There was a prominent family in Pine Bluff named Baim. Well, there still is, but the family's law firm is not quite as well known amongst the locals as the former Baim's department store on Main Street was. I believe the original Baim patriarch in Pine Bluff was Samuel Baer Baim, based on his being the oldest grave among many Baims at Bellwood Cemetery. (Born in 1875, died in 1956. His wife Sarah Baim was born in 1876 and died in 1951.) Anyway, I brought up the Baim name because I'm wondering if it originally was Baym and was Americanized like so many other European names were when a family immigrated here.
Now back to Gordon Baym's 1969 book, Lectures on Quantum Mechanics, a title possibly chosen in homage to Richard Feynman's Lectures on Physics, published in 1963, although Baym's book is a graduate-level textbook and Feynman's is taken from his lectures to freshman students at Cal Tech.
Baym was saying, as quoted in my earlier post, that it is "very weird" that about half the photons in a beam of light get through two polaroids with their axes turned 45 degrees relative to each other. I very much like the fact that Baym even uses the word "weird," because this is in refreshing contrast to most stuffy graduate level texts, which are damn near unreadable--especially two that are widely used whose authors' last names are Goldstein and Jackson. Baym's book is quite readable, and his choice of how to present the subject matter is particularly illuminating, rather like the great Arnold Sommerfeld.
And here's a good example of that, taking up just after his use of "weird," and describing photons of a single frequency when he says "all" :
"--classically we would say that if any photon gets through, then since all photons are identical and all see identical conditions at the polaroid they should all pass through. The only way we can interpret what happens at the polaroid is to say each photon has a probability one-half of passing through. We are really forced into a probabilistic point of view by the fact that the energy of electromagnetic radiation is quantized!"
This is a sort of half-classical, half-quantum description. Classically, a normal beam of light is made up of many individual waves each with its own polarization direction--you can say it has many polarization directions--and a horizontal polarizer, for example, filters out all the non-horizontal components of the beam. In the quantum realm, however, it is hard to visualize how a particle, a photon, can have a polarization. But this is where Baym's discussion is heading: toward a description of photon polarization.
He makes a couple of significant points in getting there, first that there will be fluctuations in the number of photons getting through these two polaroids--the number will not always be one-half, as it would classically, where probability isn't involved--and second that "the photon, if it passes through, emerges...polarized in the x direction!" (The second polarizer in this case is oriented in the x-direction. The exclamation point is there because, if the photons are all identical as presumed, then they are somehow being forced to assume the x-direction polarization.)
Now, what I haven't discussed yet is circular polarization. Yes, the polarization direction, which is the direction the electric field of the light wave is oscillating, can change as the wave travels, rotating as the wave travels, so that it's following a sort of corkscrew or helical path, although not exactly since the field strength is oscillating. Circular polarization can be either clockwise or counter-clockwise (also known as right or left circular polarization, respectively). Now we're ready to look at photon polarization. Baym says
After discussing mathematically the meaning of state vector, scalar product, orthogonality and bases (these are coordinate systems, such as the familiar x-y system), and then showing how a polarization state vector can be expressed in terms of a basis set like x and y or left and right circular polarization, Baym says, "These equations are examples of the superposition principle; we can regard any polarization as a coherent superposition of, e.g., x and y polarization states, or equivalently as a coherent superposition of right and left circularly polarized states."Since all beams of light are superpositions of many beams consisting of one photon each, we shall turn our attention to the polarization properties of single photons. As we have already seen, it will be easy to discover the probability rules for one photon from our knowledge of the behavior of classical beams. The general laws of quantum mechanics are just generalizations of these rules.
The purpose of going through all this, remember, is to make some new discovery or interpretation of the physics of quantum superposition (photon polarization weirdness, Schroedinger's cat, EPR). Still got a long way to go, but progress is being made. Right? Right!
