# Heisenberg uncertainty - uncertainty about its meaning

1. Mar 5, 2009

### studious

HUP states that "certain physical quantities, like the position and momentum, cannot both have precise values at the same time. The narrower the probability distribution for one, the wider it is for the other." (Wikipedia)

I am not a physicist, but I have been pondering this question:
In this particular case, where we are concerned about position and momentum, does HUP mean that humans can not possibly find out precise values for position and momentum, or that the values themselves don't even exist (or "exist as a continuum" whatever that means)?

I have a particle it has some momentum and some position at some particular time. I may not/can't know both those values, but they do exist?... the particle can not be without one of momentum or position, right?

A physics students has been trying to convince me that at a particular time, the two pieces of "information" (a particle's position or momentum) don't even exist (much less humans being able find out both, which HUP is concerned with????).

(In fact, the Wikipedia page itself says that "position and momentum, cannot both have precise values at the same time." Does that mean the values don't even exist or that humans can't KNOW them precisely... if the second... why the HELL IS THERE the word 'cannot' in that Wikipedia statement?)

2. Mar 5, 2009

### Staff: Mentor

We don't know the answer to this question. The mathematics of QM makes predictions for what we will find the momentum and position of the particle to be, when we observe/measure it. It does not address the question, what the position and momentum "really are" before we measure them. This is the subject of interpretations of QM, of which there are several. There is no general agreement on which one is "correct," and there is (as yet) no way to distinguish among them by experiment, even in principle. So people argue about it a lot.

3. Mar 5, 2009

### alxm

Well, they exist in the sense that any particle will have those properties. But they haven't assumed a value before it's measured. The definition of 'measure' is narrow here. Any interaction that can, if only in theory, provide that information, counts as a 'measurement'. It's not inaccessible only to humans. It's truly not possible to measure.

This doesn't mean that all values are equally likely though. Or that these values are unknowable. It means that for a single particle, you cannot predict the exact result of a single measurement. But you can know the statistical average of many measurements, and the likelihood of finding a deviation by any given amount from that value.

The big 'weirdness' here is that we're accustomed to such statistical things as coming from our own not-knowing-about-it. I.e. if you pick a random card from a deck, there's a fifty-fifty chance of getting red or black. This is just because you don't have knowledge of the card - but the card itself was always either red or black.

In quantum mechanics, it simply did not have a value until you measured it. The card itself was fifty-fifty! (at least in the most common interpretations)

4. Mar 6, 2009

### studious

Hmm... the analogies seemed very interesting, but I'm still confused.

1. Does every particle (wave or whatever it is) have properties like momentum and position at every instance regardless of human "measurability"? (is this the question which is up to debate according to jtbell's reply?)

2. Does the actual act of measuring properties like position and momentum have any effect on their values at an instance in time? (take off from the card analogy of alxm)

3. Extension of previous question. Can there be >1 values for either position or momentum at any particular instance (e.g. two conflicting answers to the same question... two positions at the same time, etc.)? If yes and if we regard position or momentum as functions, then they can not be single-variable functions... what can they be seen as?

5. Mar 6, 2009

### DrChinese

jtbell has provided an accurate answer: we actually do not know. This leaves you in a position to select from several different interpretations which provide slightly different answers to this question. However, before you come to a conclusion, you need to know about some key papers and experiments relating to this subject. Try reading up on the EPR Paradox (which was an attempt to circumvent the HUP); Bell's Theorem; and the experiments of Alain Aspect et al (which show more clearly that the HUP is fundamental and does not relate to experimental limits).

Specifically: 2 "entangled" particles are essentially clones of each other. So you would think that you could beat the HUP by checking the position of one and the momentum of the other - since they are clones and should have identical values. Turns out that even in this situation, measuring one wreaks your ability to get a precise read on the other in such a way as to beat the HUP.

The lesson is: don't think of the HUP as an experimental phenomenon. It is deeper than that. But we don't understand why that is the case.

