I Heisenberg Uncertainty: simple explanation required please

[cemtu]

TL;DR Summary

it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

 

[PeroK]

Summary:: why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

I don't see the connection between this question and the HUP. The HUP gives a relation between the standard deviations of momentum and position measurements of a particle in any state:
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$

 

[cemtu]

I don't see the connection between this question and the HUP. The HUP gives a relation between the standard deviations of momentum and position measurements of a particle in any state:
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$

it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!

 

[Nugatory]

it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!

To measure the direction that something was traveling, we need some sort of detector. For example, we could have a screen with a hole in it, and a piece of photographic film behind the hole. A particle hits the film and leaves a dot on the film; we draw a line from the dot back to the hole and that tells us the path of the particle.

In the language of quantum mechanics, the interaction with the hole has measured the momentum of the particle as it passed through the screen and the interaction with the film has measured the position as it reached the film.

However, there’s a catch. The hole in the screen and the dot on the film both have non-zero size so there are many lines that I can draw between the two, and they aren’t exactly parallel (compare the line between the right-hand side of the dot and the left-hand edge of the hole with the line between the left-hand side of the dot and the right-hand edge of the hole). So we haven’t exactly measured the angle, there’s some uncertainty in our result. The quantum mechanical uncertainty principle says that that uncertainty cannot be reduced all the way to zero.

 

[cemtu]

thank you Nugatory!

 

[andresB]

Well, in non-relativistic QM a give uncertainty (say, the momentum of a given electron) can be made as small as desired. The product of uncertainties of variables that are linked by the HUP does have a lower limite that can't be made smaller.