Quantum interpretations and indistinguishable elementary particles

[PeterDonis]

elementary particles are identical. The indistinguishability is a consequence of that.

Yes. Nobody is disputing that. But, as I've already pointed out, this fact has nothing to do with ensemble interpretations vs. interpreting the quantum state as describing individual systems.

It starts to look now that by interpreting a physical system as an ensemble the concept of identical particles
got incorporated into Ballentine.

Can you give a specific quote from Ballentine that supports this claim?

This concept may be missing in other interpretations. Or how do other interpretations reckon with the concept of identical particles?

Um, by using the same basic math of QM that deals with it? That's how QM models indistinguishability of identical particles: by how wave functions for systems consisting of multiple identical/indistinguishable particles are constructed. What those wave functions represent according to a specific interpretation--whether they represent an ensemble or an individual quantum system--does not change how the wave functions are constructed at all. So there is no need for different interpretations to "reckon with" indistinguishability separately. It's already reckoned with in the basic math of QM that all interpretations use.

The original question could even be rephrased that way.

Rephrasing the question doesn't help any. The response is still the same. See above.

 

[PeterDonis]

By describing it as an individual physical system, it is being overlooked that every such physical system is like any other such physical system.

You still don't appear to grasp that "an individual physical system" in QM is not the same thing as an individual elementary particle. Please go back and read my posts #8 and #19 again, carefully. The supposed issue you are claiming here simply does not exist.

 

[PeterDonis]

the two particles can't even be distinguished by their locations – or rather, by the probabilities of their being found at various locations

To clarify a point that might be confusing here, in the light of what I said in post #8 earlier in this thread: if I have a single electron in a Penning trap, and I just let it sit there, I can "distinguish" it from all other electrons by saying it's the electron in that Penning trap.

But as soon as I try to do something that involves more than one electron, like put a second electron into the trap, or release two electrons from two different traps and put them through some kind of experiment and then try to put them back, I can no longer say which of the two electrons I end up with came from which place at the start. If I put a second electron into the trap, for example, I can no longer say which of the two electrons in the trap was already there and which was the one I put in. And the wave function I write down for the two-electron system in the trap will reflect that. And, as I've said, that fact is independent of any choice of QM interpretation: all interpretations will use the same wave function, constructed the same way, for the two-electron system. They just will say different things about what that wave function "means" over and above the predictions it allows us to make.