Theoretically,if we perform the double slit experiment with single photon source then after a long time we can see the interference pattern same as it will be if we had done it with two coherent sources.
In case of the single photons propagating in space there is no issue of coherence as they are completely separate and emitted by the source after some finite time,in other word,they are incoherent.
But if we do the same experiment with incoherent source we won't be able to see any kind of interference pattern. Doesn't this violent the rules of statistical regularity?For single(incoherent) photons,the position they end up is probabilistic,but for lots of such incoherent photons coming at same time,the probabilistic nature remains no more.This shows that the position of each photon are not independent events.So there should be some interaction.Is there?