The heisenburg uncertainty principle

1. Aug 25, 2010

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 cant be avoided no matter how advanced your measuring tools are?

2. Aug 25, 2010

^_^physicist

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

3. Aug 26, 2010

DrChinese

Measurement accuracy has nothing to do with this fundamental phenomenon.

4. Aug 26, 2010

tom.stoer

The uncertanty 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.

5. Aug 26, 2010

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.

6. Aug 26, 2010

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].

7. Aug 26, 2010

tom.stoer

8. Aug 26, 2010

dlgoff

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

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9. Aug 26, 2010

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.

10. Aug 28, 2010

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.

11. Aug 29, 2010

ThomasT

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?

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12. Aug 29, 2010

tom.stoer

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.

Last edited: Aug 29, 2010
13. Aug 29, 2010

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/

14. Aug 30, 2010

tom.stoer

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).

15. Aug 30, 2010

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)

16. Aug 30, 2010

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

Observer O measures the state of the quantum system S

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17. Aug 30, 2010

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

Walter Lewin MIT – The Uncertainty Principle

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Last edited by a moderator: May 4, 2017
18. Aug 30, 2010

zonde

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.

19. Aug 30, 2010

@Anybody

In ZapperZ's blog explanation on the http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html" [Broken], he states:
Is this really the whole story...? According to the http://en.wikipedia.org/wiki/3-body_problem" [Broken], we have "similar" problems in classical mechanics...

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

Last edited by a moderator: May 4, 2017
20. Aug 30, 2010

tom.stoer

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

21. Aug 30, 2010

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."

22. Aug 30, 2010

zonde

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?

23. Aug 30, 2010

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 definitly 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?"

24. Aug 30, 2010

tom.stoer

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.

25. Aug 30, 2010