11 June 2011

Yin, yang, and superposition (a beginning)

On May 5th I raised the question, "what is light?"  I meant visible light, and my answer would be that it's a cacophony of electromagnetic expectorations from atoms.  
I also said I'd be discussing photon counting next, but that will have to wait. Also, CCDs, not yet mentioned here but ubiquitous in the world of photography, will have to wait.  The first order of business will be quantum superposition, and a good place to start is with the detection and suppression of polarized light.  The interesting and very peculiar thing about superposition is that a polarized component of light that you were sure you had suppressed or killed off is able to reappear later on down the line when you look again.
Most light we see is unpolarized, or you could say randomly polarized, but quite a bit of sunlight reflected from glass surfaces (car windshields, etc) and bodies of water (lakes, etc) is polarized, which is what allows polarized sunglasses to do their thing in helping eliminate or reduce glare, a very desirable thing for driving and water sports (fishing in clear water, for instance, where polarized sunglasses allow one to see under water better) and snow skiing.
To visualize what polarized light is, first think of a symmetrical cross, like the Red Cross.  Now imagine it to be so skinny that it’s just a horizontal line and vertical line, or in math language, an x-y coordinate system.  A light wave consists of undulating (sinuous you could say) electric and magnetic fields.  For a horizontally polarized beam of light coming toward you, the electric field is undulating horizontally, along the x-axis. To get a feel for what this means, hold out your hand, palm down, and move it right and left.   That’s analogous to what horizontally polarized light is doing, and reflected glare largely consists of horizontally polarized light.  Look up Brewster's angle.
Now imagine yourself behind bars, or in front of them, moving your hand back and forth horizontally while trying to pass it through the bars.  Can’t do it!  Polarized sunglasses act like vertical bars against the passage of horizontally polarized light.  Now if you turn your hand so your palm faces left or right  and move your hand up and down, you're mimicking vertical polarization.  Vertically polarized light is all that gets through polarized sunglasses lenses. Unpolarized light, what we encounter inside and outside most of the time, has components horizontally polarized, vertically polarized, and polarized along all the angles in between horizontal and vertical.  Now try imitating that with your hand—easy, but you look like a nut doing it.   This motion should be centered on the center of the cross, meaning your hand is supposed to be passing through the origin (0, 0) of the x, y coordinate plane.  And don't move your hand closer or farther away from your body while you're doing this!  That's better.  Earlier I said to imagine the light coming toward you, but as long it's either coming  directly at you or moving directly away from your body, along the + or - z direction, your hand motion is representing the undulations, the increase and decrease of the electric field as the waves move toward or away from you.
So, a polarized sunglass lens acts like a filter, only allowing vertically polarized light to pass through.  Those waves with polarization angles between vertical and horizontal, well, the filter only allows the vertical component of their electric field to pass through.  (For instance, imagine an arrow pointing northeast.  Yeh, mapwise north is positive y and east is positive x. So this northeast-pointing arrow is leaning at 45 degrees from the vertical, hovering 45 degrees above the horizontal, and so has equal vertical and horizontal projections or components. Other polarization angles have smaller or larger x and y components, depending on whether they're closer to vertical or to horizontal.  So there.)

Here’s a little experiment you can do with polarized lenses from a pair of sunglasses:  take ‘em out, hold ‘em up, one in each hand, and put one in front of the other.  Turn one of them clockwise or counter-clockwise, and observe how much light is getting through both lenses.  If you have them turned 90 degrees relative to each other, no light will get through.  Just what you expected, right?, since their polarization axes are perpendicular.
In different words: the original light is a mixture of yin-light and yang-light.  As I was saying in more standard terminology two paragraphs ago, everything in between yin and yang can actually be partly projected on the yin axis and partly on the yang axis, so all directions in this plane are taken care of by only talking about yin and yang (or, sure, x and y components). Let’s say the first lens is a yang-type filter—all that’s left of the original light is its yang-light once it has passed through this lens.  If the second lens is a yin-type filter, it’s going to stop any yang-light. But that’s all that is left, so no light gets through.
The mystery occurs when a third polaroid lens is placed between the yin and the yang lenses, with its polarization angle aligned somewhere in between the perpendicular axes of the yin and yang.  Now some light does get through all three of these lenses!  The yang-type filter has, we thought, suppressed or killed off any yin-light.  But somehow the in-between filter, turned at let’s say a 45 degree angle to the yin and yang filters, brings back to life the supposedly killed-off yin components, allowing them to pass through the final filter. 
The first book I read on this subject was The Dancing Wu Li Masters, by Gary Zukav.  I read it in the summer of 1980, and don’t recall him using the yin-yang analogy in this context.  But he probably did.  I’ll have to check on that and get back with you, and also, when I get back, explain how this three-polarizer set-up is  an example of quantum superposition.  Meanwhile, summertime beckons.