[Physics] Why don’t electromagnetic waves interact with each other

Question

My exact question is that what refers to this phenomenon? I saw also Richards Feynman's video in that he talks about light and says that if we look at something those light waves that come from that thing are not disturbed from any other electromagnetic waves and explains this kind of way that if I can see things clearly, in front of me, although if someone stand in the right of me, can also clearly see any thing in the left of me, our light waves cross each other but the are not disturbed by each other. This is a kinda cool explanation but I don't understand that exactly, because I am not convinced that if those two electromagnetic waves would interact then I couldn't see the thing in front of me clearly

Answer 1

Here are three explanations of how to understand “why” electromagnetic waves don’t directly interact electromagnetically with each other, which are all equivalent to each other:

1. Maxwell’s equations are linear in the electric and magnetic fields, and in their sources, so the superposition of two solutions is also a solution. (For example, in Coulomb’s Law you can just add up the fields of multiple charges.)

2. Photons do not carry any electric charge and do not have their own electromagnetic field. (Note: By contrast, gluons do carry color charge and do interact with each other.)

3. The gauge group for electromagnetism is an abelian (i.e., commutative) group. (Gauge groups are something you learn about in more advanced physics courses.)

Notice that I said photons don’t directly interact with each other. They do indirectly interact via virtual electrons and positrons (or other charged particle-antiparticle pairs). Until you get to extremely intense electric and magnetic fields, this is a very tiny effect and was only recently measured.

An even tinier effect, which we will probably never be able to detect, is the gravitational interaction of electromagnetic waves or photons. Physicists believe there would be a gravitational interaction because electromagnetic waves and photons carry energy and momentum, even though photons are massless.