Question

Why two independent sources cannot produce interference?

Answer 1

Because both the source have different wavelength or frequency so it can't produce interferrence....

Answer 2

We usually generate light by black body radiation, that is by heating something until it glows. There are many sources for black body radiation, but the dominant one is usually random thermal motion causing random transient electric dipoles within the black body. The changes in these dipoles generates eletromagnetic radiation, and because the dipole changes are random so is the EM radiation they generate.

If you take two points in the black body that are close compared to the wavelength of the lattice vibrations then their motion, and hence the EM generated, will be closely correlated. However as you increase the separation between the two points the correlation will decrease and at macroscopic distance will be essentially zero.