Question

Even if the double slit experiment gives interesting (weird) results, it only concludes that each photon interacts with itself after passing the two slits. I have been thinking about a different experimental setup, where you have two well defined light sources (with specific wave lengths and phase) but no slits. And now to my questions: Has anyone ever done such an experiment, and will there be an interference pattern on the wall?

If the answer to the second question is "no", light can not be a true wave - it only has some wavelike properties. But if it is "yes", things become much more interesting.

If there is an interference pattern on the wall, there has to be an interference pattern even if both light sources are emitting single photons at random, but as seldom as, say, once per minute. That in turn would mean that the photons know about each other, even if they are separated in time with several seconds, and the light sources are independent (not entangled).

Answer 1

I am answering to the second part of your question, since the first has been covered two days ago. Have a look at interfering laser beams, and read up on holography, the ultimate in interfering beams.

even if both light sources are emitting single photons at random, but as seldom as, say, once per minute. This is wrong. For interference to happen the phases must be kept. Individual photons do not keep the phase with another photon a minute later, so no interference pattern will appear. In contrast to the double slit experiment, where each photon interacts with the slits, in your two beam experiment each photon from one beam has to interact with a photon from the other beam for an interference pattern to appear.

A laser beam appears because of induced deexcitation from the pumped up levels of the atoms of the crystal/gas. By construction more than one photon is needed to start the cascade. Without a cascade there are no phases.