OOOH! QM is onne of my very most favoritest topics in the whole world ever and stuff! I get so excited, my grammar goes to poo.
It’s been a few years since I did any QM study, but I’ll give this one a go!
You have a nice idea for an experiment, but let’s look at its most essential features:
1) Partial coverage of the “impact area” of photons against a screen (say, a photographic plate) by a directionally sensitive set of detectors.
2) It is sufficient to detect if a given photon came from ONE of the slits, for if it did not, it must have come from the other. Your detector is simply a means of determining trajectory direction, rather than simply incidence (or *splat*) location.
3) Full coverage of the detector area would correspond to having a single detector closer to one of the slits.
Quantum mechanics tells us (or at least quantum mechanicists tell us, or write to us, or have their people tell our people) that you cannot know both the position and the motion of a quantum thingy with simultaneous arbitrary precision. Similarly, an entity cannot exhibit particle-like and wave-like pheonomena simultaneously vis-a-vis its interactions with the universe (or, specifically in interactions with an observer).
One of my favorite explanatory frameworks for the Young double-slit experiment is electron interference. Since elctrons have charge, they can be measured more easilly then photons - yet their duality makes experiments with them qualitatively identical to those with photons.
Imagine eletrons passing through a double-slit screen. We can put an itsy-bitsy metal loop just in front of one of the slits, and thus detect when an electron exits that slit. When this is done (and in essense, it has been done), the interference pattern on the whole screen vanishes, and one gets two dogpiles of electrons from the two slits rather than interference bands. If one takes away the itsy-bitsy metal loop, the interference pattern returns. This happens even if the other slit is left unattended (un-detected).
Your directional detector seems to me to take the place of the itsy-bitsy metal loop. Assuming it can determine that a photon came through one slit or the other (though the notion of “determine” is a bit loose here), it would “cause” the interference pattern to vanish for the entire viewing screen or target area.
This leads me to think about one of the coolest things I learned: If you send one photon (or electron, or neutron, etc.) at a time through the slits, over time an interference pattern will show up, even though each “particle” causes just one little *splat* on the detector screen. Put a itsy-bitsy loop in, and the pattern vanishes. It’s as if the particles “talk” through time. Such time-independent correlation behavior spooks the heebie-jeebies out of a lot of phsyicists, from a metaphisical standpoint. It’s been a cause of such wild ideas as the “many-worlds” theory, and nonlocality (e.g. trans-luminal signaling).
I have some of my own crack-brained notions about how to interpret the whole ball of cookies, but that’s going too far afiled for the time being.