[MUSIC] MARCELO GLEISER: We have seen that Einstein had proposed a very bold hypothesis that light is both a particle and wave and that its physical properties depend on how we test it, that is on the kinds of experiments or natural phenomena that we are studying. So if light is made to pass through a slit, it will behave like a wave. However, if it is fired on the surface of a metal plate, it will behave like a particle. In the early 1920s, the French physicist Louis de Broglie proposed something quite amazing. He said that not only light can have this dual particle wave behavior but also every other particle of matter. For example, an electron can also be a particle or a wave depending how you look at it. De Broglie used this idea to explain Bohr's model of the atom, where electrons are locked in very specific orbits. He reasoned that if you think of electrons as waves, only a certain number of wavelengths will fit within each orbit, as we can see it in this image. In the mid 1920s, the French physicist Louis de Broglie came up with this outrageous idea. that not just light is wave and particle, but that matter can also be wave and particle. And people got very confused because they had this notion of the electron going around the nucleus, like a planet going around the sun. And they said if the electron is a wave, how can it fit around the nucleus like that? De Broglie's brilliant insight was to say, well the electron is like a standing wave, like you can see a standing wave here where you have a frequency of oscillation and have a fixed point. And standing waves, they create nodes and those nodes depend on the energy of vibration of this string. So what de Broglie said is that electrons at higher orbits are corresponding to different standing waves with different frequencies of isolation and different number of nodes. So right now you have a wave with one standing node. We're going to now look for waves with more standing nodes. So in order to go from one node to these two nodes, all I had to do is increase the frequency of oscillation which really corresponds to increasing the energy that is being given to this string. As the oscillations occur in terms of the electron, this would mean that a higher orbit of the electron having more energy would correspond to the electron wave having more nodes. Yeah. So as you can see, even an outrageous hypothesis, the electron being a matter wave ends up making sense once you have the physics right. In 1925, the Austrian physicist Erwin Schrodinger, came up with what became known as the Schrodinger equation. An equation that describes very precisely the behavior of the electron, not only in its orbit in the hydrogen atom, but under any force that it is subjected to. The equation was a great triumph of applied mathematics to a complex physical problem. But it created a lot of very serious issues. The problem here was that contrary to the equations that people were used in classical physics, where you have a mass moving in space and the equation describes that mass moving in space. the Schrodinger equation was an equation for a quantity called the wave function. Initially, Schrodinger thought that this equation describes how the negative electric charge of the electron was distributed in space. The little ways that de Broglie suggested in the hydrogen atom. However, his early interpretation was wrong, and it was Max Born that came up with the interpretation that is valid until today, even though it is a very bizarre one. Born proposed that the wave function was describing not the electron itself, but the probability that the electron could be found in a certain point in space. This is completely different from everything in classical physics, the physics known until then. In classical physics, equations are deterministic. That is, they will tell you unambiguously where something will be in the future if you know its position and velocity in the past. Now, that certainty from classical physics is lost. Instead, what you have is a probabilistic interpretation that tells you that in a given experiment, you may find an electron in this place with this energy with a given probability, but it could also be found in this other place with this other energy, with some different probability. The new quantum physics became a probabilistic theory of nature in sharp contrast with the determinism of classical physics. And not everybody was very happy with that. In fact, Schrodinger himself had a nervous breakdown because he believed he had created a monstrous theory that was against his intuition. Many giants of physics of the time, like Einstein, Max Plank and even de Broglie himself were also deeply disturbed by the new quantum theory. They all believed that nature should be understandable fully by reason, reflecting a platonic expectation that the mind can describe the deepest secrets of the world in a deterministic way. On the other hand, Niels Bohr and his former student Werner Heisenberg and others were perfectly happy with this new probabilistic physics which they thought described a very different reality than the one we know from classical physics. In 1927, Heisenberg proposes uncertainty principle to describe precisely the indeterminacy that exists at the very core of Nature, whereby you could never know with absolute precision both the position and the velocity of a particle. If we try to make a mental picture of this, Heisenberg is saying that everything in nature is jittery and that this inherent agitation is at the very core of matter and will not go away. The new quantum physics opened the door to a very, very different physical reality. [MUSIC]