I agree that the question “how many worlds are there” doesn’t have a well-defined answer in the MWI. I disagree that it is a meaningless question.
From the bird’s-eye view, the ontology of the MWI seems pretty clear: the universal wavefunction is happily evolving (or is it?). From the frog’s-eye view, the ontology is less clear. The usual account of an experiment goes like this:
The system and the observer come together and interact
This leads to entanglement and decoherence in a certain basis
In the final state, we have a branch for each measurement outcome. i.e. there are now multiple versions of the observer
This seems to suggest a nice ontology: first there’s one observer, then the universe splits and afterwards we have a certain number of versions of the observer. I think questions like “When does the split happen?” and “How many versions?” are important because they would have well-defined answers if the nice ontology was tenable.
Unfortunately it isn’t, so the ontology is muddled. We have to use terms like “approximately zero” and “for all practical purposes” which takes us most of the way back to give the person who determines which approximations are appropriate and what is practical—aka the observer—an important part in the whole affair.
The ontology doesn’t feel muddled to me, although it does feel… not very quantum? Like a thing that seems to be happening with collapse postulates is that it takes seriously the “everything should be quantized” approach, and so insists on ending up with one world (or discrete numbers of worlds). MWI instead seems to think that wavefunctions, while having quantized bases, are themselves complex-valued objects, and so there doesn’t need to be a discrete and transitive sense of whether two things are ‘in the same branch’, and instead it seems fine to have a continuous level of coherence between things (which, at the macro-scale, ends up looking like being in a ‘definite branch’).
[I don’t think I’ve ever seen collapse described as “motivated by everything being quantum” instead of “motivated by thinking that only what you can see exists”, and so quite plausibly this will fall apart or I’ll end up thinking it’s silly or it’s already been dismissed for whatever reason. But somehow this does seem like a lens where collapse is doing the right sort of extrapolating principles where MWI is just blindly doing what made sense elsewhere. On net, I still think wavefunctions are continuous, and so it makes sense for worlds to be continuous too.]
Like, I think it makes more sense to think of MWI as “first many, then even more many,” at which point questions of “when does the split happen?” feel less interesting, because the original state is no longer as special. When I think of the MWI story of radioactive decay, for example, at every timestep you get two worlds, one where the particle decayed at that moment and one where it held together, and as far as we can tell if time is quantized, it must have very short steps, and so this is very quickly a very large number of worlds. If time isn’t quantized, then this has to be spread across continuous space, and so thinking of there being a countable number of worlds is right out.
I think it makes more sense to think of MWI as “first many, then even more many,” at which point questions of “when does the split happen?” feel less interesting, because the original state is no longer as special. [...] If time isn’t quantized, then this has to be spread across continuous space, and so thinking of there being a countable number of worlds is right out.
What I called the “nice ontology” isn’t so much about the number of worlds or even countability but about whether the worlds are well-defined. The MWI gives up a unique reality for things. The desirable feature of the “nice ontology” is that the theory tells us what a “version” of a thing is. As we all seem to agree, the MWI doesn’t do this.
If it doesn’t do this, what’s the justification for speaking of different versions in the first place? I think pure MWI makes only sense as “first one, then one”. After all, there’s just the universal wave function evolving and pure MWI doesn’t give us any reason to take a part of this wavefunction and say there are many versions of this.
I agree that the question “how many worlds are there” doesn’t have a well-defined answer in the MWI. I disagree that it is a meaningless question.
From the bird’s-eye view, the ontology of the MWI seems pretty clear: the universal wavefunction is happily evolving (or is it?). From the frog’s-eye view, the ontology is less clear. The usual account of an experiment goes like this:
The system and the observer come together and interact
This leads to entanglement and decoherence in a certain basis
In the final state, we have a branch for each measurement outcome. i.e. there are now multiple versions of the observer
This seems to suggest a nice ontology: first there’s one observer, then the universe splits and afterwards we have a certain number of versions of the observer. I think questions like “When does the split happen?” and “How many versions?” are important because they would have well-defined answers if the nice ontology was tenable.
Unfortunately it isn’t, so the ontology is muddled. We have to use terms like “approximately zero” and “for all practical purposes” which takes us most of the way back to give the person who determines which approximations are appropriate and what is practical—aka the observer—an important part in the whole affair.
The ontology doesn’t feel muddled to me, although it does feel… not very quantum? Like a thing that seems to be happening with collapse postulates is that it takes seriously the “everything should be quantized” approach, and so insists on ending up with one world (or discrete numbers of worlds). MWI instead seems to think that wavefunctions, while having quantized bases, are themselves complex-valued objects, and so there doesn’t need to be a discrete and transitive sense of whether two things are ‘in the same branch’, and instead it seems fine to have a continuous level of coherence between things (which, at the macro-scale, ends up looking like being in a ‘definite branch’).
[I don’t think I’ve ever seen collapse described as “motivated by everything being quantum” instead of “motivated by thinking that only what you can see exists”, and so quite plausibly this will fall apart or I’ll end up thinking it’s silly or it’s already been dismissed for whatever reason. But somehow this does seem like a lens where collapse is doing the right sort of extrapolating principles where MWI is just blindly doing what made sense elsewhere. On net, I still think wavefunctions are continuous, and so it makes sense for worlds to be continuous too.]
Like, I think it makes more sense to think of MWI as “first many, then even more many,” at which point questions of “when does the split happen?” feel less interesting, because the original state is no longer as special. When I think of the MWI story of radioactive decay, for example, at every timestep you get two worlds, one where the particle decayed at that moment and one where it held together, and as far as we can tell if time is quantized, it must have very short steps, and so this is very quickly a very large number of worlds. If time isn’t quantized, then this has to be spread across continuous space, and so thinking of there being a countable number of worlds is right out.
What I called the “nice ontology” isn’t so much about the number of worlds or even countability but about whether the worlds are well-defined. The MWI gives up a unique reality for things. The desirable feature of the “nice ontology” is that the theory tells us what a “version” of a thing is. As we all seem to agree, the MWI doesn’t do this.
If it doesn’t do this, what’s the justification for speaking of different versions in the first place? I think pure MWI makes only sense as “first one, then one”. After all, there’s just the universal wave function evolving and pure MWI doesn’t give us any reason to take a part of this wavefunction and say there are many versions of this.