How does the double slit experiment ensure phase coherence? I am quite unsure of how phase coherence is ensured in the double slit experiment. The most typical answer that I have found is that the path length difference between the lights going in either double slit is zero, and so the phase is coherent. However, if we consider Young's experiment he used sunlight as his source which is incoherent. So in his setup, even though the diffracted light from the single slit pass through the same path length to reach the double slit, wouldn't the light still be incoherent?
I have seen explanations to this pointing out that the single slit acts as a point source for light and produces phase coherent light. If this is true, how can this be when the sunlight reaching the single slit is out of phase?
 A: I am a fan of Richard Feynman and he used his path integral theory to explain much about light.  He stated that every photon determines its own path .... and the corollary being that a photon will not travel a path if it cannot determine a path. The ideal path, the one of highest probability, is one that has an integer number of wavelengths, i.e. the distance between excited atom 1 and receiving atom 2 is ideally (or actually close to) this length, .... its all about probability.
How a photon determines a path is the result of transmission of forces (virtual photons) .... and real photons that transfer energy in/thru the EM field. It is the actual tight geometry of the DSE (narrow slits, pinpoint source, smooth screen) that only offers limited paths.  Many photons approaching the first slit are actually reflected away ... just like hitting a mirror. The ones that pass satisfy the path integral and make the pattern.
The old classical interpretation is that photons must be in phase to cancel ... but photons never cancel as it would be a violation of conservation of energy.  The classical and path integral theories have a lot of similarities mathematically and thus the classical theory is still taught today .... but you could argue its wrong to call it an "interference" pattern.
