# Why doesn't detecting a photon's position after passing through a narrow slit violate HUP?

I understand that after passing through a narrow slit a photon's momentum is uncertain, however since its position can be inferred from having passed through the slit, a subsequent position measurement fully constrains the momentum direction. Therefore as long as we know the photon's wavelength, we have simultaneously measured x and p to arbitrary accuracy.

I forsee two possible responses:

1) Even though we may start with a photon of known $$\lambda$$, passing through the slit makes $$\lambda$$ uncertain. However I've never seen this discussed; always diffraction is described as changing momentum direction, not magnitude.

2) The HUP says that a position measurement makes subsequent momentum measurements uncertain, NOT that position and momentum cannot be simultaneously determined. However this is in strong tension with every description of the HUP I've ever seen, including an answer to a previous similar question here. Note that the previous link might be considered a duplicate of this question, however, I think both that question and answer are not focused enough to be informative.

• Please note that each photon in the oicture here physics.stackexchange.com/questions/468533/are-photons-blinking/… leaves a dot which has a delta(x). The delta(p) can easily be fulfilled which you can calculate yourself as the dots are of micron size, and the wavepacket of the frequency of the photon can easily be accomodated. – anna v Mar 26 at 18:08
• @annav, your argument would only hold if we couldn't arbitrarily increase the distance between the slit and the screen, thus being able to arbitrarily reduce the angular uncertainty that results from your delta(x) – user1247 Mar 26 at 19:05
• The color of the photons gives the momentum, the point is the measurement on the screen. That is the HUP., at the point of measurement. – anna v Mar 26 at 19:11