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Imagine that there is a photon detector in front of me. Also imagine that there is a test photon traveling from my left to my right. As this test photon passes, I fire other photons right at the detector (perpendicular to the path of the test photon).
Would I see an interference pattern on the detector in front me similar to the double slit experiment? Can I use this information to test the path and momentum of the test particle?
I think you would not. In the wave theory photon which is moving from you represents as a wave which E-vector oscillates in the flat perpendicular to the you-detector line. And another photon, which is moving from left to right represents as a wave moving from left to right with E-vector oscillates in the flat perpendicular to the line left-right but parallel to the you-detector line. Therefore E-vectors of this waves oscillates in the perpendicular flats and would not interfere with each other.
Maybe this interpretation is not quiet compleat because of a finite-time of the radiation of photon from you to detector which in this case represents not a plane wave but a more complex structure.
