In Young's double slit experiment, if the two slits are illuminated with separate sources, no interference pattern is observed because

In conventional light source, light comes from a large number of independent atoms, each atom emitting light for about 10–9 sec i.e. light emitted by an atom is essentially a pulse lasting for only 10–9 sec. Light coming out from two slits will have a fixed phase relationship only for 10-9 sec. Hence any interference pattern formed on the screen would last only for 10–9 sec, and then the pattern will change. The human eye can notice intensity changes which last at least for a tenth of a second and hence we will not be able to see any interference pattern. In stead due to rapid changes in the pattern, we will only observe a uniform intensity over the screen.