Question regarding the three polarizer paradox

[sophiecentaur]

My bad. I thought it was a QM-only thing.

You don't use QM to describe what happens in your VP VHF boat antenna. RF electromagnetism make so much more sense when people want some 'understanding'. You can 'feel' the currents flowing and the result of tilting an antenna.

 

[Dale]

I think a better picture is to think of the polaroid as an array of antennae that are driven by the incident wave to emit a new wave.

I had never heard that before. Very Huygens-like.

 

[Ibix]

I had never heard that before. Very Huygens-like.

Really? I thought it was a fairly standard explanation of how wire grid (and similar) polarisers work, an anisotropic relative of the usual explanation of why EM waves don't penetrate metals. The charges can't move very far across the grid.

 

[vanhees71]

Usually the treatment is using "macroscopic electrodynamics", i.e., Maxwell's equations for $\vec{E}$, $\vec{B}$ and $\vec{D}$ and $\vec{H}$ with consitutive equations motivated from linear-response theory (in very advanced special treatments the latter derived from quantum many-body theory). Then of course the microscopic picture that the electromagnetic field is due to the superposition of the incoming (external) em. field and the em. field from the motion of the charges in the material.

For a treatment in the latter spirit see the very nice textbook by Schwartz:

M. Schwartz, Principles of Electrodynamics, Dover Publications (1972)

It's a bit like a book with the didactical intentions of Purcell in the Berkeley physics book done right, though there are still some rough edges in there (e.g., the use of the concept of "relativistic mass").

 

[Demystifier]

Argh! That's also a paradox now. Well, I've to reformulate next week's problem set for my students to make them solve a paradox rather than some projection operator applications ;-)).

Well, it's always more fun to solve a straightforward problem when it is presented as a "paradox". At least to me.

 

[sophiecentaur]

Well, it's always more fun to solve a straightforward problem when it is presented as a "paradox". At least to me.

That's probably true. It can bring out your argumentative side and makes you more determined to disprove the paradox. Everyone loves a Devil's Advocate.

 

[Andy Resnick]

Can it be explained classically?

Yes, using Jones vectors. The 3-polarizer setup is a very useful (and classical) way to demonstrate the behavior of spin-polarized atoms in magnetic fields. The Pauli spin matrices serve double-duty as Hermitian polarization operators.

The central concept common to both is 'change of basis states'.