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## Neumaier Thermal Interpretation of QM, valid?

I'm concerned about one aspect of the "statistical interpretation". It appears that most people take it to be defined by Ballentine's 1970 article, which I haven't read myself. The reason why I'm concerned is that the quotes I've seen seem to contradict Bell's theorem. This is from section 4.4 of "Ensemble interpretations of quantum mechanics. A modern perspective", by Home and Whitaker. PDF.
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 $|\psi(\mathbf{r})|^2$ in 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”.
Reference [3] is of course Ballentine's article. What does this have to do with Bell? I don't have a rigorous argument, because I don't even know if there are Bell inequalities for position and momentum like the ones we've all seen for spin component operators, so I can only argue by analogy. What Ballentine said in 1970 about position and momentum can definitely not be said about spin components, because that statement would lead directly to a Bell inequality called the CHSH inequality (see pages 215, 216 in Isham's book for a derivation), which is violated by QM and by nature. This makes me believe that Ballentine's statements about position and momentum can't be correct either.

I suspect that Ballentine didn't know Bell's theorem (which was published in 1964) when he wrote the article in 1970, and that if he had, he wouldn't have said those things.

 Quote by unusualname But in any case, the minimal statistical interpretation says so little beyond what the basic mathematical shut up and calculate method says that I'm not sure it can be regarded as an interpretation at all.
The way I see it, the only thing that really differs between ensemble/statistical, "shut up and calculate", and a many-worlds interpretation that isn't crippled because someone insisted on removing the Born rule, is how they answer the question of whether QM describes what "actually happens" to the system at all times (even between state preparation and measurement).

Ensemble/Statistical: It doesn't.
MWI: It does.
"Shut up and calculate": I don't care.

Since the question can't be answered by experiment, "shut up and calculate" is the only one of these "interpretations" that doesn't say anything unscientific. (If anyone is wondering how I define "describes" and "actually happens" in this context, the answer is that I don't. I consider them primitives, not terms that need to be defined. I don't think they can be defined in a way that improves on the situation we have if we take them as primitives).

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 Quote by unusualname Non-interactive quantum zeno experiments for example. At least that what I think Omnes mentioned in his 1992 Rev Mod Phys article on Interpretations of QM: R Omnes - 'Consistent Interpretations of Quantum Mechanics' Rev Mod Phy Vol 64 No 2 1992 p339-383 http://rmp.aps.org/abstract/RMP/v64/i2/p339_1 (pdf 44 pages ~9mb) However, I can't find the relevant paragraph, so I might be thinking of another paper.
Ballentine published this paper:

Comment on ‘‘Quantum Zeno effect’’, Phys. Rev. A 43, 5165–5167 (1991)
 Quote by Ballentine (abstract) The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ‘‘collapse of the wave function,’’ but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ‘‘wave-function collapse.’’
It has 60 citations, but I haven't followed them through to see what if any

 But in any case, the minimal statistical interpretation says so little beyond what the basic mathematical shut up and calculate method says that I'm not sure it can be regarded as an interpretation at all.
It makes a connection between the maths and experiments, which is enough
to satisfy me.

 Quote by unusualname the final correct interpretation should by minimal set of ideas to correctly describe a linear probabilistically evolving universe, with a mathematical equation that exactly describes microscopic reality
"exactly describes microscopic reality" sounds like a different theory rather than
a mere interpretation.

Recognitions:
 Quote by Fredrik I suspect that Ballentine didn't know Bell's theorem (which was published in 1964) when he wrote the article in 1970, and that if he had, he wouldn't have said those things.
It might be wise to read Ballentine's 1970 paper (which does indeed have a section
on Bell's theorem), also the chapter in his textbook on the same subject, before
forming a firm view such things.

 Quote by strangerep Ballentine published this paper: Comment on ‘‘Quantum Zeno effect’’, Phys. Rev. A 43, 5165–5167 (1991) It has 60 citations, but I haven't followed them through to see what if any counter-comments are advanced. It makes a connection between the maths and experiments, which is enough to satisfy me. "exactly describes microscopic reality" sounds like a different theory rather than a mere interpretation.
I'm not sure how Ballentine's thinking has developed with the huge number of sophisticated experimental results in the last 20 years, but perhaps it is possible to make the ensemble interpretation consistent with everything so far discovered, since it doesn't say much beyond the basic mathematical model of QM. But it's terribly dull ;-) .

The point is, that the really correct interpretation will probably naturally explain microscopic reality, even if it has to be a fundamentally probabilistic equation. I'm not sure why you think that's a different theory, do you really think the correct (and simplest) theory of QG will still rely on a vague "interpretation"? Well, maybe you'll be correct, but I hope it is not like this.

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 Quote by strangerep It might be wise to read Ballentine's 1970 paper (which does indeed have a section on Bell's theorem), also the chapter in his textbook on the same subject, before forming a firm view such things.
OK, that proves that my guess about why he said those things was wrong. I have downloaded the 1970 article now. PDF. So far, I have only had time for a very quick look at the section on Bell's theorem. It doesn't seem to address my concern. I might read some more later, but I'm not sure I can really take the time to do that now.

I haven't read all the relevant parts of his book, but I've read some of it. He certainly didn't say anything similar to the statements that bother me now in the parts I've read. (I would definitely have remembered that). But he might have said it some part I haven't read, so I can't rule it out.

The statements that bother me say that it's possible that a particle has a well-defined position and a well-defined momentum at all times. It would imply that as far as position and momentum are concerned, QM probabilities are really just ignorance probabilities. Since this is definitely not the case with spin components, I find it very hard to believe that it can be true for position and momentum.

Aren't there any Bell inequalities for position and momentum that can rule that out? (This question is for everyone, not just Strangerep).

 Quote by JesseM So, I think it's misleading to call Neumaier's interpretion a "local" one,
Jesse, I note that Arnold hasn't yet responded here.

Maybe he did not recognize his misspelt name in the THREAD TITLE, etc?

It should be Neumaier.

PS: If it's not fixed, searches may miss it. Can you fix it?

Cheers, GW

Recognitions:
 Quote by Gordon Watson PS: If it's not fixed, searches may miss it. Can you fix it? Cheers, GW
Unfortunately no, only the moderators ("mentors") can change thread titles (being a "science advisor" doesn't mean any mod-like powers like editing other people's posts), for this forum it would have to be Doc Al or ZapperZ.

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 Quote by JesseM Unfortunately no, only the moderators ("mentors") can change thread titles (being a "science advisor" doesn't mean any mod-like powers like editing other people's posts), for this forum it would have to be Doc Al or ZapperZ.
Moderator's Note: Thread Title has been corrected

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