The heisenburg uncertainty principle

[NanjoeBot]

I was reading about this, but I'm unclear on something. Does the Heisenberg principle arise due to limitations in technology? Or is it an absolute physical phenomena that can't be avoided no matter how advanced your measuring tools are?

 

[^_^physicist]

The uncertainty principle is fundamental. You can even derive the result by using the commutator relation: [x,p]=ih*2pi

 

[DrChinese]

I was reading about this, but I'm unclear on something. Does the Heisenberg principle arise due to limitations in technology? Or is it an absolute physical phenomena that can't be avoided no matter how advanced your measuring tools are?

Measurement accuracy has nothing to do with this fundamental phenomenon.

 

[tom.stoer]

The uncertainty principle applies to all self-adjoint, non-communiting operators A and B in any Hilbert space. So it is a mathematically sound result which can be applied to physics.

Beyond that it becomes subject to ontological interpretation:

If one interprets QM such that a physical system IS a state vector in a Hilbert space, than this quantum system has the property that the values of a and b ARE uncertain.

If one interprets QM such that the a state vector in a Hilbert space ENCODES OUR KNOWLEDGE regarding an ensemble of identical physical systems, than OUR KNOWLEDGE regarding the values of a and b APPEAR to be restricted by the uncertainty principle

In any case it has nothing to do with our inability to construct a better measuring device.

 

[Zhabka]

Isn't the uncertainty principle also inherent in the Fourier transformation used to create a particle via the superposition of waves? The more wavelengths used, the more certain the position but the less certain the momentum. Or at least that's just how I first learned it.

 

[tom.stoer]

You are right; it's inherent in Fourier transformation.

But this should not surprise you as the Fourier transformation is nothing else but a unitary operator mapping the L² Hilbertspace into itself. All what I am saying is that the uncertainty principle applies to all Hilbert spaces (not just L²) and to all operators A and B, not only to x and p which are related by the Fourier transformation.

Caveat: the details of this generalized uncertainty principle depend on the (value of the) commutator [A,B].

 

[tom.stoer]

For a derivation look at http://en.wikipedia.org/wiki/Uncertainty_principle

 

[dlgoff]

I really like ZapperZ's blog explanation on the http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html" .

 

[tom.stoer]

Good explanation, but still focussed on experiment.

I prefer to prove the uncertainty principle as a mathematical theorem and then apply it to an experiment. This avoids the misconception from the very beginning. Of course there is the drawback that one has to invest some time to understand (or believe in) the proof.

 

[sweet springs]

Hi. The paper at http://pra.aps.org/abstract/PRA/v67/i4/e042105 titled "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement" proposes new alternative uncertainty relation.
Regards.

 

[ThomasT]

I really like ZapperZ's blog explanation on the http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html" .

I like ZapperZ's explanation also. So, I ask, can we simply say that the uncertainty relation between, say, p and q, has to do with the stadarnd deviation of measurments of p, delta p, and the standard deviation of measurements of q, delta q, so that, given the assumption of a quantum of action, h, then the relationship between measurements on p and measurements on q will be, (delta p) (delta q) >= h?

Now, for those who say that this has nothing to do with measurement. That's absurd. Because the quantum theory is predicated on the assumption of the existence of a fundamental observable, the quantum of action. In fact, the quantum theory is ONLY about measurements, no more and no less. On what other basis would you develop a statistical probabilistic theory?

 

[tom.stoer]

Now, for those who say that this has nothing to do with measurement. That's absurd. Because the quantum theory is predicated on the assumption of the existence of a fundamental observable, the quantum of action. In fact, the quantum theory is ONLY about measurements, no more and no less. On what other basis would you develop a statistical probabilistic theory?

I do not agree!

The reason that quantum mechanics is based on observables (operators in Hilbert space) does not mean that it's about measurement only. The whole apparatus of standard quantum mechanics does not explain what this measurement really is, nor does the observable itself "observe" or "measure" something.

I would say that the concept or meaning of "measurement" has rarely been addressed within quantum mechanics. This changes somehow in the context of decoherence etc., but even ther it is not used in order to construct the theory or to give it a new axiomatic basis. For the latter one measurement as a process is totally irrelevant (all one says is that an obervable is an operator corresponding to some property that could be measured in principle, but nobody says how this could be done in practice).

