|MadSci Network: Physics|
I think that the reason you were directed to a previous question on interference is because this is really the only way that two light waves can actually influence each other in the absence of matter. It is possible through superposition for these waves to cancel or enhance each others amplitude at certain points in time and space, but they cannot change each other's direction.
The direction of an electromagnetic plane wave can be changed by reflection or refraction due to interaction with charged particles (i.e. electrons) in matter. I will briefly use the case of reflection as an example:
An electromagnetic plane wave can be described as oscillating electric (E) and magnetic (B) fields at right angles to each other, both perpendicular to the direction of propagation (click here for an illustration). When light hits a mirror, the energy of the E field is absorbed by electrons in the silver, which start oscillating at the same frequency as the incoming light. The oscillation of the electrons causes the energy to be re-emitted as another E field with opposite phase and a new direction. The B field is unchanged. Since the direction of the light is determined by the orientations of the E and B fields, the re-emitted (reflected) light is going in a different direction from the incident beam. (unfortunately I can't find an illustration of this online).
What is the point? What I am saying is that light changes direction by being absorbed and re-emitted by charged matter. Since light is uncharged and massless, light waves cannot cause each other to reflect or refract.
At least, what we normally call light can't do this.
If you crank up the frequency to that of high energy gamma radiation (of the sort produced in cosmic rays or particle accelerators) it IS possible for two very high energy photons to scatter each other. But that is another story, and the photons produce their own charged particles to make this work, so matter is still involved. If you are interested in this, here is an answer I wrote here about photon-photon scattering.
I hope this helps. Please feel free to contact me at firstname.lastname@example.org if you would like further explanations of anything I wrote.
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