Graduate Faraday effect breaks photon interaction laws

[dmerrett]

I was taught that photons ( non-ionizing at least) never interact. So Its really bugging me that most info on faraday effect invokes B field as the cause of ( for example) rotation effects. Since EM-waves (IE Photons) themselves propagate a (oscillating) Magnetic field through infinite space, This means that hypothetically, the magnetic fields of photons can influence each other.
My naïve guess is that what's actually happening is the effect is due to the EM-wave interacting with the matter that produce the B-field. (EG electron rotation in ferrites), and that most explanations are just lazy because the effect is typically explained in DC B fields produced by a source of nearby matter.
Can anyone explain this apparent contradiction?
Thanks. DM

 

[vanhees71]

Note that the Faraday effect refers to in-medium electrodynamics. The effect of the magnetic field is on the charges making up the medium, leading to a modified in-medium Green's function for the propatation of em. waves. In the vacuum within classical field theory electromagnetic fields are non-interacting, because they don't carry electric charge.

BTW: You should not use the word photon in the classical-physics forum, because it's a notion of quantum field theory (or in this case specifically quantum electrodynamics). Indeed in QED there is an interaction between photons, elastic photon scattering (aka Delbrück scattering), which is a higher-order quantum-correction effect (of the order $\alpha^4$).

 

[tech99]

My understanding is that the E-field of the wave causes an electron to move, and it is then deflected by the stationary magnetic field. The electron then radiates a a cross -polarised component. As the effect takes place in matter, for instance in ferrite or in the Ionosphere, I am not surprised that interaction between two frequencies or waves might occur. Interaction would result in creation of additional frequencies. In the Ionosphere it is called the Luxemburg Effect; I have also observed cross modulation in ferrite isolators.

 

[jasonRF]

I was taught that photons ( non-ionizing at least) never interact. So Its really bugging me that most info on faraday effect invokes B field as the cause of ( for example) rotation effects. Since EM-waves (IE Photons) themselves propagate a (oscillating) Magnetic field through infinite space, This means that hypothetically, the magnetic fields of photons can influence each other.
My naïve guess is that what's actually happening is the effect is due to the EM-wave interacting with the matter that produce the B-field. (EG electron rotation in ferrites), and that most explanations are just lazy because the effect is typically explained in DC B fields produced by a source of nearby matter.
Can anyone explain this apparent contradiction?
Thanks. DM

In a vacuum, classical electromagnetic waves do not interact. In matter they can of course interact.

I'll stick to a plasma medium since it can include Faraday rotation. The typical derivation that explains the phenomenon begins with a fluid-theory description that is linearized about a configuration that includes a DC magnetic field and DC charged particle densities. After linearization the model no longer includes wave-wave interactions that are present in the full nonlinear theory. This is not about being lazy. Rather, it allows us to quantitatively understand observations without doing a lot of unnecessarily complicated calculations. Using the full nonlinear theory to understand the propagation of short wave radio signals in the ionosphere would be silly - people who use that approach never accomplish much.

When we are interested in a phenomena that are fundamentally nonlinear (such as wave-wave interactions), then we do not linearize the models. Sometimes other approximations help yield analytical solutions in these cases.

edit:

My understanding is that the E-field of the wave causes an electron to move, and it is then deflected by the stationary magnetic field.

this is the picture that the linearized theory provides. Of course, the wave itself has a magnetic field component which will also deflect the electron, but that is captured in a nonlinear (second-order) term that will usually be much smaller than the first-order interaction of the electrons with the wave E-field and the first-order interaction of the electrons with the DC B-field. If the nonlinear term is large enough then the linearization is no longer justified.

jason

 

[Vanadium 50]

The answer has been posted, but in dilute form.

In the Faraday Effect, the magnetic fields do not affect the light. They affect the medium in which the light travels.