How Does the Uncertainty Principle Apply to Electron Beams and Gas Molecules?

[manofphysics]

1)Consider a beam of electrons in a CRO striking the phosphor screen.How does the uncertainity principle pan out here?
Technically, we are getting the exact position of the electron due to the point made on the screen.And, we can most certainly calculate the velocity by estimating the time in which the electron went from the cathode to the screen.So, both momentum and position are known.

2)Consider a gas enclosed in a container(high density,so wave functions overlap).What is the reason here for the uncertainity in the gas molecules ?Because , as such we are not interacting, or measuring the position of each molecule explicitly.
We have just left the gas in the container independent of any more interference.

I know my questions may sound elementary to some but I'll be grateful for any clarifications.

 

[Hootenanny]

1)Consider a beam of electrons in a CRO striking the phosphor screen.How does the uncertainity principle pan out here?
Technically, we are getting the exact position of the electron due to the point made on the screen.And, we can most certainly calculate the velocity by estimating the time in which the electron went from the cathode to the screen.So, both momentum and position are known.

Heisenberg's uncertainty principle says nothing about a single measurement, it only refers the to distribution of several measurements.

2)Consider a gas enclosed in a container(high density,so wave functions overlap).What is the reason here for the uncertainity in the gas molecules ?Because , as such we are not interacting, or measuring the position of each molecule explicitly.
We have just left the gas in the container independent of any more interference.

I'm afraid that I don't understand the question. The uncertainty principle applies to measurements, unless we measure the positions/velocities of the gas molecules we cannot say where they are or how fast they are going.

 

[DrChinese]

I think you are aware that the uncertainty principle says that you cannot know P and Q simultaneously. You will instead get a distribution of values. There is nothing to stop you from attempting to measure both values to unlimited precision, but they will not represent the particle simultaneously.

It is sometimes easier to see this point if you consider spin/polarization instead of momentum and position. If you measure spin in x-axis and then measure spin in y-axis, does the particle still have the same spin in the x-axis as previously measured? (All we need to do is perform another check on x-axis spin to accomplish this.) The answer is NO, that value will be totally random (i.e. complete uncertainty). So we knew the values at 2 points in time precisely, but not simultaneously.

 

[JustSam]

If the electron is traveling in the x-direction, then the timing gives you the x-momentum, and the impact on the screen gives you the y-position and the z-position. I don't think there is any uncertainty principle involved in these three measurements, as they commute. It is only momentum and position along the same axis that do not commute.

 

[Hootenanny]

If the electron is traveling in the x-direction, then the timing gives you the x-momentum, and the impact on the screen gives you the y-position and the z-position.

The flash would also give you the x-position.