There are three conventional explanations. 1) The systems were different all way long, but in the beginning the difference was invisible for us (hidden parameters). 2) The difference emerged from a non-deterministic process before or during the measurement (collapse). [...]
Actually, that’s the distinction I missed! The notion of “collapse” specifically refers to a non-deterministic process, not to a deterministic process that would at some point reveal the previously existing hidden variables.
I suggest fourth point of view: Don’t ask in what state the system is, this is meaningless. Ask only what measurement outcomes are possible, given the outcomes we had from the already performed measurements. If you do that, there is no paradox to solve.
That would basically be the “ensemble interpretation,” right? The theory tells you the probability distribution of outcomes, which you’ll see if you repeat the experiment prepared the same way a bunch of times (frequentism!), and that’s all there is to it. I do have a lot of sympathy for that view, as you might guess from the recent discussion of subjective probabilities, though I cannot say that my superficial understanding of QM gives me much confidence in any views I might hold about it.
The theory tells you the probability distribution of outcomes, which you’ll see if you repeat the experiment prepared the same way a bunch of times (frequentism!), and that’s all there is to it.
Well, the quantum probabilities are certainly frequentist. However, I don’t suppose strict Bayesians deny that there are probabilities with frequentist interpretation. I am also not sure about the label ensemble interpretation. It seems that its proponents somehow deny the validity of QM for small, non-ensemblish systems, which is a position I don’t subscribe to. After all, both collapse and many-world interpretations are no more Bayesian and no less frequentist than the ensemble one. The hidden parameters are deterministic, but have their own well known problems.
As for the frequentist-Bayes controversy, although I am probably more than you sympathetic to the Bayesian position, I have some sympathy for frequentism. I think both interpretation can coexist, with different sensible meanings of “probability”.
prase:
Actually, that’s the distinction I missed! The notion of “collapse” specifically refers to a non-deterministic process, not to a deterministic process that would at some point reveal the previously existing hidden variables.
That would basically be the “ensemble interpretation,” right? The theory tells you the probability distribution of outcomes, which you’ll see if you repeat the experiment prepared the same way a bunch of times (frequentism!), and that’s all there is to it. I do have a lot of sympathy for that view, as you might guess from the recent discussion of subjective probabilities, though I cannot say that my superficial understanding of QM gives me much confidence in any views I might hold about it.
Well, the quantum probabilities are certainly frequentist. However, I don’t suppose strict Bayesians deny that there are probabilities with frequentist interpretation. I am also not sure about the label ensemble interpretation. It seems that its proponents somehow deny the validity of QM for small, non-ensemblish systems, which is a position I don’t subscribe to. After all, both collapse and many-world interpretations are no more Bayesian and no less frequentist than the ensemble one. The hidden parameters are deterministic, but have their own well known problems.
As for the frequentist-Bayes controversy, although I am probably more than you sympathetic to the Bayesian position, I have some sympathy for frequentism. I think both interpretation can coexist, with different sensible meanings of “probability”.