Does anyone actually use the term ensemble interpretation ?

[PTM19]

OK, that one isn't weird by itself, because if (for example) the hidden variables aren't observables, there's no conflict with Bell's theorem. But these statements look like they would very much be in conflict with Bell:

For example, he states [3, p. 361], “a momentum eigenstate. . . represents the ensemble whose members are single electrons each having the same momentum, but distributed uniformly over all positions”. Also on p. 361 of ref. [3], he says, “the Statistical Interpretation considers a particle to always be at some position in space, each position being realised with relative frequency u/i(r)~2in an ensemble of similarly prepared experiments”. Later [3, p. 379] he states, “there is no conflict with quantum theory in thinking of a particle as having definite (but, in general, unknown) values of both position and momentum”.​

I'm very surprised by this. Could it be that in 1970, when this was written, Ballentine still didn't understand Bell's theorem? (Bell's theorem was published in 1964).

From what I've read in Bohm interpretation both momentum and position of a particle are precisely defined at all times, we just cannot *know* both of them at the same time for practical reasons, since Bohm interpretation agrees with Bell I think the statement you quote is fine.

As for ensemble interpretation (my personal favorite (without PIV) since it doesn't postulate anything beside what can be directly verified by experiments) as was stated the main difference from CI is that according to ensemble QM cannot say anything about individual events and is only applicable to ensembles. And yes it is open to hidden variables (which I also think is the way to go - the next successful theory of matter will be based on contextual hidden variables ;)

 

[Truecrimson]

From what I've read in Bohm interpretation both momentum and position of a particle are precisely defined at all times, we just cannot *know* both of them at the same time for practical reasons, since Bohm interpretation agrees with Bell I think the statement you quote is fine.

I think Bohm formulation agrees with Bell's test because it's nonlocal.

What surprises me in Ballentine's book is that he thinks that the violation of Bell's inequality rules out only locality, due to Stapp's analysis.