# This forum gives conflicting info on the HUP

atyy
Ah, now I think I see the source of confusion. One should distinguish two things:
1) SINGLE measurement, from which no information about probability distribution can be extracted (except that the obtained value has probability larger than one).
2) Statistical ENSEMBLE of similar measurements, from which the probability distribution can be extraced.

I was talking about the former, while it seems that you are talking about the latter. If I simultaneously measure position and momentum ONLY ONCE, I cannot extract any information about the joint probability distribution.

But then again, even in classical mechanics I can repeat many times the simultaneous measurement of position and momentum. From such a measurement I CAN extract the joint distribution. Moreover, by using the theory called classical STATISTICAL mechanics I can even predict or explain the joint distribution I measured. So your claim that "classical definitions for joint distribution don't exist" is certainly wrong.
My claim is correct, because it was for quantum mechanics.

What I don't understand is: what do mean by an "accurate" measurement? To define an accurate measurement in some sense, one needs a "correct" answer. In classical mechanics, one way to define a "correct" answer is that one correctly infers the value of the property that the particle had at a certain time. However, for joint measurements this definition of "correct" can't carry over to quantum mechanics, because the joint distribution of position and momentum doesn't exist in general.

Ken G
Gold Member
Satisfied?
I'm sorry, I don't see why you think that quote has the slightest relevance to anything that was said in our exchange. I know quite a bit about Smolin's ideas, you have not told me anything I didn't already know. I was pointing out a problem in his rhetorical device of saying that modern physics can determine whether it was Aristotle or Einstein that was right or wrong in regard to the relativity of space. Again, I can only tell you, that's just not how science works, and it is harmful to science to frame it that way. What actually happens is, scientists find insights that advance science, no one is ever right or wrong in any absolute sense. Truth in science is highly provisional, that is perhaps the main beauty of science-- it is constantly questioning and seeking knowledge. Science is not about what you know, it is about what you don't know. It seems my perspective is lost on you, but it doesn't matter, I was wrong to bring it up at all because it's not relevant to the thread and should be dropped anyway.

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atyy
Bumping this just in case Demystifier did not see my response in #101.

Ken G
Gold Member
If Demystifier doesn't take up that cause, I would offer that measurements in science are always axiomatic. There is nothing more basic than a measurement in empirical science, nothing that we use to check that we are doing measurements "accurately"-- other than a body of other measurements we already regard as accurate by experience. We do check precision, and if ten people get ten badly different answers, we label that measurement "imprecise" and drop it from our set of approved techniques. But it is problematic to define a measurement as accurate by saying it agrees with some theory (other than the most basic theories that we already regard as axiomatic).

If quantum mechanics were ever regarded as axiomatic, then the definition of an accurate measurement as one that mimics a projection would be appropriate. I believe that Demystifier's core stance is that all axiomatic approaches to measurement must be classical, so you will always need a better definition of a measurement than that the result agrees with quantum mechanics theory. After all, if you are looking for chinks in the armor of QM as it is currently postulated, you certainly can't have someone scratching their head and saying "what did I do wrong in my measurement, my answer did not come out like QM."

But there is a case where the Ozawa definition could be appropriate, which is when we are not regarding measurements as a test of QM, but rather, as a proxy for understanding what QM is predicting, a lens on the theory if you will. In the form of a gedankenexperiment, which is used to describe a theory not reality, it is fine to use Ozawa's approach, to see in effect what QM thinks a measurement is, rather than what we have axiomatized it to be.

Demystifier
What I don't understand is: what do mean by an "accurate" measurement?
To help me answer that question, can you quote where exactly did I say that a measurement is "accurate"?

atyy
To help me answer that question, can you quote where exactly did I say that a measurement is "accurate"?
It's implicit in the OP. If it's not there, then one can trivially measure all values simultaneously.

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Demystifier
My claim that one can simultaneously measure both position and momentum is also compatible with a modern view of quantum measurements based on POVM's (positive operator valued measures). The POVM measurements generalize the more traditional projective measurements.

There is no simultaneous eigenstate of both position and momentum, implying that there is no projector operator to a definite value of both position and momentum. Yet, coherent states can be used to construct a POVM corresponding to a generalized simultaneous measurement of both position and momentum.

For a recent brief pedagogic introduction to modern theory of quantum measurements see also
http://lanl.arxiv.org/abs/1406.5535
The author is the same guy who lead the team which first performed a weak measurement of Bohmian trajectories:
https://www.physicsforums.com/blog.php?b=3077 [Broken]

For an authoritative theoretical treatment see the book
A. Peres, Quantum Theory: Concepts and Methods,
especially Secs. 12-9 and 9-5.

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