 Analysis of the two-slit experiment where you put things through two slits, they arrive on the detector one by one, and then only over time, doing that lots of times, you get an interference pattern, is an excellent way to talk about the core conceptual changes that happened when quantum mechanics arrived in its final, modern form. But it's not actually the experiment that quantum mechanics was invented to explain. Quantum mechanics was invented to solve a whole bunch of problems that have been growing over the latter half of the 19th century. It doesn't even explain the name quantum mechanics, why is it called quantum? Now a history of quantum mechanics is connected with the odd properties of light, and the way light interacts with matter. So quantum mechanics started with the idea of photons. In 1807, Young publishes double-slit experiment for light. But it wasn't until about 1818, where Poisson's spot had been observed, that people really believed that light was indeed a wave. But it was nearly 50 years later that Max will combine the equations for electricity and magnetism together, and discover that there was a possibility of an electromagnetic wave that would propagate. And he also realized that that wave would propagate the speed of light, and made the large jump that maybe light was indeed electromagnetic wave. And if you understand that light is an electromagnetic wave, then you'll understand how much energy it carries, you'll understand how it interacts with charged particles. And over the following decades, people started to realize that basically all matter was made of charged particles. At a microscopic level, you had a nucleus in the middle, and then a cloud of electrons around the outside, which people still sort of visualized as particles, because the wave theory of matter hadn't been invented at that stage. And so if you understand electromagneticism, and you understand that matter is made of charged particles moving in particular ways, then basically you can figure out exactly how they interact, and exactly what should happen. In the late 1800s, it was certainly felt that people were really closing in on the truth of the matter. They were figuring out the fundamental physics, the fundamental laws of the universe, and it was all coming together. They just had to work out a few details. Now, unfortunately, some of those supposedly small details were starting to cause some really big problems. Now, historically, the first of those details arose when people tried to marry their understanding of light as an electromagnetic wave with the other great success of physics, which was thermodynamics. Thermodynamics was the physics behind the Industrial Revolution. It told us how energy could be transformed between different forms, and how we could manage temperature to build engines and machines that would eventually let us use so much more energy than we could produce with our own hands. And this is effectively what transformed technology for humans. Now, in 1893, Wilhelm Wien applied the laws of thermodynamics to light itself. And he showed that if light is in thermal equilibrium with its surroundings, then its frequency spectrum has to shift proportionally with its temperature. In other words, if you have some object, say an iron bar, and this iron bar has a very good absorber or emitter of light at all frequencies, it's what's called technically a black body, then if you heat that up, it goes hotter and hotter, and it's going to give out radiation, and that radiation is going to get hotter and hotter. And we know that if we heat iron enough, then it will turn red. And that's because if we take the power coming off it from the light, as a function of frequency, then it's going to have some peak. Then for the low frequencies, we're going to have the red end of the spectrum, and above that we're going to have the rest of the rainbow. Then at a given temperature, we're going to see that we're going to get mostly a peak around the red area of the spectrum, and therefore that thing's going to look red. Now as we make this hotter, Wien's law says that if we increase the temperature by a certain amount, then we're going to take this frequency pattern and shift it up a little bit. We can see there that what we're going to get is lots of these colors coming through, and if we have lots of these colors, then we tend to get something that's white, and so that's when something gets hotter, it turns to white hot. And when it gets hotter again, we just shift out the frequency once more, and we can see that we're going to get mainly blue. So we're mainly going to get these blue colors and very little of the rest, and so it's going to be blue hot. And so that's why when you heat up a piece of steel, say, first it goes red, then it goes white, then it goes blue, because we're just shifting up the peak in our distribution there. And then over the turn of the century, two things happened in rapid succession. The first is that this calculation was done in a lot more detail by Rayleigh and Jeans, and they got the functional form for this power spectrum, where this is the frequency, this is Boltzmann's constant from thermodynamics, the T is the temperature, and C is the speed of light. And there are two important things to realize from this. The first is that it worked very well for the low frequencies. So the Rayleigh-Jeans law got these early frequencies very accurately correct. And the second thing is that it's obviously wrong because it grows without bound. You can see that this frequency, as the frequency goes up, more and more power comes out without bound. And so there's this infinite amount of power coming out at higher frequencies. And this is called the ultraviolet catastrophe. And it was called that simply because the Rayleigh-Jeans law was quite accurate for low frequencies like infrared or visible frequencies, but went spectacularly wrong in the ultraviolet regime and above. So despite the fact that the Rayleigh-Jeans law was properly treating thermodynamics and it was properly treating light as a electromagnetic wave, it steadfast refusal to act reasonably, never mind like experimentally observed fact, was extremely frustrating to another person working on the same problem, who was Max Planck. And in 1900, he became so frustrated with the difficulty of making his model fit experimental observation that he started making some crazy assumptions. In particular, he made one assumption that led him to get the right form for the black body law.