What we see in measurements is of course that all quantum objects and observables respect the HUT. But we also know (e.g. from Bell) that it is not unreasonable to say that quantum mechanics says something about properties of quantum systems before they are measured! Bell's theorem forbids local hidden variables. This can be seen as an ontological statement of what quantum mechanics not is; it has something to with our knowledge about a specific quantum system (therefore its not fundamentally ontological), but it has also something to do with the character of quantum theory itself (and therefore it has an ontological meaning). Of course it is observed in experiments, but it is a deeper result about the whole concept of quantum mechanics.

We have to be careful not to start a philosophical discussion. The question is is the moon there even if nobody looks at it?. I would say yes, and I would therefore conclude that the moon has a certain orbit around the earth. In the same sense quantum systems have certain non-classical properties even before or w/o measurement.

 

[unusualname]

tom's view agrees pretty much with Heisenberg's own interpretation of his result, eg in his autobiography he states that the principle was inspired by einstein's remark that "it is the theory which decides what one can observe"

For an in depth overview including some historical details see

http://plato.stanford.edu/entries/qt-uncertainty/

 

[tom.stoer]

tom's view agrees pretty much with Heisenberg's own interpretation of his result, eg in his autobiography he states that the principle was inspired by einstein's remark that "it is the theory which decides what one can observe"

Flattering to read these two names in one sentence :-)

That was not really my intention. I was only addressing the fact that there is the common misconception that quantum mechanics is a theory that addresses measurement. It is true that this is how quantum mechanics is used - writing down the Schrödinger equation or something like that - do the calculation - confirm it by experiment". It is also true that Heisenberg, Einstein, Bohr et al. very bothered by things like measurement, being, knowledge etc. They used Gedankenexperimente to express their ideas. It has long been discussed if QM is about ontological entities (in a veiled sense) or about epistemology only. The fact that we cannot know something to exist (e.g. sharp values for x and p simultaneously in standard QM interpretation) has some people led to the conclusion that QM is about knowledge, information and/or measurement only. Whereas knowledge and information may be the correct interpretation, measurement is certainly NOT.

Looking at quantum theory today one has to say that thought- and Gedankenexperiments were interesting ideas, but never made sound as construction principles!

Neither Heisenberg nor Einstein made the step from the observable to the measurement as fundamental entity in QM (besides thought- and Gedankenexperiments). Looking at any problem in QM the role of the observables is rather clear from the very beginning, whereas the measurement process itself is never addressed. You can introduce observables as you like w/o ever explaining how to measure them. Nobody will care about it. It's always up the the experimentalist to design a clever apparatus that does the job, but there is no feedback loop for the construction or adjustment of the theory (even the MWI which was a major turn never talks about the measurement process itself).

 

[unusualname]

Yes, I think Heisenberg only produced his "thought experiments" to help give his interpretation some intuitive background (mainly in response to Schrodinger's discovery of a wave interpretation). If you follow the historical development (eg see Jagdesh Mehra's comprehensive essays in 'The Golden Age of Theoretical physics" or "The Historical Development of Quantum Theory") it's clear Heisenberg considered these trivial and unimportant arguments, but needed to convince others that Wave Mechanics was not a superior physical interpretation (Which it seemed might be the case for a year or two until the physical interpretations of the wave were abandoned)

 

[DevilsAvocado]

In fact, the quantum theory is ONLY about measurements, no more and no less. On what other basis would you develop a statistical probabilistic theory?

If that’s true, then maybe Bohr and the guys should have started with the unsolved http://en.wikipedia.org/wiki/Measurement_problem" ...?

[PLAIN]http://upload.wikimedia.org/wikipedia/en/thumb/b/b0/Observer-observed.gif/350px-Observer-observed.gif
Observer O measures the state of the quantum system S

 

[DevilsAvocado]

I really like ZapperZ's blog explanation on the http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html" .

Agree, and here’s a video showing exactly what happens in ZapperZ’s example:

Walter Lewin MIT – The Uncertainty Principle

https://www.youtube.com/watch?v=<object width="640" height="505">
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<param name="allowFullScreen" value="true"></param>
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</object>

 

[zonde]

I do not agree!

The reason that quantum mechanics is based on observables (operators in Hilbert space) does not mean that it's about measurement only. The whole apparatus of standard quantum mechanics does not explain what this measurement really is, nor does the observable itself "observe" or "measure" something.

I would say that the concept or meaning of "measurement" has rarely been addressed within quantum mechanics. This changes somehow in the context of decoherence etc., but even ther it is not used in order to construct the theory or to give it a new axiomatic basis. For the latter one measurement as a process is totally irrelevant (all one says is that an obervable is an operator corresponding to some property that could be measured in principle, but nobody says how this could be done in practice).

