How do we measure the position of a particle?

[the_pulp]

I'd like to know with some precision how the position of a particle is measured. Just to focus the potential answers, I'd like to know some details of it because perhaps with that I could get a better understanding of some basic principles such us:
1) commutation relation of x and p
2) some ideas of non measurability of the position operator in QFT
3) perhaps there is more stuff like this that I am not seeing right know

Thanks

 

[Simon Bridge]

You measure the position of a particle by throwing other particles at it. Was there a particular example you had in mind?

 

[the_pulp]

If you throw other particles at it, how do you know the position where they hit? You perhaps know the position of the particles (lets call them B) used to measure the position of particle A, and perhaps the momentum of B, so perhaps you can calculate where and when B hits A, but, isn't it that we can't know the position and at the same time the momentum of B.
I mean, I know the whole math around it, but I can not "see" the experiment.

Thanks

 

[Simon Bridge]

The particles rebound, and are stopped in a detector.

The detector also works by hitting particles with other particles ... the devil is in the details. The idea is to make the detector process as simple as possible so typically we'd stop the particles completely in the detector.

If the particles are charged, the detector can be a bit of metal attached to a wire - so a stream of particles produces a current which can be measured with a galvinometer. It the particle is unstable, we can stop it in a scintillator so we can see the flash of light it gives off.

What we care about is the direction the particle came from as it was detected - we do this by moving the detector around (or having lots of them in different places). If we know the direction we fired the particle, and the direction it was going when it was detected, then we can work out the position of whatever it hit.

If we use photons as our particle - we can get an idea of the position of the target from the rebound angle, and the momentum of the target by the doppler-shift of the photon. So you can measure the two at the same time... just not to arbitrary accuracy. This should not be confused with the observer effect.

Unfortunately, Quantum Mechanics is "the math around it", if we could produce an intuitive picture of what it is saying, some sort of visual model, then we wouldn't need QM - it would all be classical.

The commutator is directly related to the Heisenberg uncertainty.
The math abstracts out a lot of the mess of an actual experimental measurement so you can consider ideal situations and extrapolate from them.