Heisenberg uncertainty principle

[angy]

Hello!

I have a doubt about Heisenberg uncertainty principle.
Suppose that a particle moves along x-axis with a given uncertainty in velocity.
Can I say something about its motion along y-axis?
Thanks

 

[ZapperZ]

Try reading this:

https://www.physicsforums.com/showpost.php?p=2669839&postcount=14

Zz.

 

[angy]

Thanks, your explanation is very helpful.
However, I still can't understand something.
What if there is no slit?
Maybe, is it not possibile otherwise to measure velocity in x-direction?

 

[ZapperZ]

If there is no slit, then there is no restriction anywhere, and you don't have an exact knowledge what an electron is doing.

Note here that your starting premise is already "AFTER" a measurement, because you already know with certainty that it is moving in a particular direction. One has to be careful in setting up the scenario because by saying that, you've already made a determination one way or the other.

Zz.

 

[angy]

Thanks a lot!
Sorry, I still have a doubt.

The fact that the electron is moving in x-direction means that the y-component of its velocity is zero, isn't it? Therefore, the uncertainty in velocity in y-direction is zero. The conclusion is that we can say anything about the position along y-axis.

Is it a correct way of thinking, or am I mistaking?

 

[ZapperZ]

Thanks a lot!
Sorry, I still have a doubt.

The fact that the electron is moving in x-direction means that the y-component of its velocity is zero, isn't it? Therefore, the uncertainty in velocity in y-direction is zero. The conclusion is that we can say anything about the position along y-axis.

Is it a correct way of thinking, or am I mistaking?

Again, think of HOW you are going to ensure that it is moving ONLY in the x-direction? Do you put a small hole at the electron source so that you only collect the ones that will go through that hole, and then call that the x-direction? After all, only those that have the right velocity component from the source to that hole will make it through.

But as soon as you do that, we are back to the single slit problem. What do you think is the spread in the velocity/momentum in the y-direction and z-direction? Do you think this spread will corresponds to how small you make that hole, i.e. the more you try to confine your electron to have very little y and z direction motion?

You simply can't say "I have an electron moving in the x-direction", because that's the whole point of quantum mechanics, that what you think are obvious and trivial, are no longer just that!

Zz.

 

[angy]

I think you brightened my day!

Therefore, it depends all on how I measure the speed the electron. If I don't know how the measurement is made, I can't say anything about the motion along an orthogonal axis.