What we see in measurements is of course that all quantum objects and observables respect the HUT. But we also know (e.g. from Bell) that it is not unreasonable to say that quantum mechanics says something about properties of quantum systems before they are measured! Bell's theorem forbids local hidden variables. This can be seen as an ontological statement of what quantum mechanics not is; it has something to with our knowledge about a specific quantum system (therefore its not fundamentally ontological), but it has also something to do with the character of quantum theory itself (and therefore it has an ontological meaning). Of course it is observed in experiments, but it is a deeper result about the whole concept of quantum mechanics.

We have to be careful not to start a philosophical discussion. The question is is the moon there even if nobody looks at it?. I would say yes, and I would therefore conclude that the moon has a certain orbit around the earth. In the same sense quantum systems have certain non-classical properties even before or w/o measurement.

I would say it's reasonable to say that quantum mechanics is about measurement.
Can we say that QM describes particles? It does not seems so.
Can we say that QM describes measurement equipment? Not really.
But still QM predicts probabilities for outcomes of physical measurements so it describes physical things relevant to measurement.
So I would say that QM keeps track of things relevant to measurement irrespective of where they actually are. Therefore it's centered around measurement more than around anything else.

 

[DevilsAvocado]

@Anybody

In ZapperZ's blog explanation on the http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html" , he states:

However, physics involves the ability to make a dynamical model that allows us to predict when and where things are going to occur in the future. While classical mechanics does not prohibit us from making as accurate of a prediction as we want, QM does!

Is this really the whole story...? According to the http://en.wikipedia.org/wiki/3-body_problem" , we have "similar" problems in classical mechanics...

Can anybody explain the difference between HUP and the "classical uncertainty" in the Three-body problem?

 

[tom.stoer]

I would say it's reasonable to say that quantum mechanics is about measurement.
Can we say that QM describes particles? It does not seems so.
Can we say that QM describes measurement equipment? Not really.
But still QM predicts probabilities for outcomes of physical measurements so it describes physical things relevant to measurement.
So I would say that QM keeps track of things relevant to measurement irrespective of where they actually are. Therefore it's centered around measurement more than around anything else.

The logical conclusion "A is not B" and " A is not C" => "A is about C" is definately not valid.

It is an illusion to say "quantum mechanics is about measurement" as quantum mechanics is not able tell you what "measurement" really is. But quantum mechanics tells you in detail what a particle "is", a certain state characterized by certain observables in a specific Hilbert- or Fock space. Perhaps you don't like such an explanation of what a particle "is", but quantum mechanics is very clear about that - at least formally. But there is nothing in the formalism of quantum mechanics that say something about the measurement; measurement only comes in on the level of interpretation.

Instaed of measurement I would say quantum mechanics is more about "information presented by systems". It is by no means clear how to measure something experimentally which is available as information in principle. Quantum mechanics does not tell you how to relate observables to measurement.

In addition quantum mechanics is about something like "veiled reality" as Bernard d’Espagnat" calls it, about a kind of "restricted realism" or something like that. Quantum mechanics tells you something about "reality" - unfortunately mostly negatively as it explains which concepts do NOT apply to the quantum world; take Bell's theorem and Kochen-Specker as an example.

All this is enough reason for me to prefer a "negative ontological" interpretation of the HUT, instead of a purely phenomenological one. Quantum mechanics forbids certain measurements not because the experimental setup itself does not comply with quantum mechanics - it does - but because the properties you want to measure do NOT EXIST.

Look at Bell's theorem. What you want to measure (hidden local variables) is not a problem for the apparatus (the two devices are perfectly prepared and separated from each other and are ready to perform any measurement you like), it is instead the case that the system itself does not have the property you are asking for.

So again my conclusion is that the HUT has a "negative ontological root cause" valid even w/o any attempt to measure anything at all.

 

[DevilsAvocado]

... This can be seen as an ontological statement of what quantum mechanics not is; it has something to with our knowledge about a specific quantum system (therefore its not fundamentally ontological), but it has also something to do with the character of quantum theory itself (and therefore it has an ontological meaning). Of course it is observed in experiments, but it is a deeper result about the whole concept of quantum mechanics.

I would say it's reasonable to say that quantum mechanics is about measurement.

I agree with tom. Unambiguous communication was the scientific goal for Niels Bohr:

"What is it that we human beings ultimately depend on? We depend on words. We are suspended in language. Our task is to communicate experience and ideas to others. We must strive continually to extend the scope of our description, but in such a way that our messages do not thereby lose their objective or unambiguous character."

