uncertainty

[Brainee]

You cannot measure both the position and speed of a particle at the same time. When does this show?

[Phi for All]

As I understand the HUP, if you're trying to determine the position of an electron, you need a photon to collide with it and travel back to the device you're using to measure it. The photon imparts some of its momentum to the electron, so the more accurately you measure it's position, the more uncertain you are about its speed, and vice versa. Trying to be more accurate about the electron's speed means you can't be as certain about where it is. 

[Genady]

Just a few clarifications:

1. A 'speed' of particle is not well defined. The uncertainty principle relates rather position and momentum.

2. Position is a three-dimensional vector in space, say along x, y, and z axes. Momentum also is a three-dimensional vector. The uncertainty principle relates position and momentum of a particle along the same axis. Its position along axis x, for example, and its momentum along axis y can be measured at the same time.

3. Position and momentum along one axis cannot be measured simultaneously because there is no such state in which a particle would have a definite position and a definite momentum along one axis. This inability is a matter of particle states rather than that of measurements.

[exchemist]

25 minutes ago, Genady said:

Just a few clarifications:

1. A 'speed' of particle is not well defined. The uncertainty principle relates rather position and momentum.

2. Position is a three-dimensional vector in space, say along x, y, and z axes. Momentum also is a three-dimensional vector. The uncertainty principle relates position and momentum of a particle along the same axis. Its position along axis x, for example, and its momentum along axis y can be measured at the same time.

3. Position and momentum along one axis cannot be measured simultaneously because there is no such state in which a particle would have a definite position and a definite momentum along one axis. This inability is a matter of particle states rather than that of measurements.

Indeed. However the OP seems to be asking for practical examples in which position/momentum uncertainty is experimentally apparent. I can't think of one offhand. Can you? 

There are classic examples of the related energy/lifetime uncertainty in things such as the width of spectral lines (uncertainty broadening), but position/momentum? Hmm. 

[Genady]

How about the fact that electron doesn't fall onto a nucleus in spite of their electrical attraction? Electron cannot be localized on the nucleus and stay there because otherwise it would be in a state with very precise position and momentum.

Edited January 9, 2023 by Genady

[studiot]

Compton scattering

 

https://aapt.scitation.org/doi/10.1119/1.13648

[exchemist]

1 hour ago, Genady said:

How about the fact that electron doesn't fall onto a nucleus in spite of their electrical attraction? Electron cannot be localized on the nucleus and stay there because otherwise it would be in a state with very precise position and momentum.

I suppose you could look at that way. But that's still a bit theoretical, compared to the width of a spectral line. Is there not some classic experiment that shows how increasing precision in position leads to lower precision in momentum (i.e. a broader frequency distribution, or something? How about limitations on focusing a laser beam to a point, or something like that?  

 

[Genady]

1 hour ago, exchemist said:

I suppose you could look at that way. But that's still a bit theoretical, compared to the width of a spectral line. Is there not some classic experiment that shows how increasing precision in position leads to lower precision in momentum (i.e. a broader frequency distribution, or something? How about limitations on focusing a laser beam to a point, or something like that?  

 

Here is something (better than nothing, I guess):

Researchers demonstrate Heisenberg uncertainty principle at macro level (phys.org)

[exchemist]

50 minutes ago, Genady said:

Here is something (better than nothing, I guess):

Researchers demonstrate Heisenberg uncertainty principle at macro level (phys.org)

OK, but isn't this the "observer effect", rather than a true demonstration of the HUP?

[Genady]

Doesn't particle diffraction demonstrate the uncertainty principle? The narrower the opening, i.e. the uncertainty in position, the wider the range of directions, i.e. the uncertainty in momentum. E.g.:

220: Single-slit Diffraction and the Uncertainty Principle (Mathcad Version) - Chemistry LibreTexts