"My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose" - JBS Haldane
Have you ever gotten a new camera, and decided to finally learn something about how photography works? You know, f-stops, exposure, ISO, all that stuff? I have. Multiple times, actually, because I can't seem to remember it. I'm learning again now. I was trying to figure out how aperture--the size of the hole light passes through in the lens--affects focus. I learned (once again), that the smaller the hole is, the greater your depth of field will be. Not only will your subject be in focus, but the background will be too. Make the hole bigger, and the background will be all blurry. But then I started wondering why that actually happens. Why does light that goes through a little hole stay more focused than light that goes through a big hole? That ignited my curiosity about light and lenses, and before long I had gotten out an old physics book from college to try to wrap my head around all that stuff.
That got me thinking about an idea I've always found fascinating. When you really start looking at how light behaves, it almost starts to seem intelligent. I mean, it's not really, but it gives that impression. Consider this: lenses work because they refract light, which just means they bend light rays. The reason they do is that light travels more slowly in glass than air. If you shine a beam of light through a thick piece of glass (at an angle) and onto a wall, it will bend and slow down when it enters the glass, and then bend again when it leaves. And here's where it gets weird--if a beam of light goes from point A to point B, as shown below, somehow it's able to choose the one path, among the many possible, that takes the least amount of time. That path isn't necessarily a straight line, because if it moves more slowly in glass, then it should alter its course so the distance through the air is farther, and the distance through the glass shorter.
The classic analogy is a with a lifeguard rushing to save a drowning swimmer. Imagine you're that lifeguard, standing on the beach. You look out to your left and see the swimmer in trouble, as shown below. Should you make a beeline--running, and then swimming, straight at him? No...sometimes the fastest route between two points isn't a straight line. You can run faster than you can swim, so you should run a little farther down the beach, so you don't have to swim so far. There's an optimal route that's faster than any other. Most lifeguards won't hit on it exactly. But light is smarter than a lifeguard, at least in that sense. It finds the fastest route, and it does so at, well, the speed of light. It doesn't matter if it has to bend and straighten its way through several layers of air and glass--the path it chooses will be the one that takes the least time.
How does it do that? How does it "know" which path to take? Christian Huygens came up with a plausible answer back in 1678, by thinking of light as moving in a wave, and of a wave front as the combination of many smaller waves. He was able to model refraction that way, as in this image. As the wave fronts approach the glass at an angle, each one changes angles as it slows down and enters. The change in direction will be at an angle that minimizes the time it takes for light to get from one point to another. Huygens was also able to model reflection this way, and a guy named Fresnel applied the idea to other "wavy" phenomena, like diffraction and interference. Nature is full of things that move in waves, and thus behave in all these ways, including water waves, sound waves in the air, and even seismic waves through the earth. Applying the idea to light helped turn the tide of scientific opinion away from Newton's idea theory that light was made of particles, and got physicists thinking of light as ripples propagating through space.
The Huygens-Fresnel idea does seem to provide a mechanism for how light "chooses" the shortest path, and it accurately predicts what that path will be. The problem is, light doesn't really work that way. At least, it's a lot more complicated than Huygens realized. Since the early 20th century, physicists have known that light is as much particle as wave. A beam of light is composed of countless discrete particles called photons. Each one has a frequency, which is what determines the color of visible light. Physicists once thought that brightness (amplitude) was analogous to the height of water waves--brighter light was thought to have higher crests and lower troughs. But it turns out that all photons of a particular wavelength carry the same amount of energy. A bright light is just spewing out more photons per second than a dim light.
This gums up the works for Huygens' wave theory. Even if you send one photon at a time through a piece of glass, light will still pick the fastest path. That's pretty crazy when you thing about it. How can a single particle do that? The simplistic wave theory also falls apart when you look closely at reflection. If you shine a light on a pane of glass, most of it will go straight through. But up to 16% of the photons will bounce back, which is why you see a dim reflection even in transparent glass. Light reflects from both the front side and the back side of the glass, and how much it reflects depends on how thick it is. And that's where it gets crazy once again. If you put a light detector inside a very thick pane of glass and aim a stream of photons at it, you can measure how many photons are reflected by just one surface--the front--and you'll find it's about 4% in most kinds of glass. But if you send the light all the way through the glass, and measure how much is reflected, you find a strange trend. As you keep making the glass thicker, you find that the amount of light reflected will rise and fall regularly--rising gradually from zero up to 16 percent, falling back toward zero, and then rising again. Think about that zero percent. That means, even though four percent of photons bounce off the front surface of glass, if you add a back surface it can cut that percentage to zero. What?? How does the light "know" how far away the back of the glass is when it's just getting to the front? Somehow it does, even if the glass is several meters thick. It's like light isn't just smart...it's psychic.
Of course, it's not really, but the truth is just about that weird. All this stuff is explained by the theory of quantum electrodynamics, or QED. Let's go back to light taking the fastest path through a piece of glass. If I understand it correctly, QED says that each photon takes every path from one point to another--even long ones, where it goes way off to the side and then back again. It spreads out all over the place in a very un-particle-like way, but then arrives as a particle. Each of those paths has a certain "probability amplitude" (the quantum world is all about probabilities) and oddly enough, most of the paths are about equally probable. But the probabilities mostly cancel each other out, except for those very close to the one that takes the least time. So that's the direction the light goes. A similar interaction of probabilities determines how much light will reflect off glass of various thicknesses. That all sounds crazy, and I certainly don't understand it in any deep sense, but apparently the math works just fine. Even physicists who have mastered the equations can't really explain what's going on--they don't understand why those equations work.
But they do work, smashingly. QED describes the quantum basis for most of the physical processes we see all around us; how light moves, how electrons orbit nuclei, how atoms bond together to create different materials...basically everything except nuclear physics, gravity, and certain kinds of radioactivity. Not only that, it's one of the most accurate theories in science. One of the originators of the theory, Richard Feynman, compared its accuracy to measuring the distance across the United States with a margin of error smaller than the width of a human hair. But the theory is also completely mind-boggling. As Feynman also said, "The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is--absurd." Light, and everything else at the quantum level, is pretty freaky stuff. But Feynman had a deep reverence for nature, and I think his point was more about common sense than nature itself. Light is more fundamental and ubiquitous than we are--it's pervaded space and time since the universe began. Looking at nature at a wide angle, we're the anomaly, not light or any other quantum phenomenon. If we find that it's absurd from the point of view of common sense, then we've discovered yet another flaw in common sense. Who are we to say what's absurd?
QED: The Strange Theory of Light and Matter / Richard Feynman
I never explained how depth of field works. Here's a video that does
Good video introduction to QED
An even more mind-blowing, but more widely known, phenomenon of quantum physics is demonstrated by the double slit experiment. Good video on it here.