 In the last video we talked about how the electromagnetic field is quantizing to discrete bits called photons. The mathematical theory that describes this is called quantum electrodynamics, or QED for short. QED was invented by American physicist Richard Feynman, and the main calculational tool he had was diagrams. In these diagrams, which we now call Feynman diagrams, a straight line represents a charged particle, and a wiggly line represents a photon. We can interpret them as being spacetime diagrams for different interaction processes. For example, these are two different Feynman diagrams describing electron-electron scattering events, where a photon is emitted from one electron and absorbed by the other, causing them to scatter from each other. In the diagram on the left, the photon is emitted by the bottom electron and absorbed by the top, and in the diagram on the right, the photon is emitted by the top and absorbed by the bottom electron. These are referred to as two different time orderings of the same process. And in the diagram on the right, the photon is emitted by the bottom electron and absorbed by the top electron. You may have noticed that the arrow on the line representing the charged particle points forward in time in the diagram. Now you may wonder, what does a line with an arrow pointing backwards represent? The answer is that it represents an antiparticle. The direction of the arrow doesn't actually mean that antiparticles travel backwards in time. It's just a confusing bit of notation that physicists use to differentiate antimatter from matter in Feynman diagrams. In most cases, any diagram that we can draw that follows these rules will represent a physically possible process. The beauty of Feynman diagrams is that we can encode aspects of the theory into the rules for how we can draw valid Feynman diagrams or QED. The first rule is that at every vertex there must be a photon. A vertex is a point on the diagram where an interaction happens, so this rule encodes the fact that any possible electromagnetic interaction must be mediated by a photon. The second rule is that there can't be any unconnected bits on the diagram. All this rule is saying is that we are only interested in what's happening in a particular interaction. The next rule is that the conserved quantities of quantum electrodynamics should remain conserved at each vertex on the diagram. This rule just ensures that all of the conservation laws of the electromagnetic interaction are satisfied. Our final rule is that at any vertex there must be exactly one arrow pointing in and one arrow pointing out. This is essentially just a special case of rule number three, as it ensures matter does not turn into antimatter and that charge is conserved. To see this, let's draw a vertex where both arrows point inwards and check to see if charge is conserved. On the left hand side we have two electrons each with a charge of negative one, so the total charge on the left hand side of the vertex is negative two. On the right hand side of the vertex we have a photon which is neutrally charged, so has a charge of zero. Since two does not equal zero, this vertex is not allowed. Now that we have our rules for making valid Feynman diagrams, we can go forth and just start drawing diagrams, and then we can interpret the different stories that they tell. One interesting thing to note is that if you have one valid Feynman diagram, you can rotate it so that it tells a different story. On the top left I have drawn a diagram that describes the annihilation of a particle-antiparticle pair into a photon. If we then rotate that diagram by 90 degrees, we get a new story that describes a particle emitting a photon. If we rotate it by 90 degrees again, our diagram then describes a photon spontaneously turning into an antiparticle-antiparticle pair, which we call spontaneous pair production. And indeed, we can use other symmetries as well, such as charge inversion, to create Feynman diagrams describing new processes. The rules for drawing Feynman diagrams with other fundamental interactions are essentially the same, except that different conservation laws will be relevant. We will explore this in more depth in the following videos.