Carrier wave double slit experiment

[kurt101]

If you created the following double slit experiment would you still see interference?

1) Modify the slits so that the path from photon source through one of the slits to the detector is much shorter than the path through the other slit.
2) put a shutter in front of the photon source so that you can precisely coordinate photons leaving the source with photons arriving at the detector.
3) After opening the shutter. only keep the photons that could have arrived through the shortest path.
4) Close the shutter long enough for photons to stop arriving at the detector and repeat starting at the previous step until you get a pattern.

The purpose of the experiment is to make sure there is not a carrier wave initiated at the photon source that causes the interference pattern you see in the double slit experiment.

 

[kurt101]

It occurred to me right after I wrote the question that because you have knowledge of which way the photon took you would not get interference. So based on this experiment you could not eliminate the possibility that there is a carrier wave.