Experimental Verifications of the UPs?

[nonequilibrium]

Hello,

I'd differentiate between two different UPs:

1) The one talking about the standard deviation and which is in essence a statistical UP only appearing when comparing N identically prepared measurements;

2) The historical one talking about experimental errors and thus supposedly applicable to one measurement;

Whilst (1) has been long proven, (2) seems to stay at a more heuristic level and is often regarded as a misinterpretation of (1). Nonetheless (2) is of great historical importance as it was this version of the UP that was discussed in the famous Bohr-Einstein debate. And as far as I know, despite being unproven, I haven't seen (2) being disproven either.

So I was wondering: what's the experimental status of (1) and (2)?

 

[Vanadium 50]

There is no #2.

I can take a single particle and measure conjugate variables as accurately as I like.

 

[Ken G]

But isn't #2 really about the simultaneous knowledge we can have of a single particle? In other words, #1 talks about variances in a collection of measurements, so is very concrete and demonstrable, but #2 talks about what we can know, which requires more in the way of an information model.

 

[nonequilibrium]

There is no #2.

Then what was the whole Bohr-Einstein debate about? Just meaningless to you?

But isn't #2 really about the simultaneous knowledge we can have of a single particle? In other words, #1 talks about variances in a collection of measurements, so is very concrete and demonstrable, but #2 talks about what we can know, which requires more in the way of an information model.

I understand your first sentence and I think it's a good point. I'm not sure what you're saying in your last sentence: are you implying that demonstrating/refuting it experimentally is not initially a well-defined action due to the fact that #2 needs a way to know what is correct information and what not?

 

[Ken G]

I understand your first sentence and I think it's a good point. I'm not sure what you're saying in your last sentence: are you implying that demonstrating/refuting it experimentally is not initially a well-defined action due to the fact that #2 needs a way to know what is correct information and what not?

What I mean is, if I claim the variances of complementary observables in an ensemble satisfy some relation, I can then do split the ensemble in half, do one type of measurement on one half and another type on the other half, and see if the variances obey the principle. So that's easy enough to check. But if I cull out a single particle, and say that my knowledge about that particle satisfies some kind of UP, I cannot demonstrate that fact by doing measurements on that particle directly, I also have to have some way of asserting the connection between what my knowledge is, and what is intrinsically true about that particle. I believe that was the core of the debate-- Einstein asserted there was a difference between what I can say about a particle, and what is actually true about a particle, and Bohr said that physics is all about what we can say, so there is no difference.

 

[nonequilibrium]

I believe that was the core of the debate-- Einstein asserted there was a difference between what I can say about a particle, and what is actually true about a particle, and Bohr said that physics is all about what we can say, so there is no difference.

Hm, I won't pretend I fully understand that yet, but I see what new direction that turns into, one I had missed, apparently. It sounds interesting. Can you refer me to a source that talks about that view? (preferably not something big like a book, more the size of a paper)

 

[Ken G]

Often a good place to start for an overview is good old Wikipedia:
http://en.wikipedia.org/wiki/Bohr–Einstein_debates

 

[nonequilibrium]

I had read that already, I don't think it contains your viewpoint.

 

[Vanadium 50]

Then what was the whole Bohr-Einstein debate about? Just meaningless to you?

There is nothing in QM that says you cannot measure x and p, or any two conjugate variables with arbitrary precision. There never was. You only get an uncertainty relation when discussing multiple measurements, or better still, when discussing the preparation of a state that will be measured multiple times.

As far as "meaningless to you", I don't understand why people who don't understand quantum mechanics get so snippy to people who do.

 

[nonequilibrium]

I didn't mean it as snippy, but I blame the unpersonal aspect of the internet for that. It's easy to misread somebody's intent.

I meant it as a genuine question: to me it seems as though the Bohr-Einstein debate was about something in the direction of #2 and certainly not about #1. Do you disagree with this statement, or do you agree and just say that at the time Bohr and Einstein were confused about what the essence was? (that last part is a rephrasal of what I meant with "just meaningless to you?")

 

[Ken G]

I had read that already, I don't think it contains your viewpoint.

Let me clarify my statement by inserting the bracketed phrases: "I believe that was the core of the debate-- Einstein asserted there was a difference between what I can say about a particle [using the language of quantum mechanics, our current best language for talking about particles], and what is actually true about a particle, and Bohr said that physics [i.e., quantum mechanics] is all about what we can say, so there is no difference."
The Wiki link describes two thought experiments that Einstein suggested that could, in principle, establish truths about particles that quantum mechanics said were fundamentally undetermined. (Einstein didn't buy the uncertainty principle as a fundamental truth, he felt the real truth could not have an uncertainty principle but that it was an artifact of limitations in quantum mechanics. Bohr argued that the limitations of quantum mechanics were limitations of reality itself.) That's what I meant that Einstein felt there was a difference between the actual truth about particles, and what we could say about them based on applying quantum mechanics (our current best theory for predicting behavior). Each time, Bohr stymied Einstein's argument, by showing that even in principle, the experiments Einstein suggested did not establish those truths about the particles at all-- the truths that could be established were the same as truths that could be framed in the language of quantum mechanics. In other words, Bohr argued that the language of quantum mechanics gave us as complete a description of the objects as was possible even in principle, whereas Einstein hoped for a gulf between what quantum mechanics could say and what could be true in principle.

Since we are talking about the UP in the language of what is possible to know about a single particle, it falls under the heading of your #2. I don't think Einstein would have had any problem with a UP of type #1, such that ensembles show variances that obey some rule, because quantum mechanics quite demonstrably got that right. He merely wanted the truth about the particles, even individual ones, to be something different than how quantum mechanics frames it.

 

[ThomasT]

Then what was the whole Bohr-Einstein debate about?

It was about realism vs instrumentalism. Einstein wanted a 'realistic' theory of the deep reality underlying instrumental behavior based on inferences from that instrumental behavior. Bohr and Heisenberg argued that that was a problematic approach to theory-making because the only unambiguous reality is the reality of observed and reproducible instrumental behavior.

The formal uncertainty relations follow from the quantum hypothesis (the assumption of a fundamental quantum of action) and the limitations of the wave and particle descriptions. The # (1) UP in the OP is the experimental meaning of this.

Just my two cents. Refer to Ken G, Vanadium 50 or other more knowledgeable contributors for elaboration, as well as Heisenberg's "The Physical Principles of the Quantum Theory".