electromagnetismvisible-lightwaves
I want to understand what is the physical significance of negative amplitude of a light wave?
In an ac electrical circuit, I understand that negative amplitude signifies the amplitude measured when the electron flow direction is reversed. Now it is easy to visualize and interpret.
Now in a light wave, what does it even mean by negative amplitude? Again, same question with respect to electro magnetic waves?
You are right that the oscillations of the electromagnetic field need not have any spatial extent. The oscillations, as you point out, are in the strength of the electric and magnetic fields. If I understand your question correctly, you are asking why then can some objects distinguish between the two different polarizations of light.
This is because anisotropic materials (those which do not have exactly the same structure in all directions) can act differently to electric fields which lie along their different axes. In the image below the material in the middle does not support an electric field in the horizontal direction. When you try to establish an electric field in the horizontal direction, energy is taken out of the source which is trying to establish it (the light in this case). So, this material, which acts as a typical polarizer, only allows light which is polarized in the vertical direction to pass.
There are other ways to distinguish between the two different polarizations of light. Birefringent crystals, for instance, have a different index of refraction for the two different polarizations of light. They therefore deflect the two different polarizations of light by a different amount.
One has to distinguish the two frameworks: the classical, light; the quantum, photons.
The classical electromagnetic wave, of which visible light is a part of the frequency spectrum, emerges out of zillions of photons, the quantum of light. This happens because the photon has an energy E=h*nu, where h is the Planck constant and nu the frequency of the classical wave that will emerge from zillions of photons . It also has a spin and can be described by a quantum mechanical wave function that allows the build up of the classical wave from the quanta. The energy of the classical wave is the addition of the individual photon energies building up an amplitude.
Is the sine wave just a way to represent the periodic change in field strength, or do the fields occupy a volume such as would be generated by rotating a sine wave about its axis?
The sine wave and cosine wave belong to the classical electromagnetic wave. Not to individual photons. Individual photons have a probability of appearing in space that is described by a sine/cosine wave, but not a distribution of its energy in space time. The photon's energy is one whole quantum. The emergent classical wave has a sinusoidal energy distribution in space time of the same frequency .
Does a light quantum have length, or is it only an instantaneous value at a point in space (and then how can it be red- or blue-shifted)?
The photon has no length, it is an elementary particle . The shift in frequency that is assigned a change in color is an emergent effect from the zillion of photons. For the individual photon, a red shift means a lower frequency/energy h*nu, a blue shift a higher frequency/energy h*nu.
How does the magnetic field component satisfy the requirement that all field lines be closed?
The photon does not have a magnetic field component, it is characterized by the potential entering Maxwell's equations and it will build up the magnetic and electric field components of the emergent classical wave. By itself it is a particle characterized by a probability distribution for its space time location.
Does light even behave like this on a discrete level?
On a discrete level, in the double slit single photon experiments which show interference patterns by individual photons, i.e. the probability distribution manifesting in the build up of the experiment, the emergence of the classical wave that coincides with the quantum frame is displayed clearly.
Best Answer
Exactly what means when you throw a pebble in the water of a lake. A wave appears, and you see that there are "valleys" and higher parts, that spread in circles. There where are valleys the level of the water is negative with respect to the original surface of the lake, and where there are higher parts the level is bigger (positive) than the original surface.
The only difference between the water waves and the light waves, is that in the light, what oscillate are the electric and magnetic field, see picture (electric field - blue, magnetic - pink). To see how these fields evolve in time see e.m. waves .
In the water, if you look at a fix point you see the water going up, reaching a maximal height, then going down, reaching the minimum (most negative level) and so on. With the electric (and magnetic) field in the light it goes the same - look at the figure in the e.m. waves . At a given point in space the electric and the magnetic field increases getting maximally positive, then decreases up to maximally negative, and so on. Just pay attention - the pictures for the e.m. field correspond to linear polarization. Sometime you will learn about circular and elliptic polarization.