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
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