Back in my sophomore year at college, I saw one of the most beautiful things I’d ever seen.
It was an equation on the blackboard in my quantum mechanics class.
Yes, you’re right. I was popular with the ladies.
My professor, Dr. Bill Reay, showed the class that day exactly where the uncertainty principle comes from. It wasn’t how Heisenberg derived it, but it was a beautiful derivation based on two things: one, classical wave mechanics; and two, the crazy idea that electrons can behave as waves.
As soon as that idea is unleashed on the world, uncertainty comes along automatically. It is amazing in its beauty and simplicity. I wrote about it once before, but I want to try again.
First imagine an electron as a wave. What in the world does that mean? Well, an electron as a particle would occupy one discreet place in space. It is there absolutely, and is absolutely nowhere else.
If you give an electron wave properties, it still has to behave like an electron. Electrons are generally one place and not another. Sort of. Think of an electron as a “wave pulse.” Here’s a picture.
The key thing to realize is that the electron is mostly still in one general place. The line (which could represent space as easily as time) stretches off to infinity in both directions pretty much on zero. So there’s (pretty much) no electron back there <– or up there –>, only in the middle is there a good chance of finding the electron.
Now that the electron is a wave, though, some strange things start to happen. We make the wave pulse by adding up lots of waves together. This is called superposition. The superimposed waves essentially cancel everywhere except in the general area where the electron is. But each of these superimposed waves has a slightly different wavelength. It’s the difference in wavelength that causes the canceling, and that wavelength difference gives us a range of uncertainty about the electron.
Suppose we make that wavelength difference smaller. What happens to our wave pulse? It spreads out! We’re less certain of the location of the electron if we know its wavelength better. Suppose we make the wavelength difference greater? Now we can locate the electron better, but we know much less about its wavelength. These two variables, position and wavelength (and for an electron, wavelength matches up with momentum), are like silly putty. If you squash it one way, it comes squirting out somewhere else. There’s an inherent uncertainty in an electron (and any other particle-wave) that you just can’t get rid of. That’s the uncertainty principle!
This is to me the beauty and wonder of quantum mechanics. It is exactly classical mechanics, with this one, historical, bizarre idea. Particles have a wavelength! Once you get that, all the weirdness of quantum mechanics, living/dead cats, quantum entanglement, the double slit experiment, all of it, comes along for free. From just one weird thought. Now THAT is beautiful.