While we're at it, Feynman figured out something about polarization of light and complex numbers that he seemed to view as the best illustration of why complex numbers are "real". An attempt at a lay explanation appears in Jim Ottaviani and Leland Myrick's 2011 graphic biography "Feynman". I couldn't make sense of it. Jim Propp On Thu, Jun 4, 2015 at 10:48 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Join the club! I found this link enlightening, but it's surely only a start --- particularly regarding quantum-theoretical aspects (which I haven't even attempted to address yet).
https://en.wikipedia.org/wiki/Polarization_%28waves%29
WFL
On 6/4/15, Allan Wechsler <acwacw@gmail.com> wrote:
This whole discussion has exposed an area of deep ignorance in my physical knowledge. I find myself now not sure whether polarization is an ensemble property of a whole cohort of photons, or whether it is something one can attribute to a single photon, and how much "state" there is at each level. After about ten minutes I declared myself utterly incapable of thinking about the problem, and if someone has an elementary reference to point me at, that would be greatly appreciated. (Or, if somebody could hazard a math-fun-level explanation of the basic concepts, that would be even better!)
On Thu, Jun 4, 2015 at 12:00 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
A monochromatic beam of light may be resolved as the sum of two linearly polarised beams in perpendicular planes, their phases displaced by some constant angle p . The device must reverse this displacement, delaying (say) one linear component by angle 2 p .
Now consider an individual photon in such an input beam. The corresponding output phase must somehow be smeared between values at separation 2 p , in general impossibly. So sticking my neck out, I conclude that
*** Salamin's demon (or genie?) is nonexistent. ***
Caveat: my regrettable ignorance concerning elementary physics in general and optics in particular has been only barely perceptibly ameliorated by wrestling with this engaging problem. But even if I have (once again) blown it above, at least I now understand circular polarisation: an ultimately simple business which previously appeared ineffably mysterious.
Fred Lunnon
On 6/1/15, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Here is a puzzle concerning the optics of polarized light. Every state of polarization has its opposite. For linear polarization, it's linear but rotated 90 degrees. For circular polarization, it's circular with opposite helicity. For general elliptic polarization, it's elliptic with the ellipse rotated 90 degrees, and the helicity reversed. On the Poincaré sphere, opposite states of polarization are represented by diametrically opposite points. The puzzle is to construct an optical device that reverses the polarization state. For any input, the output is the opposite polarization. Or, prove that it can't be done. -- Gene
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