Say that there is some code which will run two instances of you, one where you see a blue light, and one where you see a green light. The code is run, and you see a blue light, and another you sees a green light. The you that sees a blue light gains indexical knowledge about which branch of the code they’re in. But there’s no need for the code to have a “reality” index parameter to allow them to gain that knowledge. You implicitly have a natural index already: the color of light you saw. I don’t see why someone living in a Many-Worlds universe wouldn’t be able to do the equivalent thing.
So I guess I would say that in some sense, once you’ve figured out the rules, measurements don’t give you any knowledge about the wave function, they just give you indexical knowledge.
The wave function is a fluid in configuration space that evolves over time. You need more theory than that to talk about discrete branches of it (configurations) evolving over time.
I agree that once you have this, you can say the knowledge gained is indexical.
I think it’s something like: Sometimes you find that the wavefunction |ψ⟩ is the sum of a discrete number of components |ψ⟩=|ψ1⟩+|ψ2⟩+⋯ , with the property that for any relevant observable A, ⟨ψi|A|ψj⟩≈0 for i≠j. (Here, “≈0” also includes things like “has a value that varies quasi-randomly and super-rapidly as a function of time and space, such that it averages to 0 for all intents and purposes”, and “relevant observable” likewise means “observable that might come up in practice, as opposed to artificial observables with quasi-random super-rapidly-varying spatial and time-dependence, etc.”).
When that situation comes up, if it comes up, you can start ignoring cross-terms, and calculate the time-evolution and other properties of the different |ψi⟩ as if they had nothing to do with each other, and that’s where you can use the term “branch” to talk about them.
There isn’t a sharp line for when the cross-terms are negligible enough to properly use the word “branch”, but there are exponential effects such that it’s very clearly appropriate in the real-world cases of interest.
You can derive “consistent histories” by talking about things like the probability amplitude for a person right now to have memories of seeing A and B and C all happening, or for the after-effects of events A and B and C to all be simultaneously present more generally. I think...
Thanks! To the extent that discrete branches can be identified this way, that solves the problem. This is pushing the limits of my knowledge of QM at this point so I’ll tag this as something to research further at a later point.
You might be interested in the work of Jess Riedel, whose research agenda is centered around finding a formal definition of wavefunction branches, e.g. https://arxiv.org/abs/1608.05377
Say that there is some code which will run two instances of you, one where you see a blue light, and one where you see a green light. The code is run, and you see a blue light, and another you sees a green light. The you that sees a blue light gains indexical knowledge about which branch of the code they’re in. But there’s no need for the code to have a “reality” index parameter to allow them to gain that knowledge. You implicitly have a natural index already: the color of light you saw. I don’t see why someone living in a Many-Worlds universe wouldn’t be able to do the equivalent thing.
So I guess I would say that in some sense, once you’ve figured out the rules, measurements don’t give you any knowledge about the wave function, they just give you indexical knowledge.
The wave function is a fluid in configuration space that evolves over time. You need more theory than that to talk about discrete branches of it (configurations) evolving over time.
I agree that once you have this, you can say the knowledge gained is indexical.
I think it’s something like: Sometimes you find that the wavefunction |ψ⟩ is the sum of a discrete number of components |ψ⟩=|ψ1⟩+|ψ2⟩+⋯ , with the property that for any relevant observable A, ⟨ψi|A|ψj⟩≈0 for i≠j. (Here, “≈0” also includes things like “has a value that varies quasi-randomly and super-rapidly as a function of time and space, such that it averages to 0 for all intents and purposes”, and “relevant observable” likewise means “observable that might come up in practice, as opposed to artificial observables with quasi-random super-rapidly-varying spatial and time-dependence, etc.”).
When that situation comes up, if it comes up, you can start ignoring cross-terms, and calculate the time-evolution and other properties of the different |ψi⟩ as if they had nothing to do with each other, and that’s where you can use the term “branch” to talk about them.
There isn’t a sharp line for when the cross-terms are negligible enough to properly use the word “branch”, but there are exponential effects such that it’s very clearly appropriate in the real-world cases of interest.
You can derive “consistent histories” by talking about things like the probability amplitude for a person right now to have memories of seeing A and B and C all happening, or for the after-effects of events A and B and C to all be simultaneously present more generally. I think...
Thanks! To the extent that discrete branches can be identified this way, that solves the problem. This is pushing the limits of my knowledge of QM at this point so I’ll tag this as something to research further at a later point.
You might be interested in the work of Jess Riedel, whose research agenda is centered around finding a formal definition of wavefunction branches, e.g. https://arxiv.org/abs/1608.05377