctant to engage with extraordinarily contrived scenarios in which magical 2nd-law-of-thermodynamics-violating contraptions cause “branches” to interfere. But if we are going to engage with those scenarios anyway, then we should never have referred to them as “branches” in the first place, and also we should be extremely wary of applying normal intuitions in situations where the magical contraption is “scrambling people’s brains” as Scott puts it.
As a meta point, I might drop out of this conversation at any point (including maybe right now), gotta get back to work. :)
Agreed. Roland Omnes tries to calculate how big the measurement apparatus of Wigner needs to be in order to measure his friend and gets 10 to the power of 10E18 degrees of freedom (“The Interpretation of Quantum Mechanics”, section 7.8).
Well, that’s one of the problems of the MWI: how do we know when we should speak of branches? Decoherence works very well for all practical purposes but it is a continuous process so there isn’t a point in time where a single branch actually splits into two. How can we claim ontology here?
I don’t think it’s a problem—see discussion here & maybe also this one.
Thanks, I see we already had a similar argument in the past.
I think there’s a bit of motte and bailey going on with the MWI. The controversy and philosophical questions are about multiple branches / worlds / versions of persons being ontological units. When we try to make things rigorous, only the wave function of the universe remains as a coherent ontological concept. But if we don’t have a clear way from the latter to the former, we can’t really say clear things about the parts which are philosophically interesting.
So much the worse for the controversy and philosophical questions. If anything, the name is the problem. People get wrong ideas from it, and so I prefer to talk in terms of decoherence rather than “many worlds”. There’s only one world, it’s just more complex than it appears and decoherence gives part of an explanation for why it appears simpler than it is.
Unfortunately, what I would call the bailey is quite common on Lesswrong. It doesn’t take much digging to find quotes like this in the Sequences and beyond: