# What experiment demonstrates Heisenberg's uncertainty principle?

1. Mar 25, 2012

### mycotheology

When I read about the uncertainty principle, I keep reading about these experiments where they fire electrons through a single or double slit and observe the diffraction but I can't these experiments relate to Heisenbergs uncertainty principle. So when they fire the electrons, they know their momenta, then when they reach the slit, they diffract and their momenta changes and eventually, when they hit the screens, they know their positions. I'm real confused, how do these experiments show that when you know the momentum of a particle, you can't know its position and vice versa?

2. Jan 29, 2015

### jk22

I'm interested in that too. I imagined that if you make a laser ray passes through a slit it should modify the wave length distribution of the light ?

Else i found such an ecperiment paper but i havent read it carefully yet : http://cds.cern.ch/record/499984/files/0105061.pdf

3. Jan 29, 2015

### Staff: Mentor

Check out the following:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The reason you get interference is the unknown momentum as it passes through the slits - see equation 3. The reason its unknown is the slit is a position measurement.

Thanks
Bill

4. Jan 30, 2015

### Wes Tausend

mycotheology,

I think I can recommend observing a related experiment that I believe demonstrates the Uncertainy principle. It involves a 1/2 hour video shown for college students and the video is only available to network connections in the US and Canada, so I hope you reside in such an area.

The video is called Particles and Waves and delves into quantum physics just a bit. Near the end of the video, the instructor, Dr. David Goodstein, demonstrates how light behaves as both particles and waves using polarized lenses. When demo'ing the particle aspect, he clearly shows that light can pass through a third set of carefully aligned polarized lenses in a particle probability function only, a phenomenen that cannot be answered any other way but probability. The video is found at http://www.learner.org/resources/series42.html . You must allow temporary pop-ups, click on the VoD box to the right of the Particle and Waves lesson #50 near the bottom, and the resulting small video window pop-up can be "full-paged" for easy viewing like a youtube video.

As a review, light is normally transmitted as an envelope in all 3 dimensions, and a single polarized lens, with it's many tiny parallel scratches, allows only a corresponding orientation portion to pass, such as the vertical orientation. Continued passing through a second polarized lens may be accomplished only by orienting the second lens scratches also vertical. Thereafter turning the second lens 90° will then block all light with one lens blocking vertical and the other horizontal waves. The uncertainy trick (proof) is when Dr. Goodstein adds a third polarized lens (at about the 26 minute mark) that obviously passes light as a probability function only.

As a review, I like to think of a polarized lens like a picket fence. A jumprope held by two people on the ends can be shaken only up and down in a wave-like action between the vertical fence slats. Adding another picket fence behind the first allows this to continue, unless the second picket fence is turned 90° (horizontal). With one vertical and one horizontal, all rope waves are impeded. Since this is a simple wave experiment, there is no corresponding particle probability insight, but it does clearly explain the wave likeness regarding polarized lenses. Good luck and I hope you have access to a North American network.

Wes
...

5. Jan 30, 2015

### jk22

Interferences comes from the wave aspect, but the spreading if you have only one slit could be explained classically imagining small balls bouncing against the wall in the slit. Of course this is possible only if the particle is extended in space, so i'm not sure if this spreading is a test of the hup.

6. Jan 30, 2015

### jk22

Erm i meant if the slit border is for example modelized by a quarter of circle and the particle can be considered a point.

7. Jan 30, 2015

### Staff: Mentor

Why do you think it has a wave aspect? You do know that De-Broglies hypothesis was superseded at least by 1926 when Dirac came up with his transformation theory?

The paper I linked to explained it by the Heisenberg Uncertainty Principle and principle of superposition. Did you read it?

You will find many threads on this forum explaining the issues with the so called wave-particle duality. It's not something the quantum theory actually has (at least in the way beginner texts elucidate it) - for example my standard textbook Ballentine doesn't mention it. Its a hangover from the early days of QM and beginner texts.

Thanks
Bill

Last edited: Jan 30, 2015
8. Jan 30, 2015

### ZapperZ

Staff Emeritus
Most obvious experiment: the single slit:

Zz.

Last edited by a moderator: May 7, 2017
9. Jan 30, 2015

### Staff: Mentor

The paper I linked examines the same thing but models an exact position measurement as a delta function.

Thanks
Bill

Last edited by a moderator: May 7, 2017
10. Jan 30, 2015

### ZapperZ

Staff Emeritus
I'm familiar with the Marcella paper, having quoted it several times. However, the "HUP" effect here is buried within the QM derivation. His emphasis in that paper is more of deriving the diffraction/interference patterns without using the typical wave picture, but rather entirely using the quantum mechanical treatment, something that most books often overlook.

Zz.

11. Jan 30, 2015

### vanhees71

Again I must stress that the Marcella paper is highly misleading, precisely because it doesn't include the HUP, because it doesn't work with proper states but plane waves! I guess, I've to write up something about this, using wave packets. It's really astonishing that nobody seems to have written up this paradigmatic example, used in almost all textbooks at the beginning in such a hand-waving way. It's usually treated in the sense of an heuristic argument a la Einstein-de Broglie, and this is didactically very dangerous and shouldn't be done in modern lectures/textbooks anymore.

Another in the textbook literature is the use of the photo-electric effect, where the wrong (!) claim is made that it proves the quantization of the electromagnetic field, although it's well known that it is completely understandable using the semiclassical approximation (classical radiation field interacting with quantized bound electrons) and 1st-order time-dependent perturbation theory.

The third nogo, and imho it's the worst of all, is the use of the Bohr-Sommerfeld model for the hydrogen atom. No comment is necessary about this one!

12. Jan 30, 2015

### ZapperZ

Staff Emeritus
I don't understand this criticism. It appears that you don't seem to get the CONTEXT of his paper, which is to clearly show that one can get such interference pattern without the use of the classical wave treatment, something that many books simply said can be done, but never showed. What is wrong with the use of plane wave states as a special case? There are many phenomena that make use of such states as the starting point.

We have gone over this numerous times (and really, it shouldn't be brought up here since it is highly off-topic). Many of the newer papers that addressed this will use the standard photoelectric effect as an evidence, but not the definitive smoking-gun, for photons. However, as has been repeated, no semi-classical model exists to explain multiphoton photoemission, resonant photoemission, etc. You're welcome to take a crack at it.

Zz.

13. Jan 30, 2015

### vanhees71

I agree, the photon statement was off topic, but I stand to my criticism against the Marcella paper. It's ironic if you quote it in connection with the HUP! Not only uses it plane waves (which are not representing states, because they are not square integrable) but also a zero-width slit!

Of course, nowhere is a classical-wave (nor classical-particle) picture in the full QT treatment of the single-slit, double-slit or grating experiments with quanta. I never claimed something in this direction.

14. Jan 30, 2015

### ZapperZ

Staff Emeritus
I did not quote the Marcella paper in this thread, nor have I used it in connection with the HUP. Check again!

I also do not see the issue with using delta functions for the slit width as a demonstration of one extreme limit of the situation. This was a pedagogical treatment to illustrate that it can be done without further added complications.

We're not going to resolve this here because this has become a matter of taste. When you publish your more realistic treatment of this very same topic (preferably in EJP where Marcella published his), we can discuss this further.

Zz.

15. Jan 30, 2015

### Staff: Mentor

Can you elaborate on that? From the paper:
'Because position and momentum are non-commuting observables, a particle passing through slits always has an uncertainty in its y-component of momentum. It can be scattered with any one of the continuum of momentum eigenvalues py = psinθ , where −π /2 ≤ θ ≤ π /2. Measurement of a well-defined scattering angle θ constitutes a measurement of the observable p ˆ y and, therefore, the basis vectors in Hilbert space are the momentum eigenvectors py.'

I know that paper has issues - and they have been discussed in a few threads.

The trouble is the paper that examines those issues is not exactly what I would call elementary:
http://arxiv.org/pdf/1009.2408.pdf

Thanks
Bill

16. Jan 30, 2015

### vanhees71

Yes, but don't listen to his words but look at his deeds. He's using plane wave, which represent a situation, where the momentum has no uncertainty. Of course, it's not a state. So it's no contradiction to what he correctly states in words, but then he should use wave packets. The same holds for idealizing the slit to a 0-width $\delta$ distribution, which implies 0 width for position at the slit.

Of course you can start with harmonic waves, using the Helmholtz equation to find the propagator (for the case of a finite-width slit of course), but then you have to fold it with an appropriate wave packet to get the story correct, and of course, the typical setup can be understood as a potential-scattering problem (asymptically free particles going in, asymptocially particles going out).

17. Jan 30, 2015

### ZapperZ

Staff Emeritus
Again, I do not see this being a problem at all. The momentum in the direction of propagation may not have any uncertainty, but this momentum is actually quite irrelevant to this case. This is because the momentum that is involved in the HUP (and consequently, the formation of the interference pattern he's dealing with in his paper) is the transverse momentum, i.e. parallel to the plane of the slit!

I do not see any loss in the pedagogical illustration by using such plane waves.

Zz.

18. Jan 30, 2015

### vanhees71

There's no spread in transverse momentum for a plane wave. It's a generalized (!!!) momentum (as a three-vector!) eigenstate of momentum!

19. Jan 30, 2015

### ZapperZ

Staff Emeritus
There is AFTER the slit!

Zz.

20. Jan 30, 2015

### Staff: Mentor

But that sort of thing is used all over the place in QM eg Dirac's classic. It's not square integrable - and Von Neumann was correctly scathing of it. But we now have the Rigged Hilbert Space formalism - such states are viewed simply as an idealisation for mathematical convenience. The same with modelling a narrow slit by a Dirac Delta function.

Thanks
Bill