Polarization of Light: 2 Degrees & Longitudinal Electric Field

[captain]

I have question about the two degrees of polarization of light. I know for a fact that light has only two degrees of polarization for a fact, which just means that light is transverse, but i want to understand what does the longitudinal electric field that you get from a columb field mean really. I have been told there are no degrees of freedom associated with it but i am still not clear. I have also heard that electric and magnetic fields are made up of photons but this static electric field doesn't seem to be made up of photons since its longitudinal and photons don't have three degrees of polarization. What does this mean? Also if you have moving particle, you can boost to frame in which it's stationary and from that rest frame it will look as though the particle emits a static electric field with no magnetic field. If someone could really clarify all of these misconceptions that would be much appreciated. Thanks in advance.

Edit: I am not sure if this is supposed to go in quantum or classical. I am guessing that its quantum.

 

[RedX]

that's a good question and I'm not quite sure I know the answer.

far from any charges, light, which is the electromagnetic field, has only two polarizations - nothing quantum about this, this is what Maxwell's eqns. say.

when charges are brought forth, the electromagnetic field is different, there are fields that don't propagate like light. light in free-space obeys a differential equation that tells you how it varies in space, independent of any charges.

that this additional non-light electromagnetic field has zero degrees of freedom means that it's uniquely determined by specifying how the charges are moving. light does not have this uniqueness, because then you say there is no charges at all, but the electromagnetic field is not specified - you can have light here, or there, or over there, etc.

add: you can always add the solutions of light in empty space to space where there are charges.. in differential equation-speak, there are infinitely many homogeneous solutions, but one particular solution, and this particular solution is the zero degrees of freedom that result from adding the charges which makes it nonhomogeneous. Or something like that.