# Uncertainty Principle logic help

1. Jun 13, 2008

### chrisphd

Does the uncertainty principle contradict the idea that an object can be at rest relative to an observer? For example, in physics class we examined an electron in a box, and we assumed the walls of the box are stationary relative to the observer. But the uncertainty principle says delta p times delta x > hbar/2. So the walls of the box would have a definite position and momentum relative to the observer, violating the principle. Where is my error in logic.

2. Jun 13, 2008

### gendou2

The atoms in the walls of the box behave according to quantum mechanics.
They will have uncertain positions, too.
However, I would expect thermal energy to introduce more error into this experiment than uncertainty.

3. Jun 13, 2008

### chrisphd

Your missing the point here. I know that the particles in the box exhibit uncertainty. But for the thought experiment, it was assumed that the walls of the box where stationary. However, i am asking, doesn't assuming another object is stationary to an observer contradict the uncertainty principle, as we are assuming we are able to know the exact position and momentum of that object.

4. Jun 13, 2008

### gendou2

If you assume something to be true, then it is true.

The uncertainty principle is a restriction on what can be measured, not what can be assumed.

Last edited: Jun 13, 2008
5. Jun 13, 2008

### chrisphd

Not so. Certain things can be assumed to be true in a thought experiment, but if such assumptions contradict the laws of nature then the thought experiment achieves nothing. It is like assuming speed of light is greater than c to deduce a fact. The fact will be irrelevant to physics, as in physics the speed of light is c. The uncertainty principle is more generally that one cannot know exact position and momentum rather than one cannot measure exact position and momentum. This is because in order to know something about an observable, you need to measure it.
Basically, for the conclusion to be correct, the premises of the argument must also be correct. I am wondering if the assumption is an incorrect premise.

Last edited: Jun 13, 2008
6. Jun 13, 2008

### Fredrik

Staff Emeritus
When you calculate the energy eigenstates and the corresponding eigenvalues (i.e. the energy levels) of a "particle in a box" you're just solving the Schrödinger equation for a potential with a certain shape (zero in a certain interval and infinity everywhere else). The uncertainty principle says something about the shape of the wave function, not about the shape of the potential, so there's no disagreement there.

7. Jun 13, 2008

### chrisphd

My question in simplest terms is, can an object be at rest relative to an observer and not violate the uncertainty principle?

8. Jun 13, 2008

### gendou2

I don't see why not. It can have these properties, but good luck measuring both at once.

9. Jun 13, 2008

### chrisphd

Well, one reason why not is because relative to the observer, he would observe a momentum of 0, and therefore he would know the exact momentum of the object. Uncertainty principle is error in position times error in momentum is greater than hbar/2. However if he knows exact momentum, the left hand side of the equation will be 0 violating the law

Last edited: Jun 13, 2008
10. Jun 13, 2008

### gendou2

If you had asked "Can an object be measured at rest relative to an observer and not violate the uncertainty principle?" so the answer is still yes.

Now, if you asked, "Would an electron ever be measured at rest relative to an observer?" then the answer is no. You'd get an electron cloud if you measured an electron that's part of an atom. If you confined an electron with a very focused laser beam, you could get it to stay within a very tiny area. With good enough equipment, you could still notice it move when it's position is measured optically.

Last edited: Jun 13, 2008
11. Jun 13, 2008

### chrisphd

That is good news. But i still don't see how it is possible looking at the mathematics.

12. Jun 13, 2008

### gendou2

Holy mother of..., you've never seen anything stay still before??
All sorts of objects stay still relative to an observer when measured.
I'm looking around my apartment, and most of the objects I see appear still.
Sure, there is large error in my measuring tool (bad eyesight).
The uncertainty in the position of my bookshelf is well under the threshold of detection.

13. Jun 13, 2008

### chrisphd

LOL. One could argue that the things are you are looking at only appear to be stationary. They are still moving at very low speeds, but you have failed to measure their speed to high enough degree of accuracy. However, i'm not saying that its not possible to measure the speed of an object to be 0 relative to an observer. I'm just wondering how it doesn't violate the uncertainty principle.

14. Jun 13, 2008

### gendou2

I'm sorry for not explaining myself well.

The bottom line is, as Fredrik said, we're not talking about a material box.
We're talking about a wave function.
I think that's what was initially misleading.

Say we capture an electron with an electric field.
We measure the position of the electron a bunch of times.
The probability to find the electron at any location is the square of the wave function.
The wave function has a maximum, and that maximum may be stationary.
This is not to say that the electron is stationary.

15. Jun 13, 2008

### chrisphd

Ok. But the question still remains, is it possible to measure something to be stationary and not violate the uncertainty principle?

16. Jun 13, 2008

### gendou2

That question is not unique.
If the object is small enough so that uncertainty is significant, then uncertainty effects the results of experiment.
If the object is large, then you can measure it to within the accuracy of your instruments.

You could measure an electron in the same exact place twice, but it would be a coincidence. The next time it may be somewhere else, because the photon you used to measure it last time sent it off on on a new trajectory.

Furthermore, the more accurate you want your measurements to be, the shorter wavelength of light you need to use. Shorter wavelength means higher energy, means higher momentum delivered to the poor electron being so cruelly observed.

Last edited: Jun 13, 2008
17. Jun 13, 2008

### Fredrik

Staff Emeritus
It isn't possible to measure something to be stationary, period. This would make the wave function zero everywhere (and turn the uncertainty principle into $\infty\cdot 0\geq\frac\hbar 2$)

Last edited: Jun 13, 2008
18. Jun 13, 2008

### chrisphd

Why would the wavefuntion be 0?

19. Jun 13, 2008

### gendou2

What about my bookshelf? It's stationary, in a classical sense.

I think what chrisphd is struggling with is that our classical concept of stationary is as unreal in quantum mechanics as absolute space is in general relativity.

Last edited: Jun 13, 2008
20. Jun 13, 2008

### gendou2

Actually the wave function would be zero everywhere but one point, where it would be 1.
You don't see particles behave like this in nature, though.