Saturday, June 4, 2011

Photon Polarization

A calcite crystal laid upon a paper with some letters showing the double refraction

A recent paper on double-slit trajectories tilted

Watching Photons Interfere: "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"

is featured at Chad Orzel's highly educational and entertaining weblog, Uncertain Principles, here
It's entertaining as well as informative, but not overly so if one refreshes and bones up or learns for the first time what "photon polarization" is.

The mathematics of Photon Polarization are not difficult, and Photon Polarization is an important field. Its entry in Wikipedia is quite long, so I leave with the introduction and contents of the Wiki article and wish you all great joy exploring on your own:

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized. Their polarization state can be linear or circular, or it can be elliptical, which is anywhere in between of linear and circular polarization.
The description contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well, and forms a fundamental basis for an understanding of more complicated quantum phenomena.
Much of the mathematical machinery of quantum mechanics, such as state vectorsprobability amplitudesunitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description.
The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave.
Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.
Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with two pairs (or one broken pair) ofpolaroid sunglasses.
The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (calledspin), as well as energy, with the photon.



1 comment:

Phil Warnell said...

Hi Steven,

If one is content with the answer “because’ being given to one’s queries then the standard answer might seem to be adequate. However, if one would like to know “what” things are, “how” they are and even perhaps “why”, then it fails as being an answer which should be considered as reasonable. Somehow positivists find much comfort in this and yet for the “honest” realist it is quite the opposite.

“One might still like to ask: “How does it work?. What is the machinery behind the law?” No one has found any machinery behind the law. No one can “explain” any more than we have just “explained” . No one will give you a deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced.”

-Richard Feynman, “The Feynman Lectures on Physics”, Volume 3, page 1-10 (1965)

“But in 1952 I saw the impossible done. It was in a paper by David Bohm (5). ....... But why then had Born not told me of this ‘pilot wave’? If only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing ‘‘impossibility’’ proofs, after 1952, and as recently as 1978? . When Pauli, Rosenberg and Heinsenberg, could produce no more devastating criticism of Bohm’s version than to brand it as “metaphysical” and “idealogical”. Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?

-John Stewart Bell, “On The Impossibility of The Pilot Wave”, CERN, Geneva, Ref.Th.3315-CERN (1982)