Does the conservation of momentum and conservation of energy apply to electrons that have light shone on them, and if so, why cant we tell their position and velocity by measuring the amount of light it absorbed, and the direction of the reflected light?
2 Answers
To understand the results of the electron's interaction with the photon, you have to generate a very precisely measured photon, or else you won't be able to tell where the electron is because you're not quite sure about the properties of the photon you used to measure it.
So, you go and find yourself a very, very narrow atomic transition or something, which produces photons of a very consistent energy. Let's say the width of this transition in momentum of the photon is 1 neV/c, and the photon is produced anywhere in a...
Oh, damn. Full stop! We can't just set up these initial conditions to make our experiment work! Quantum mechanics puts limits on how good our knowledge of the initial position of the photon can be given how good our knowledge of the momentum is. It must be the case that the photon's initial position can be anywhere over a range at least
[math]\Delta x = \frac{\hbar}{2(1\text{neV/c})}\approx 100\text{m}[/math]
We're doomed from the very beginning. You're guaranteed never to be able to set up a light source precise enough to make an uncertainty principle-beating measurement of the electron.
So, you go and find yourself a very, very narrow atomic transition or something, which produces photons of a very consistent energy. Let's say the width of this transition in momentum of the photon is 1 neV/c, and the photon is produced anywhere in a...
Oh, damn. Full stop! We can't just set up these initial conditions to make our experiment work! Quantum mechanics puts limits on how good our knowledge of the initial position of the photon can be given how good our knowledge of the momentum is. It must be the case that the photon's initial position can be anywhere over a range at least
[math]\Delta x = \frac{\hbar}{2(1\text{neV/c})}\approx 100\text{m}[/math]
We're doomed from the very beginning. You're guaranteed never to be able to set up a light source precise enough to make an uncertainty principle-beating measurement of the electron.