"It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature."

"Our task is not to penetrate into the essence of things, the meaning of which we don’t know anyway, but rather to develop concepts which allow us to talk in a productive way about phenomena in nature."

"There is no quantum world. There is only an abstract quantum physical description."​

 

[zonde]

It is an illusion to say "quantum mechanics is about measurement" as quantum mechanics is not able tell you what "measurement" really is. But quantum mechanics tells you in detail what a particle "is", a certain state characterized by certain observables in a specific Hilbert- or Fock space. Perhaps you don't like such an explanation of what a particle "is", but quantum mechanics is very clear about that - at least formally. But there is nothing in the formalism of quantum mechanics that say something about the measurement; measurement only comes in on the level of interpretation.

I find it easier to think about peculiarities of QM measurements if I consider measurement of phase.
From that perspective - can you tell what is the phase of particle if I don't specify in respect to what it is measured?

 

[tom.stoer]

I think we nearly agree, bu I am afraid that you didn't get my idea completely.

I do not say that quantum mechanics is "only about talking about phenomena". Neither is it "about the ontological reality of the quantum world". It's somehow in between.

Of course quantum mechanics' (physics') concerns are phenomena, information, predictions etc., but in addition quantum mechanics makes some negative statements about reality. It is by no means a naive theory in the sense of realism which explains "the existence of things", but it is neither a purely phenomenologic theory in the sense of empirism which denies the ability to talk about existence but restricts to "what we observe".

There are a few things quantum mechanics has to say about reality: quantum mechanics says clearly that nature is not locally realistic. This is a negative statement, the absence of a certain property, something that is not realized in nature. But it is definately not a purely phenomenological statement on the level of the measurement, or a statement regarding limited abilities of a measurement apparatus'. It is a ontological statement!

In the last couple of days I posted an example regarding a pub where you want to meet a friend. Suppose you go to that pub and your friend is not there. First of all this is a statement on the level of the phenomena (you do not see him). But quantum mechanics, especially Bell's theorem or the HUT, does more for you. It says that he/she is not there! So it is clear why you don't see him, because he is absent - not because something is wrong with you eyes. Local hidden variables are not "not measured" because of the measurement, but because the formalism rules them out.

Unfortunately all these statement are negative, they always talk about the absence of something, nevertheless they are ontologically, they are stements about "reality".

We should focus again on the HUT, not only on it's interpretation. All what I want to explain is why I think that explanations regarding the HUT based on limitations of measurements are missleading or at least incomplete.

Hope this is (or already was) clear.

A related philosophy joke: Two behaviorists have sex. One turns to the other and says, "That was good for you: how was it for me?"

 

[tom.stoer]

I find it easier to think about peculiarities of QM measurements if I consider measurement of phase.
From that perspective - can you tell what is the phase of particle if I don't specify in respect to what it is measured?

No, let's do it the other way round: Please tell me how to measure phase, and then try to construct the related observable from that information.

 

[DevilsAvocado]

quantum mechanics says clearly that nature is not locally realistic.

This will zonde never agree on!

A related philosophy joke: Two behaviorists have sex. One turns to the other and says, "That was good for you: how was it for me?"

Complementarily.

 

[DrChinese]

A related philosophy joke: Two behaviorists have sex. One turns to the other and says, "That was good for you: how was it for me?"

Heh, how about this:

 

[DevilsAvocado]

Heh, how about this:

Hehe, nice DrC!

 

[ThomasT]

@ tom.stoer, thanks for your reply (or replies, now, wrt your responses to some subsequent remarks by other contributors). I made the statements I did at least partly to elicit some interesting responses. This has been the case, so thanks to all contributors. I've never been satisfied that I had a fully comprehensive way of talking about the uncertainty relations to myself. Anyway, just a few comments and then I do hope that you and other more knowledgeable contributors, (and there are lots of people at PF capable of contributing to a clarification of this who haven't posted in this thread yet), will continue to synthesize your thoughts on this -- perhaps refining it to the very best explanation, and perhaps the most comprehensive (the definitive?) exposition of the meaning of the uncertainty relations ... ever. Or is that already out there and I just haven't read it (or understood it?) yet?

However, my statements and questions (that you replied to) weren't just meant to elicit interesting responses. They were also more or less sincere.

The OP, NanjoeBot, asked:

Does the Heisenberg principle arise due to limitations in technology? Or is it an absolute physical phenomena that can't be avoided no matter how advanced your measuring tools are?

