It seems like this experiment is possible:
- Fire a photon, and start a timer
- The photon travels through the slit(s)
- The photon strikes a plate -- the timer is stopped.
Based on where on the plate the photon struck, the time it took, and the speed of light, it seems possible to deduce through which slit the photon passed.
Or, would the times correspond with a direct line from the source to destination?