Applications of

Quantum Mechanics

Quantum Mechanics

Implications of

Quantum Mechanics

Quantum Mechanics

32. Light, Photons and Polarization.

Summary

The polarization states of photons are explained. Polarization experiments on light are described.

A photon is the name given to a ‘piece’ of light. In this treatment, where it is justifiably assumed there are no particles (see No Evidence for Particles), it refers to a wave function with mass 0, spin 1, and charge 0. Each photon (wave function) travels at the speed of light. If it has wavelength , its energy is hc/ and its momentum is h/ where c is the speed of light and h is Planck’s constant.

Each photon has two possible states of

*polarization*, which is analogous to spin or angular momentum (See Spin and the Stern-Gerlach Experiment). This can be visualized in the following way: A photon can be thought of (at least classically) as consisting of oscillating electric and magnetic fields. If a photon is traveling in the z direction, its electric field can either oscillate in the x direction, so the photon is represented by x, or its electric field can be oscillating in the y direction, so it is represented by y. These are the two states of polarization.

It can also be polarized so its electric field oscillates in any direction, say at an angle to the x axis. In that case, the photon state can be represented as a (linear)

*combination*of the x and y polarizations,

(32-1)

There are certain materials (such as Polaroid) that act as filters in that they let through only that part of the photon polarized in a certain direction. Schematically, in terms of the wave function, if we have a polarizer P,x that lets through only x photons, then the y part is blocked, so(32-2)

What this translates into experimentally is the following: Suppose we have a beam of light that contains N photons in state (32-1) crossing a given plane per sec., each moving at the speed of light. Then a 100% efficient detector put in the beam will record N ‘hits’ per second. But if we put an x polarizer in the beam, as is done schematically in (32-2), the detector will record only N cos^{2}hits per second. And if we put in a y polarizer, the detector will record only N sin

^{2}hits per second. (This is in agreement with the |a

_{i}|

^{2}probability law of principle [P10] in The Probability Law.

Thus the polarization state of Eq. (32-1) acts

*as if*it were composed of both a photon polarized in the x direction

*and*a photon polarized in the y direction. But if we measure, we find an x photon on a fraction cos

^{2}of the measurements and a y photon on a fraction sin

^{2}of the measurements, but we never find both an x photon and a y photon on a single run! Not so easy to understand!

There are crystals that can separate the photon into its x and y polarization parts, so that the x polarized part travels on one path and the y polarized part travels on another path. One can put a detector in each path, and one can have an observer that looks at each detector. If we send a single photon, in state (32-1), through this apparatus, the wave function of the two detectors plus the observer is still a sum of just two terms:

(32-3)

But now the whole ‘universe,’ photon, detectors and observer, has split into two states. In particular, if you are the observer, there are two states of you! On a fraction cos^{2}of the runs, the “x, yes; y, no” version will correspond to your perceptions; and on a fraction sin

^{2}of the runs the “x, no; y, yes” version will correspond to your perceptions. On a given run, quantum mechanics does not say which version will correspond to your perceptions. So this experiment and the state of Eq. (32-3) give another example of quantum mechanics presenting us with more than one version of reality—one version of you perceiving polarization x

*and, at the same time*, another version of you perceiving polarization y.