I think that there is general agreement (and we, generally, proceed from the assumption) that the uncertainty relations aren't due to "limitations in technology" -- ie., that these relations are indeed an absolute physical instrumental phenomenon that "can't be avoided no matter how advanced your measuring tools are". This is the way I've learned to think about it. I also gather that this is the way that you've learned to think about it.

Then I asked myself: "does the archetypal uncertainty relation, (delta p) (delta q) >= h, involve quantities that are physically, and therefore unambiguously, defined only wrt certain instrumental operations/behaviors?; and I answered, to myself, yes.

So, I asked:

... can we simply say that the uncertainty relation between, say, p and q, has to do with the standard deviation of measurments of p, delta p, and the standard deviation of measurements of q, delta q, so that, given the assumption of a quantum of action, h, then the relationship between measurements on p and measurements on q will be, (delta p) (delta q) >= h?

And of course there's no disagreement with this -- but the implications, and the precise physical meaning, of this are not exactly clear.

Then I followed up with some, more provocative, statements and a question:

Now, for those who say that this has nothing to do with measurement. That's absurd. Because the quantum theory is predicated on the assumption of the existence of a fundamental observable, the quantum of action. In fact, the quantum theory is ONLY about measurements, no more and no less. On what other basis would you develop a statistical probabilistic theory?

Ok, at this time I think I should retract my assertion that "the quantum theory is ONLY about measurements, no more and no less" (apologies to Heisenberg). It certainly does seem that qm is, at least somewhat, about a deeper reality. And this is perhaps the crux of the difficulty that an ignorant layman such as myself has in trying to understand qm. Ie., what parts, exactly, of the quantum theory are about the behavior of entities in a deeper reality and what parts are exclusively about instrumental behaviors? I don't know, exactly, although I have some ideas about this. Is it just me, or are these hard questions? The text I learned (what I remember) a functional, probabilistic representation of qm from didn't really answer this (Bohm's 1950 text -- a Dover edition which, although purchased new, got so beat up from flipping through pages that it became viirtually unreadable, and anyway I no longer have it).

And the following diverges from the main theme of this thread.

------------------------------------------------------------------------------

I do not say that quantum mechanics is "only about talking about phenomena". Neither is it "about the ontological reality of the quantum world". It's somehow in between.

I think that this is a very revealing statement in the sense that it expresses the frustration of lots of physicists I've talked to about topics like this. Nevertheless, keeping in mind that qm is "somehow in between" in it's descriptive powers, perhaps you and other knowledgeable contributors can come up with something better than now exists in the PF's library regarding the uncertainty relations. Not to mention ZapperZ's blog of course -- and I do wish that he, the Zapper, whoever he is, would sort of tie things together, so to speak. (I think he might be working at some national laboratory or whatever and so must be carefull lest they eliminate him.).

There are a few things quantum mechanics has to say about reality: quantum mechanics says clearly that nature is not locally realistic.

How does it 'clearly' say that? You say above that qm is 'somehow in between' in what it has to say about reality, which would seem to suggest that qm doesn't say anything 'clearly' about 'reality'.

How about something like this instead: the statistical predictions of qm, and, by implication, the formalisms of qm, are incompatible with certain local realistic formalisms of certain experimental preparations. Now, what does that tell us about the nature of reality. Hard to say, eh? Most probably not that much I would conjecture.

This is a negative statement, the absence of a certain property, something that is not realized in nature. But it is definately not a purely phenomenological statement on the level of the measurement, or a statement regarding limited abilities of a measurement apparatus'. It is an ontological statement!

Ok, so how do we 'know' that nature isn't 'locally realistic'? Well, is it because we assume that the detection attributes in certain data streams correspond to certain properties in an underlying reality? But why should we assume that? No reason that I can think of. As you noted above, we don't really know what the qm formalism, or the detection attributes, or anything else have, exactly, to do with the deep reality of nature. We just don't know. Period -- at least for now.

 

[zonde]

I think we nearly agree, bu I am afraid that you didn't get my idea completely.

I think I get your idea. You think that negative statements are crucial part of QM.
But I don't agree with you. Negative statements have very limited value.
Real test for a theory is verification of it's positive predictions.

And it is not clear for me how negative statements can be regarded as ontological.

 

[zonde]

No, let's do it the other way round: Please tell me how to measure phase, and then try to construct the related observable from that information.

We have to have interference between two particles and then we should detect only the cases of positive interference (within some margins of allowed results).

