Free How to Teach Physics to Your Dog by CHAD ORZEL

as short as I can, but this is important stuff. Polarized light is the best system around for giving concrete examplesof quantum effects. We’ll need it for this chapter, and also chapters 7 and 8.”
    “Oh, all right. As long as I can erase stuff later.”
    “We’ll see what we can do.”
SUPERPOSITION AND POLARIZATION: AN EXAMPLE SYSTEM
    We can show both the existence of superposition states and the effects of measurement using the polarization of light. Polarized photons are extremely useful for testing the predictions of quantum mechanics, and will show up again and again in coming chapters, so we need to take a little time to discuss polarization of light, which comes from the idea of light as a wave.
    A wave, such as a beam of light, is defined by five properties. We have already talked about four of these: the wavelength (distance between crests in the wave pattern), frequency (how many times the wave oscillates per second at a given point), amplitude (the distance between the top of a crest and the bottom of a trough), and the direction in which the wave moves. The fifth is the polarization, which is basically the direction along which the wave oscillates. An impatient dog owner out for a walk can attempt to get his dog’s attention by shaking the leash up and down, which makes a vertically polarized wave in the leash, or by shaking the leash from side to side, which makes a horizontally polarized wave.
    Like a shaken leash, a classical light wave has a direction of oscillation associated with it. The oscillation is always at right angles to the direction of motion, but can point in any direction around that (that is, left, right, up, or down, relative to the direction the light is moving). Physicists typically represent the polarization state of a beam of light by an arrow pointing along the direction of oscillation—a vertically polarized beam of light is represented by an arrow pointing up, and a horizontally polarizedbeam of light is represented by an arrow pointing to the right, as seen in the figure below.

    Left: vertical polarization, represented as an up arrow. Middle: horizontal polarization, represented as a right arrow. Right: polarization between vertical and horizontal, which can be thought of as a sum of horizontal and vertical components.
    • • •
    “Wait, what are these pictures, again?”
    “Imagine that you’re right behind the beam of light, and looking down the direction of motion. The arrow indicates the direction of the oscillation of the wave. An up arrow means that you’ll see the wave moving up and down; a right arrow means that you’ll see it moving side to side.”
    “So . . . an up arrow is like chasing a bunny that bounds up and down, while a right arrow is like chasing a squirrel that zigzags back and forth?”
    “Sure, that works.”
    “Are up and to the right the only options?”
    “You can have arrows in other directions, too. An arrow to the left also indicates a side-to-side oscillation, but it’s out of phase with the arrow to the right.”
    “So, a right arrow is a squirrel that zigs to the right first, and a left arrow is a squirrel that zags to the left first?”
    “Yeah. If you insist on examples involving prey animals.”
    “I like prey animals!”

    • • •
    The polarization of a wave can be horizontal or vertical, but also any angle in between. We can think of the in-between angles as being made up of a horizontal part and a vertical part, as shown in the figure above. Each of these components is less intense (that is, it has a smaller amplitude, indicated in the figure by the length of the arrow) than the total wave, but they add together to give the same final intensity at some angle. You can think of this addition as a combination of steps, just like the way that we can get from one point to another by either taking three steps east followed by four steps north, or by taking five steps in a direction about 37° east of due north.
    “So, an