- #106
atyy
Science Advisor
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@kith and @Fredrik, a couple more thoughts on collapse in the Ensemble Interpretation. Above I outlined two ways that collapse may be avoided.
1) Couple to ancillae, and push all measurements to the end of time. However, this means that successive measurements are not allowed, which is fine. However, Ballentine does describe successive measurements. He even says that a filtering measurement is a method of state preparation, which implies successive measurements since one would presumably make a measurement on the state prepared by the previous measurement.
2) Use the Stinespring theorem, which shows that every completely positive map, including collapse, can be described as unitary evolution on a larger Hilbert space. I don't think this eliminates the need for a postulate equivalent to collapse, because we know that this map occurs only with some probability, given by the Born rule. Although the map can be described as unitary evolution, I don't see how its probability is obtained without the form of the Born rule that includes collapse (unless Many-Worlds works, but that's not Ballentine's Ensemble Interpretation).
1) Couple to ancillae, and push all measurements to the end of time. However, this means that successive measurements are not allowed, which is fine. However, Ballentine does describe successive measurements. He even says that a filtering measurement is a method of state preparation, which implies successive measurements since one would presumably make a measurement on the state prepared by the previous measurement.
2) Use the Stinespring theorem, which shows that every completely positive map, including collapse, can be described as unitary evolution on a larger Hilbert space. I don't think this eliminates the need for a postulate equivalent to collapse, because we know that this map occurs only with some probability, given by the Born rule. Although the map can be described as unitary evolution, I don't see how its probability is obtained without the form of the Born rule that includes collapse (unless Many-Worlds works, but that's not Ballentine's Ensemble Interpretation).
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