Measuring velocity and position of a particle

[Farzan]

Heisenberg's imaginary microscope showed that it would be impossible to measure the position and velocity of a particle because observing it can change the position and momentum.

However, assuming the laws of classical physics apply to these particles, I think an experiment can be set up to measure position and momentum at the same time (with accuracy).

Imagine electrons are being fired in one direction. Photons are then fired perpendicular to the path of the electron. Eventually there will be a collision, with a known time and position. But now the direction and momentum of the electron are unknown.

Farther down the path there is another device that emits photons, but it's on the other side.

Repeat this experiment enough and eventually two collisions occur, the second one sending the electron in the same direction as it was originally going.

Now you know the time and location of the second collision.

At this point, use some one-d kinematics and you know the exact position and velocity along the path!

The attached picture should explain some. Please excuse my terrible paint skills

Of course, none of this could really work, due to Heisenberg's Uncertainty Principle. But why? From what I've read, it's purely mathematical. How can we be sure that technology won't increase to a level where it's possible to know the speed and position of a particle?

 

[mjsd]

don't understand how your system will give you position and moment of the e- at each of the two points?

 

[Farzan]

I forgot one important part of this setup... there should be two devices to check for photons on the other side of the path. That way, you know the collision didn't occur.

When the collision occurs, the electron should absorb the photon.

The first collision's position is known because the photon and electron should travel in straight lines. The second collision is more difficult to know, but... assuming the second photon gives it just enough momentum to cancel out the effect of the first photon, it will go East. Then you can measure the vertical displacement.

And you already know how far apart the photon emitters are.

The time it took to travel to the second detector is known, because you know when the photons are shot.

v = x/t

The velocity, and position along every point in that path, are calculated with the information. And because the mass is known, momentum is known too.

 

[neu]

However, assuming the laws of classical physics apply to these particles, I think an experiment can be set up to measure position and momentum at the same time (with accuracy).

This is the point, they don't

 

[malawi_glenn]

"How can we be sure that technology won't increase to a level where it's possible to know the speed and position of a particle?"

It is an intrinsic property of nature, the uncerntanty principle. It has nothing to do with the resolution of our measurements..

The classical laws of physics do not apply to these kind of systems.

 

[mjsd]

yes, if you believe in QM, and you should to a good extend, then the uncertainty priniciple (HUP) is a natural result (it comes out of the theory), not an empirical law. Can use wave packets to help illustrate HUP.

 

[ueit]

Measuring both momentum and position with any accuracy is trivial. Just put a screen very far from the particle source. Switch the source on for a very small time and measure the time of arrival. The distance between the source and the screen divided to the time of flight gives you the speed. The position is the spot on the screen where you detect the particle.

 

[ahrkron]

Imagine electrons are being fired in one direction. Photons are then fired perpendicular to the path of the electron. Eventually there will be a collision, with a known time and position. But now the direction and momentum of the electron are unknown.

You are already assuming then that you knew the original direction of the electron, but let's go on...

Farther down the path there is another device that emits photons, but it's on the other side.
Repeat this experiment enough and eventually two collisions occur, the second one sending the electron in the same direction as it was originally going.

Now you know the time and location of the second collision.

At this point, use some one-d kinematics and you know the exact position and velocity along the path!

The main problem here is that, in order to know that the electron came out in the same direction of the original electron, you again need to make a measurement of its momentum.

It is possible indeed to measure the momentum, but you will then have an incomplete knowledge of this (final electron) position... which then invalidates the section that I colored in blue, since you no longer know the position of the second collsion.