the Fineman diagrams revolutionized particle physics by providing a simple system to sort out the infinite possibilities when elementary particles interacts this incredible simplicity provides some stunning insights into the nature of reality Feynman's path integral shows us that to properly calculate the probability of a particle traveling between two points we to add up the contributions from all conceivable paths between those points including the impossible paths in fact we can go even further according to fineman's approach to quantum mechanics every conceivable happening that leads from a measured initial state to a measured final state it does in a sense happen at least in the math to calculate the probability of any quantum system evolving between two states we need to sum over every conceivable intermediate state this is impossible because there are infinite possible intermediate States but as we discussed in our episode on solving impossible equations the Fineman diagrams allow physicists to quickly figure out which of the infinite possibilities need to be considered to get an answer that's good enough each diagram represents a family of interactions and tells us the equation needed to calculate the contribution of that family to the total probability the miracle of Feynman diagrams is that an absurdly simple set of rules allows you to easily find all of the important interactions today we're going to learn these rules then you're going to apply them to do some quantum field theory yourself there are spacetime t-shirts at stake we're going to stick to quantum electrodynamics the first and most predictively powerful quantum field theory QED talks about the interaction of the electron field with the electromagnetic field that means interactions between electrons their antimatter counterparts the positron and photons in Fineman diagrams we depict the electron as an arrow pointing forwards in time or the positron is an arrow pointing backwards in time we'll soon see the power of representing antimatter as time reversed matter the photon is shown as a wavy line time Direction is irrelevant for the Fertile throw these on a plot of space versus time and we have a Fineman diagram a useless one none of these particles are doing anything worth calculating for this to be interesting the electric and electromagnetic fields need to interact this is where we start to see the power and simplicity of this approach particle / field interactions are represented as a vertex a point where the lines representing the different particles come together it turns out that there's only one vertex that's possible in QED one with an arrow pointing in and arrow pointing out and a single photon connection it looks like this this vertex alone represents six very different seeming interactions and it can be used to construct infinite Fineman diagrams let's look at the possibilities oriented like this with time increasing upwards this vertex represents an initial electron that emits a photon after which both particles move off in opposite directions but if we rotate this vertex so that photon is coming in from below we have a picture in which an electron absorbs that incoming photon the photon vanishes and its momentum is completely transferred to the electron rotate again and the picture is of a photon coming in and giving up its energy to produce an electron-positron pair a process we call pair production rotate again and now we have a positron absorbing a photon and a positron emitting a photon and finally an electron and a positron and naya lating each other to produce a photon and that's it all the ways that the electromagnetic and electron fields can interact every single QED interaction is built from these but why only this interaction well because of conservation laws energy and momentum conservation requires that particles not to vanish or appear from nothing which guarantees that if something goes in then something else must come out charge must also be conserved if one electron or positron goes in then one electron or positron respectively must leave if an electron and positron both go in then their charges cancel so a zero charge photon must leave similarly if a photon creates a negatively charged electron it must also create a positively charged positron there are other more complex ways in which in going outgoing particles can balance charge but as we'll see all of these can be built up from this one vertex before we look at those more complex interactions here's another important rule the overall interaction described by set of fiber diagrams is defined by the particles going you and the particles going out these are the particles that we actually measure we know their properties for example their energy and momentum and they obey Einsteins mass-energy equation we say that these particles are on the mass shell or just on shell they sit on the shell structure you get when you plot einstein's equation of energy momentum and mass on the other hand everything that happens between ingoing and outgoing tracks has questionable reality each possible diagram the results in the same ingoing and outgoing particles is a valid part of the possibility space for that interaction the particles that have their entire existence between vertices within the diagram but don't enter or leave are called virtual particles their correspondence to anything resembling real particles is debatable they are also by definition unmeasurable otherwise they'd be one of our in going around going part these particles do not obey mass energy equivalence so they are off shell these particles aren't even limited by the speed of light or the direction of time which leads to all sorts of fun let's go back to the simple interaction we looked at in our recent episode electron scattering can be depicted as two electrons going into an interaction and then two electrons going out we know the momentum of the ingoing and outgoing electrons any combination of the fundamental three paths vertex that can lead to this final result has to be considered simple examples are the exchange of a single photon to transfer momentum between electrons or the exchange of two or more photons but we can add as many of these vertices as we life including the electrons exchanging photons with themselves at different stages in the process or photons momentarily splitting into virtual electron positron pairs as long as the final result is the same any of these are possible part of the beauty of Fineman diagrams is that each of these diagrams themselves represents an infinite number of specific interactions to start with each of the particle paths are actually infinite paths as well as infinite possibilities for particle momenta we have to consider even impossible faster-than-light paths and this is really important for any particle besides the in going and out going on shell particles any energy speed an even direction in time is possible this last point is bizarre but really powerful for example for two electrons exchanging a single photon it doesn't matter if we draw the photon go from the first to the second or the second to the first even though this seems like a very different interaction we can think of the differences just being the photon travelling forward in time in one case and backwards in the other the math describing the transfer covers both cases let's look at an even weirder example of this is Compton scattering an incoming electron and an incoming photon bounce off each other one way that can happen is for the electron to emit a new photon and later absorb the old incoming photon in that intermediate stage between vertices the electron is a virtual particle which means we include all possible paths it might take as long as they lead to producing the same final electron and photon that includes paths backwards in time mathematically a time reversed electron looks exactly like a positron like this the same particles go in and out but now the interactions look very different instead of an electron emitting and then absorbing a photon we have on one side that incoming photon creating an electron-positron pair that new electron becomes our outgoing electron but the positron annihilation incoming electron to produce the outgoing photon these may seem like wildly different processes but in the math represents by Feynman diagrams they're exactly the same the interpretation of the interactions is irrelevant all we care about is the topology of the diagram in other words how are the vertices connected to each other this fact makes Fineman diagrams and incredibly powerful tool in simplifying quantum field theory calculations vastly reducing the number of contributing interactions that need to be separately solved the interpretation of antimatter as time reversed matter is one that some including Richard Feynman took quite seriously we're in adult deep into that idea in an episode very soon but for now only of you a chance to play with fireman diagrams yourselves so either challenge question for you when an electron and a positron interact electromagnetically we call it bhava scattering it's an interesting case the most important Feynman diagrams for bhava scattering are the two cases involving a single virtual photon and they include two vertices each those diagrams seem to describe very very different events but they lead to exactly the same results use the rules I described in this episode to draw both of the two vertex diagrams for barber scattering and describe what's happening in each of these vertices then I want you to try to draw all the possible for vertex diagrams for the latter don't bother with what we call the self energy diagrams in which electrons or positrons emit and then reabsorb the photon send your neatly drawn Fineman diagrams to PBS space time at gmail.com within one week of the release of this episode include in the subject line the words Fineman diagram challenge because we filter by subject line will randomly choose five correct answers to win a spacetime t-shirt and that includes a choice from brand new t-shirt designs one will be an exclusive for challenge winners and patreon supporters introducing the mighty astra Chicken von Neumann conqueror of the galaxy and available to everyone including challenge winners the heat death of the universe is coming a fun reminder in t-shirt form of the eventual cold dark end of space-time to all of our patreon