Light rays don't interfere with each other

[kent davidge]

In the ray model of light we learn that two light rays don't interfere with one another. That is one crosses the path of the other and both follow their path as they were doing before.

In terms of quantum theories could we say that in this situation the electromagnetic field is not interacting with itself?

 

[DrClaude]

This has been discussed in other threads before. For instance,

I was using the word "linear" in a more restricted sense. The "bare" QED Lagrangian is linear in the sense that its only interaction term $\bar{\psi} \gamma^\mu A_\mu \psi$ just has one power of the EM field $A_\mu$. In other words, there are no first order two-photon processes, i.e., no vertex where multiple photon lines meet.

But there are, as you note, nonzero contributions to the photon-photon scattering amplitude from higher-order processes; the diagrams for these processes involve multiple vertices, at each of which there is just one photon line. (@vanhees71 made a similar point in post #3; as he notes, the actual amplitude for photon-photon scattering, taking into account all of the higher order processes, is very small.) I agree, in the light of both of your posts, that QED is nonlinear in this sense, and that this sense of "linear" vs. "nonlinear" is more appropriate for this thread.

Photons can in fact scatter off each other "indirectly", via intermediate virtual electron-positron pairs. See e.g. page 4 (problem 3) of this document:

http://faculty.ucmerced.edu/dkiley/Physics161Fall2011HW2solns.pdf

The cross-section (i.e. the probability) is very small because the Feynman diagram has four vertices as opposed to only two in electron-electron scattering.

 

[kent davidge]

I would like to take a full look at these quoted threads if you provide me with the links.

 

[kent davidge]

(@vanhees71 made a similar point in post #3; as he notes, the actual amplitude for photon-photon scattering, taking into account all of the higher order processes, is very small.)

As I suspected

 

[DrClaude]

Clicking on the arrow $\uparrow$ after the "said:" will bring you to the quoted post in the original thread.