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OK, what about light propagation according to the path-integral formulation of quantum electrodynamics? That's complex in quite a literal sense, though unfortunately "complex" isn't a top-1000 word so I had to say it a different way. Anyone who's read Feynman's lovely book "QED" will recognize the approach. To find how a bit of light goes from one place (at one time) to another (at another time), look at every way it could take, straight or not. Imagine a little line that starts by pointing to the right and that turns as the bit of light goes along: if it goes two times as far, the line turns two times as much, and so on. But the line is always, say, one foot long. Now, do this for every way the light could go. Take all those lines and lay them end to end, and see how far the two ends are. The further they are from one another, the more light gets to that place at that time. (Of course you can't really do this because there are too many lines to lay end to end, but you can look at only some of the ways the bit of light could go, and then look at more, and more, and you will find that the answers change less and less. As long as you look at enough ways, you will get about the same answers for where the light goes.) You may have heard that light goes in straight lines, and how far it goes in a given time is always the same. You can work that out using these ideas: what happens is that for a way the light could go that is not straight, or that goes too far or not far enough for the time it takes, if you change them a bit then the turn in the line changes a lot, so when you add up the lines for these slightly changed ways the lines all point different ways and when you lay them end to end you get something much shorter than if they all pointed the same way. But for the straight line that goes just far enough for the given time, it happens that a small change in the way the light goes makes a smaller change in the way the line turns, so when you add up the lines for these slightly changed ways you get something that is still very long because the lines all point about the same way. And that means that, if you fix how long it takes, the places the light can go in a straight line, going just far enough for the given time, are places that make the lines add up well, so lots of light goes there. But for all the other places in the world the lines do not add up well because they all point different ways, so very little light goes there. And that is why light goes in a straight line and always so far in a given time. The same ideas tell you why light does what it does when it meets a mirror. And they tell you why, by blocking off some parts of the mirror so that light that reaches them disappears, you can actually make more light go to some places than if the whole mirror were still there. The color of the light comes from how fast those little lines turn around. When you block off some parts of a mirror, the ways the light likes to go (that is, the ways for which the little lines end up all pointing about the same way) will change with how fast the lines turn. So light of different colors goes different ways, and if light falls on one of these blocked off mirrors you see red in one place, blue in another, and green in the middle, like when it rains and you look away from the sun. Those round things with music on are like mirrors but with little bits blocked off (that is how the music is stored on them, but that is another story), which means that when light falls on them you get the same red-then-green-then-blue thing. Pretty! And all because of the way those little lines go around and you add them all up. |