Light interaction

[Zolar V]

Why is it that light passing through a space does not interact with other forms of light passing through the same space. IE (from feynman: light from you appears to me as color X, but passing through the same space light from person Z to person A. the light waves do not interact with each other.)

Yet if we were to put up a small colored lense light interacts so heavily with it.

[Schrödinger's hat]

Well, there are some interactions between photons, they're very uncommon though.

I'm not sure what level of explanation you're after, one thing that may help is the maxwell equation is linear (the equation for two photons is the same as the equation for 1 photon multiplied by 2 on both sides).

Another way to put it is, particles with integer spin don't interact very often, this is related to the Pauli exclusion principle. This is the reason for the above point, but it gets more into the reasons behind the equations being the way they are.

I'm not really very comfortable with this level of QM yet, so I'll leave it here. Maybe someone more familiar with the subject can help, if you're still having trouble.