 

[tom.stoer]

@ThomasT:

I would like to empasize what I said above, namely that QM makes NEGATIVE statements about reality in the sense that QM tells us something about the ABSENCE of certain QUALITIES (I call it qualities just to indicate that it's not just an attribute with a value) or in the sense that QM tells us that something will NOT work / will NOT happen / will NOT be observed IN PRINCIPLE.

This "in principle" is due to certain "limitations or absence qualities of nature", not because of limitation in the measuring process which is not addressed at all, neither in terms of the description of the devices, not in terms of using a theory of measurement in the QM principles.

In that sense these statements are not speculations "about a deeper reality beyond that"; they are theorems about this deeper reality - unfortunately NEGATIVE or NO-GO theorems.

It is a philosophical qestion if you accept a negative statement regarding "X not having quality A". I would say that it's reasonable to assume that the moon is there even if nobody is looking at it. If you accept this statement then you agree to something called realism (even if there is a variety of different "realisms" in philosophy). As soon as you have accepted "reality" it makes sense to ask about qualities of reality. Now quantum mechanics tells you something about these qualia in the negative sense; it says that "local realism" is absent in "reality" (Bell), it says that classical probability theory does not apply to "reality" (Kochen-Specker). Even my very first statement "that the moon is there even if nobody is looking at it" is below or beyond the phenomenological level.

You may call realism speculative, but if you deny it you have to explain where physical laws reside if not in this "reality". If you limit physics to its purely phenomenological domain you have no chance to find a home for your physical laws except for god or solipsism.

 

[tom.stoer]

You think that negative statements are crucial part of QM.
But I don't agree with you. Negative statements have very limited value.
Real test for a theory is verification of it's positive predictions.

Yes, I think that negative statements are crucial. They are crucial if one wants to explain what nature really IS. Unfortunately one has to accept that they are negative in the sense that in most cases they tell you what nature not is - what a pitty - but this is essentially what survives from realism.

But of course I agree with you that positive predictions and their verification have much more value in practice! QM has not been widely accepted because the HUT tells you what can't be achieve in principle, but because thousands of experiments tell you what can be achieved in practice.

But note that Popper rephrased "verification" into something like "failure of falsification". He said that a failed attempts of falsification do support a theory. This is exactly what Bell and the experimentalists did: explain an approach how to falsify QM and gather support for QM from these failed attempt.

And it is not clear for me how negative statements can be regarded as ontological.

I hope this became clear in the meantime.

 

[zonde]

Yes, I think that negative statements are crucial. They are crucial if one wants to explain what nature really IS. Unfortunately one has to accept that they are negative in the sense that in most cases they tell you what nature not is - what a pitty - but this is essentially what survives from realism.

I like the way it is said in wikipedia:
"Like all theorems applied in physics, a no-go theorem is only as good as its assumptions, including hidden implicit assumptions."
But what is our strategy in case of no-go theorems and in case of ordinary theorems making positive statements.
Well if we want to increase our predictive abilities we have to stick to assumptions of ordinary theorem.
However it is the other way around with no-go theorems. If we want to increase our predictive abilities we have to relax some assumptions of no-go theorem and look if it helps. In a sense we have to spread our research.

But note that Popper rephrased "verification" into something like "failure of falsification". He said that a failed attempts of falsification do support a theory. This is exactly what Bell and the experimentalists did: explain an approach how to falsify QM and gather support for QM from these failed attempt.

The problem with experimental verification is that any real experiment invoke number of additional assumptions to those in theory.
This is not a major problem for theory making positive statements. But it can be a real nightmare in case of no-go theorem.

In case of Bell theorem it seems quite clear that it rules out non-contextual hidden variables. This is where I see the promising direction where to go (in context of what I said about relaxing assumptions) - contextual hidden variables.
Therefore I cling to phase measurement as it is contextual and is not covered by Bell theorem.

 

[DrChinese]

And, by the way, I think you should pay attention to, and respect, Zonde's posts. He really is much more knowledgeable than both of us. And yes, I know, you're wondering how I know these things (like, eg., that billschnieder is a working scientist) -- well I just know these things and I'm not going to tell you how I know these things.

You ARE funni. That's exactly what I was thinking, and I am waiting in suspense for the answers...

 

[arkajad]

The mathematical formalism of quantum mechanics does not tell us that we can not measure precisely and simultaneously position and momentum. Quantum mechanics is simply not able to tell what will happen in such a case. Its mathematical formalism is inadequate for this. There are however extensions of the standard formalism that are more powerful and can describe processes that the standard textbook QM can not describe.