In the standard double-slit experiment, the setup is static, and the interference pattern can be predicted from considering all the potential paths a photon could have traveled. My question is: how long do these possible paths (from the source to the screen) need to exist prior to the photon traveling them? Would it be sufficient for the slits to exist only for the briefest moment the photon can pass through?
Has this type of experiment been theorized or conducted?
Apart from the space separation element, which is unclear, this is the same experiment as sending in a very short pulse of light. The effect is just a broadening of the frequency spectrum of the light. The result is a superposition of diffraction patterns corresponding to the various frequencies with their intensity proportional to the spectral weight.
Your question might be connected with the Wheeler Delayed choice Experiment, where the possible paths seems to change during the photon's flight. Please also check the Elitzur-Vaidman-bomb tester, where this possibilities are changed in a more dramatic way.
Both articles will guide you through thought experiments where the possible paths changes during the experiment and what is the possible interpretations about it. Basically, the intuition that photons should have well pre defined trajectories in the beginning of the experiment fails and we should always avoid counter-factual reasoning to understand these experiments.
