# Ballentine: Statistical Interpretation of QM

This is a continuation of discussions from another thread:

I believe it deserves its own thread instead of hijacking the other one.

"Ref 3" in what follows is this paper:

L.E. Ballentine, "The Statistical Interpretation of QM",
Rev Mod Phys, vol 42, no 4, 1970, p358.

[...] on p. 361 of ref. [3], [Ballentine] 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.
It's easy to get a misleading impression by quoting bits out of context.

The context of Ballentine's remark on p379 is that "it is possible to
extend the formalism of QM by the introduction of joint probability
distributions
for position and momentum (section 5 of his paper).
This demonstrates that 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."

It's also essential to understand Ballentine's points about the
distinction between state preparation and measurement. See p365,366.
"The statistical dispersion principle which follows from QM formalism
is a statement about the minimum dispersion possible in any state
preparation. This is distinct from errors of simultaneous measurements
of q and p one one system." This argument should be understood
in the context of Ballentine's discussion of his Fig 3.

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 ;-)
If "dull" means no accompanying fairy stories, then I'm ok with that. :-)

unusualname said:
Do you really think the correct (and simplest) theory of QG will still rely on
a vague "interpretation"?
theory of QG will not contradict experimental results. :-)

But you're kinda putting words in my mouth. I don't think the statistical
interpretation is "vague".

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strangerep,

what you (and Ballentine) would say about a single electron passing through the double-slit setup. Does this electron pass through one slit? Or through two slits at once?

Eugene.

what you (and Ballentine) would say about a single electron passing through the double-slit setup. Does this electron pass through one slit? Or through two slits at once?
I thought you might bring that up! :-)

I can't say what Prof Ballentine would say, since I don't have the necessary

One of the (other) reasons for starting this thread is that Ballentine still speaks
in terms of "particles", though in a strictly statistical context. In such a context,
theory contains.

Also, I had intended to pursue some of this in parallel with Arnold's thread
over on Independent Research forum -- since it's not entirely clear to me
where the overlap between Ballentine's statistical interpretation and his use
of the word "particle", and Arnold's interpretation with emphasis on fields, starts
and ends.

Interestingly, I just noticed that Ballentine mentions a quote of Mott about how
"students shouldn't be taught that [...elementary particles...] are not particles",
which seems to be at odds with the picture that Mott himself portrayed in his
alpha particle track analysis paper which we discussed in other threads.
But I need to read a bit more of both to form a better view about that.
Maybe I'll bring it up in Arnold's thread -- later. :-)

Sorry for the tricky question. As far as I can tell, the only non-controversial answer could be: "I don't know".

Eugene.