6. Mar 9, 2009

### \$tefan

Heisenberg uncertainty is caused by photons hitting elemental particles, so just looking at the particle will change it's position. Thats why you cannot determine its place and speed. Or is this a wrong summary of Heisenberg uncertainty?

7. Mar 9, 2009

### malawi_glenn

well, yes, since then there is no intrinsic indeterminism of the state, only experimental resolution. When one derives the HUP, only the non-vanishing commutator of P and X observables is used.

The 'disturbing the system' analogy is for classical, newtonial mechanical, systems only.

8. Mar 9, 2009

### WaveJumper

The 'meaning' of the HUP and why it's there at all, has more to do with philosophy than physics. The HUP is a limitation that prevents us from digging much deeper into the quantum world.

9. Mar 10, 2009

### dpk

actually particle and wave both have momentum & position but we canot find mathematically

10. Mar 10, 2009

### DrChinese

Welcome to PhysicsForums, dpk!

Your viewpoint is considered an acceptable interpretation of QM, but is not generally accepted as a fact. Other acceptable interpretations deny that particles/waves have well-defined attributes at all times.

11. Mar 11, 2009

### mn4j

Usually, a clear understanding of uncertainty principles is muddied by wanderings in to the realm of interpretations of QM or philosophy. However, it is a very simple principle, not limited to Quantum systems or to position and momentum for that matter.

The uncertainty between the two comes from the way they are defined. One is based directly on a variable, while the other is based on the derivative of the variable. For every two operators for which one operates on a variable and the other on the derivative of the variable, you will have an uncertainty relationship. Position and momentum are just one example.

In classical wave mechanics, you have uncertainty between
- Wavelength and Position
- Frequency and time ( given ONLY a very short pulse in time, the frequency will be very uncertain and vice versa)

Another example, consider a soccer ball moving through air. If you are presented ONLY with a snapshot of the scene at a precise point in time, you will only be able to give a precise position of the ball, not it's momentum. This is because, by definition, you need more than one position to calculate the momentum. In other words, the momentum is based on $$\Delta{x}$$

NO soccer ball has a well defined momentum at all positions. This says nothing about the soccer ball, but about the ACTUAL meaning of momentum and position. Momentum by definition must cover a range of positions. This is where the uncertainty comes in. It has nothing to do with Quantum mechanics at all.

The uncertainty principle is not about metaphysics or what can or can not be measured. It's simply derived from the mathematical definition of the terms or operators, in the same way as when we say there is uncertainty between an ocean and a water molecule. In one case the definition implies a multitude of the other, except in the case of position and momentum, one implies the differential of the other with respect to a common variable.

12. Mar 11, 2009

### DrChinese

This is demonstrably wrong. Experiments on soccer balls will NOT reveal the HUP as your description implies. This is a quantum phenomenon and you must be looking a quantum-size objects to see it. Many well-documented quantum spin experiments - in which particle characteristics can be observed without disturbing them in any way - demonstrate the non-classical nature of the HUP.

It would really make more sense if you would simply denote your personal opinions - especially the misleading ones - as such. That way the OP and other readers can judge the value of your post for themselves.

13. Mar 11, 2009

### Naty1

That is also not correct... the correct formulation: Robertson–Schrödinger relation
at
http://en.wikipedia.org/wiki/Uncertainty_principle#Robertson.E2.80.93Schr.C3.B6dinger_relation

which leads to a specific list of uncertainty relations:(like position, momentum)

http://en.wikipedia.org/wiki/Uncertainty_principle#Other_uncertainty_principles

I hadn't seen that list before....

14. Mar 11, 2009

### mn4j

I think you should check your facts before you speak:

If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound. (Heisenberg 1930, p. 15)

These reciprocal uncertainty relations were given in a recent paper of Heisenberg as the expression of the statistical element which, due to the feature of discontinuity implied in the quantum postulate, characterizes any interpretation of observations by means of classical concepts. It must be remembered, however, that the uncertainty in question is not simply a consequence of a discontinuous change of energy and momentum say during an interaction between radiation and material particles employed in measuring the space-time coordinates of the individuals. According to the above considerations the question is rather that of the impossibility of defining rigourously such a change when the space-time coordination of the individuals is also considered. (Bohr, 1985 p. 93)

15. Mar 11, 2009

### mn4j

Apparently, you did not read the derivation section of the link you posted where it says:
When linear operators A and B act on a function ψ(x), they don't always commute. A clear example is when operator B multiplies by x, while operator A takes the derivative with respect to x.
Or do you claim this statement to be false as well?
Do you agree that this is not limited to quantum systems?

16. Mar 11, 2009

### DrChinese

The HUP is essentially limited to quantum systems, does not apply to classical objects as you imply. (Of course, when progressively more complex/larger quantum objects are involved, there is an element of uncertainty still present.)

So let's get specific about something which is not ambiguous: particle spin. There are spin components which are non-commuting, *and* one does not involve a derivitive of the other as you claim. These obey the HUP, and do not exist in the classical world. This is a clear sign that the HUP does not rest on a classical principle as you seem to claim.

You are taking time and diverting the attention of readers of this forum by twisting the meanings of words and harping on points that don't really apply to the subject at hand. This is not fair to those who are not aware of your agenda. I come here to participate in legitimate discussion of science.

Why don't you operate in a straight-forward manner instead of hiding - here and in other threads - from your real agenda: pushing a variety of classical and/or realist positions. Please come out from behind the bushes with your views and label them appropriately - instead of creating rabbit trails to divert us under the pretense of debate.

17. Mar 11, 2009

### mn4j

Despite your diatribe and accusations, you have failed to specify what is wrong in my statements. It appears you are the one with a hidden agenda trying to project your intentions on others. I wonder why you would feel threatened if your views were based on a solid foundation.

Show me where I claimed that spin components are derivatives of each other?! Show me where I claimed that the relationship must be a derivative?! Are you utterly unable to understand the English language? Just because I mention the derivative as one example does not mean it must be a derivative relationship in every case. By your argument, it would be sufficient for someone to show energy conservation in a quantum system, and then then argue that "this proves energy conservation does not exist in the classical world".

Since you are bent on proving me wrong, explain how the momentum and position of a soccer ball are both well defined at an instant in time as in the example I gave above. Or explain how the frequency of a classical wave is well defined at an instant in time. If you are truly interested in real scientific debate, rather than religious assertions, you will not shy away from this challenge which is very relevant to the issue at hand.

I will repeat my main point in more generic terms. Feel free to explain why it is wrong.

Every pair of conjugate observables have an uncertainty relationship which derives solely from the fact that they are by definition a Fourier transform pair. Momentum and position are simply one example of such pair. There are many others. This is not limited to quantum systems as some naively think.

18. Mar 11, 2009

### Naty1

mn: ...the quote above doesn't seem related my point........ if uncertainty derives merely from a function and its derivative, how do you explain he uncertainty of two orthogonal components of angular momentum,for example,...doesn't seem like either is the derivative of the other...but I am always willing to learn...

Ooops, I just saw:
"Every pair of conjugate observables have an uncertainty relationship which derives solely from the fact that they are by definition a Fourier transform pair." I thought you said uncertainty derived solely from a variable and its derivative..or is it both?? Never came across either claim...if only life/physics were so simple..

Last edited: Mar 11, 2009
19. Mar 11, 2009

### mn4j

Where did I say that?

See http://en.wikipedia.org/wiki/Conjugate_variables
* R. Gilmore, Uncertainty relations of statistical mechanics, Phys. Rev. A 31(5), 3144-3146 (1985).

Last edited: Mar 11, 2009
20. Mar 11, 2009

### DrChinese

Are photon conjugate (non-commuting) spin observables by definition a Fourier transform pair? They aren't continuous. Seems to me these are not related in the way position and momentum are. They follow the HUP too.

What are some non-quantum observables that obey the HUP? (That is, if you are saying the HUP is not a quantum phenomena.)

In other words: the similarity of the math is not what makes something respect the HUP. Do you think Planck's constant might be a fundamental component of the equation as well?