Applications of
Quantum Physics
Implications of
Quantum Physics

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 cos2 hits per second. And if we put in a y polarizer, the detector will record only N sin2 hits per second. (This is in agreement with the |ai|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 cos2 of the measurements and a y photon on a fraction sin2 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 cos2 of the runs, the “x, yes; y, no” version will correspond to your perceptions; and on a fraction sin2 of the runs the “x, no; y, yes” version will correspond to your perceptions. On a given run, quantum physics 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 physics 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.  