Understanding Double slit and delayed choice experiment

Question

I am having some trouble with two thought experiments, so I will list both of them below and I would be most grateful If somebody could explain to me what is actually going on or where I went wrong (especially mathematically would be very nice).

1. Given I set up the double slit experiment as usual and like so - = | ("-" is the laser position, "=" the slits and "|" some screen), without doing anything else I will get an interference pattern. Now , what happens when I place a sheet of paper in there directly after the slit to separate the to path like so - =- |, I would not get an interference pattern because placing the sheet in there will constitute as a measurement correct? so what happen when I place the sheet more and more away from the slit toward the screen like so - = -| ? Because now, I can tell through which slit a photon went based on wich side of the paper it hits (given that it hist the paper at all). So what kind of pattern can I expect to see? Can the Photon "know" that I will be measuring it ? Is the "which-way" information not always encoded into the momentum of the photon anyway, or more precisely in the direction of the momentum vector?

2. This is similar to 1. with a different setup: Given again I again set up the experiment normally as - = |. Now again I get an interference pattern if I don't do anything else. Now If I cut hole into the sheet, in the middle of the interference pattern where the part with the most intensity is and put a tube behind the sheet, so that any light that goes, where the hole is goes inside the tube and based on wich side of the tube the photon hits I again can know from what slit the photon came, as the photons should travel in a straight paths right? So now I would expect the photon to behave as though It travels only through one slit right, which would mean (at least more probable than not) it will no longer go into the tube, which would mean I loose the information about through where it went, which would than mean (more probable than not) it again would go into the tube... and so on. I am no stuck I a loop of thoughts in which I am probably just because I made some classical assumption to a quantum system or so but I can find it.

As a side note, please feel free to use as much maths as needed as long as you think a B.Sc in physics can understand :)

Answer 1

1. Either the paper is (a) part of a 2-piece offset screen, or (b) it blocks one slit and you're doing a one slit experiment. It all depends on your choice of what the experiment is.

   b) If you're imply that it will show on the paper and then also the screen--that's not happening.

   a) If there is gap between then slit and paper, then it is an offset screen. There is a non-zero amplitude for the photon to go through the unblocked slit and still hit the paper (see: diffraction). So, what you have created is poorly constructed YDSE.

2. Here you just need to calculate the resolution of the tube's entrance (1.22 lambda/D). It will cause diffraction, which ruins your directional information argument. Since it's on the order of the size of an interference peak, it's resolution will be on the order of the slit separation, and you can't say anything definitive about which slit the photon traversed.