 The tendency for electrons to form interference fringes when you put them through two slits, but arrive in little blobs, leads some people to describe them as having a wave-particle duality, as though they're confused. But if we just give up the baggage of whether it's a wave or a particle, an electron is an electron. It is what it is, and we're learning about its properties. Let's just think about those properties. So in order to make an interference pattern, it has to go through two slits at once. If you cover up one of the slits, you don't get an interference pattern in the end. If you cover up the other slit, same. Only when they're both open at the same time, even if you're only putting one electron through at a time, that's the only time you get that interference pattern. So somehow each electron is individually knowing about both slits. But they're also arriving in blobs. So either we've got some kind of method of blobs knowing mysteriously whether the other slit is open, or it's actually traveling as a wave, and then for some reason becoming a blob. And if you look at which slit it's going through, so if you just, rather than covering up a slit, you just look, then it turns out that also makes the interference pattern go away. And so the final conclusion that we came to for quantum mechanics is that an electron is a wave, but when you look at it, that wave function collapses and gets very small, and so you get a very small wave when you look at it. And the tendency for things to change their behavior when you look at them makes a lot of people very uncomfortable. And if you're uncomfortable with that idea, you're in very good company. When we first started talking about two slit interference, we were trying to figure out where the light was a wave or a particle. Well, it turns out that if you turn down a light beam when you're making this beautiful two slit interference pattern, you also see these blobs appear one by one. And so quantum mechanics doesn't just describe electrons, it also describes light, and those little blobs are called photons. And in fact, absolutely everything in the universe seems to obey the laws of quantum mechanics. So everything, all kinds of matter, all kinds of light, everything appears to travel as waves, and when you look at them, it jumps. So quantum mechanics is the model for all stuff in the universe. And in fact, two slit interference has been performed on molecules containing almost a thousand atoms. So if quantum mechanics really applies to everything, big and small, then the real question shouldn't be, well in that case, why is the theory so weird? The real question should be, so why are things so simple? Why haven't I seen this strange behavior before? If I'm actually a wave and I can walk through two doors at once, then I ought to have noticed that by now. And the answer to that is that big things, things like pens and people and pebbles and so forth, have a very, very small wavelength. It turns out if you do these measurements that the wavelength is inversely proportional to the momentum of the object. So our wavelength is going to be measured in meters. The momentum of our object is going to be measured in kilograms meters per second. And Planck's constant in SI units is absolutely tiny. And so for a classical, normal-sized object that we might expect, we're going to have an absolutely tiny wavelength, which means any kind of interference pattern is going to be too small to see. We would never see those effects. Now you might wonder what happens when that momentum goes really small, so you can have something at rest. It's really hard to have something at rest. Even the tiny thermal fluctuations of a baseball give it enough momentum jiggling to give it a seriously small wavelength. And so in order to see an interference pattern, you have to very carefully control everything about your system. And it helps if it's very, very light as well, which is why we can do it fairly easily for photons or for electrons, but it's considerably harder to do for something like a large molecule. So this relationship between the wavelength and the momentum is developed in the mid-1920s by de Bois. And a couple of years later, Erwin Schrodinger developed the full mathematical description of how quantum mechanical systems change in time. And at that point, after a couple of decades of confusion and work trying to explain a rafter phenomena that couldn't be explained without quantum mechanics, quantum mechanics was finally in a form where it was really quantitatively explaining things that people had been trying to figure out for some time. But this fundamental idea that things travel as waves wasn't too controversial, but the fundamental idea that they did both travels as waves and then jump when you look at them was very upsetting to a large number of physicists, including those that were instrumental in developing the theory of quantum mechanics. Here are some of the things they said. So despite all these misgivings, quantum mechanics kept on giving us such accurate and precise answers to questions about how the universe around us works. It gives us theoretical calculations that agree with experiment up to 14 significant figures, better than any other theory we have. And the fact that it's so successful means that perhaps all of this problem with the worldview is more about our intuition and our own prejudices rather than about the world around us. After all, we don't get to tell the universe how it's supposed to work, just because that's how we expect. The universe gets to tell us how it works and we have to adjust our intuition to suit. Even a generation later, Richard Feynman said this. A couple of generations later, and physicists really are more comfortable with quantum mechanics. We're going to questioning its every axiom and trying to reform it into a more pleasing theory. And we're focusing more these days on actually doing engineering with it. We're deliberately using its strangest behaviors to build novel technologies like quantum computers.