When doing the classic double slit experiment is the time between emitting photons significant at all? Say, a single photon is emitted, the scientist waits T seconds, then emits another photon. Are there any values for T which do not cause interference patterns on the detector?
How about if the slits are closed during the time between photons?
There is no time between photons for which the interference pattern goes away. Even if you send in one photon at a time, and wait until after it has been detected to send the next one, you will still see the detections build up to make an interference pattern.
You can find lots of pages on the web describing experiments where the time between photons is large enough that they do not affect each other. I used the image from this page at Princeton as illustrations in my book, but there are lots of others. You can also do the same thing with electrons, which again, has been done many times, including this version from Hitachi which includes a nice movie of the pattern building up one electron at a time.
No, the interaction between the photon source and the screen does not depend on anything in the future. There is no retrocausality in quantum mechanics.
Of course, you only detect one "position" (in quotes because it depends on the resolution of your screen) at a time. But when you detect many events, even if they are ages apart, the interference pattern will build up.
