Hi,
I have difficulty comprehending Feynman diagrams. Although I’m a high schooler, could you please explain to me like I’m five as to what exactly a FD *shows* and what it’s used for? Thanks.
In: Physics
They *show* interactions between fundamental particles. There are a few rules about what these particles can do in the diagram, and by analyzing a Feynman diagram, you can determine if the interaction is possible and other complex things that are used in conjunction with highly complex mathematics.
In all, they allow for a pictorial representation of quantum interactions, then you can make predictions about what kinds of composite particles are possible, and what they might do.
richard feynman worked and developed what is known as quantum electrodynamics (QED). if you’re familiar with what electromagnetic fields are, QED talks about how they interact with charged particles (electrons, positrons etc.) and also interactions of light with matter. a feynman diagram is what is used to represent these interactions and supplement calculations and visualisations of the interactions physicists want to study. in some ways, you could say it’s like the quantum version of a free body diagram which you learn about in mechanics which represents all the forces on a body in a particular situation. it’s tough to explain what all you can infer from one partly because it’s quite a lot of background that is required to understand and also partly because i myself am not knowledgeable enough. but that’s the essence of it. a FD represents the interactions between subatomic particles.
Whenever you talk about particles interacting, it’s not like the sort of interactions you’re used to in your day to day life. For example, if you’re playing pool and one ball hits another ball, they interact in a pretty straightforward way (from our perspective): they hit and bounce off at predictable angles.
In the realm of quantum mechanics, though, particles don’t *touch*. Particles don’t really exist in a single point, and they have really fuzzy boundaries. It’s really a volume of space where you can *probably* find that particle if you go looking for it. So, they really can’t touch in the way we think about it. Moreover, information has to be transferred between particles. How does one particle “know” that another particle is there? They do this by exchanging virtual particles. Those virtual particles do things like transferring momentum.
As an example, imagine two electrons coming close to each other and repelling so that they fly off in different directions. One electron will emit a photon, which carries some of its momentum. Since energy came from the electron, it has to chance direction, kind of like how a rocket shoots stuff out of the engine which pushes the rocket in the other direction. Then, that photon is absorbed by the other electron, which means it gains that energy (and momentum) and shoots off in the opposite direction. That interaction is exactly what [this diagram](https://protonsforbreakfast.files.wordpress.com/2014/04/feynman-diagram1.jpeg) shows. Time moves follows the arrows from bottom to top. So you see the electrons coming in from the bottom corners, a photon is exchanged, and the electrons fly apart again.
There’s a slight hiccup in how particles are really exchanged, though. Not only is the exact location of a particle pretty fuzzy, but its very *existence* is often not a single, clear line. Einstein’s famous equation (E=mc^2 ) tells us that matter and energy are two versions of the same thing. That is, a sufficiently energetic photon can become electrons – specifically, it can become an electron and its antimatter counterpart, a positron. Conversely, if you put an electron and a positron together they annihilate each other and become a high energy photon. This happens randomly and spontaneously. That means that the virtual photon being exchanged by our two electrons in their interaction can spontaneously turn into an electron/positron pair, as long as they recombine back into an identical photon which gets absorbed by the other electron in the interaction. That interaction is modeled [like this](https://lh3.googleusercontent.com/proxy/qvDrXEGFKj7l8AVhD5bYfmHwdzl7bDbIwwiI5TqtRRpEmsuOa8kqnXO_AYiGy043a4dtTApqhlwV7xLJOPLkgXT3k3xVlOmztbRJ), where the positron is symbolized by an electron going backwards in time (ie: with a reversed arrow).
Moreover, the path the photon takes to get from one to the other is just as fuzzy as its position. The photon can take *any* possible path from one to the other – and, in fact, according to quantum mechanics it *does* take *every* possible path simultaneously, kind of. So not only can the photon become an electron/positron pair, but it can do so while taking a loop around the moon, and the electron and positron can become other particles, which themselves take a trip to Jupiter, and then they all recombine at some point in the journey, only to split apart again, endlessly, going in all possible directions, and then at some point combine back into the photon and be absorbed again. The electrons in the interaction can emit a virtual photon and then reabsorb that photon instead of it getting passed to the other electron. *That* virtual photon can turn into other particles and wander around the universe before getting reabsorbed. Those crazy possibilities get modeled with increasingly complicated diagrams which look like [these diagrams](https://www.wolframscience.com/nks/img/inline/page1060b.png).
Fortunately, you can simplify all that by ignoring most of it, because at the end of the interaction the only thing that *matters* is what is observed to happen. You can’t interact with those virtual particles at all. All you can see is that two electrons moved towards each other and then moved away from each other, which means that regardless of what happened in the process, a virtual photon went from one electron to the other, as diagrammed in the original example of a Feynman diagram. You can also do very complicated math that I don’t understand to combine all of the infinite possible paths for the infinite possible virtual particles and give them weight according to how likely they are, and then take the average of all of them, which gives you that simple, straightforward diagram.
That’s what Feynman Diagrams are for: showing you how particles interact. Different particles use different symbols and lines, and where the lines connect is where they emit or absorb particles. It’s an *abstraction* – a simple way of showing what must be happening while ignoring all the *very complicated* quantum mechanics random unpredictable craziness that is also happening.
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