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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).

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Did You read this: physics.stackexchange.com/questions/6234/… –  Georg Mar 4 '11 at 11:14
    
I am voting to close it as an exact duplicate. The only difference is that Alexander confuses the verbs "interact" and "interfere". They're very different things. A single photon surely doesn't "interact" with itself. –  Luboš Motl Mar 4 '11 at 11:34
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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.

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I don't know whether this answer really addresses the question the OP was intending to ask. Very weak laser light (so on average there is a photon once per minute) is not the same thing as emitting single photons at random. If two lasers have stable enough phases, even if the beams are attenuated to one photon per minute, you should observe interference. –  Peter Shor Mar 4 '11 at 17:21
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@Peter Shor: The phase canonically conjugate to the photon number, and a really precise restriction on the photon number such as emitting one photon a minute would induce an uncertainty in the phase by the undcertainty principle. –  Jerry Schirmer Mar 4 '11 at 18:36
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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. –  anna v Mar 4 '11 at 19:36
    
@anna: But you can attenuate a laser beam by putting it through beam splitters to get very weak coherent light. –  Peter Shor Mar 4 '11 at 23:20
    
then Jerry's comment above holds.Though I would think that logically one would need at least two photons in a beam to carry a phase information, no? The phase is with respect to the beam. See en.wikipedia.org/wiki/Coherent_state , where it is demonstrated that delta(theta)*delta(n)=1/2 . I was just commenting that one cannot emit a photon per minute. To define a phase one needs at least two photons. –  anna v Mar 5 '11 at 5:53
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If the energy is large enough, photons interactively create massive particles. So yes photons do interact.

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Even with low energy photons, there are virtual loops and photon photon interactions can happen with some probability: –  anna v Mar 5 '11 at 7:23
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