quantum field theory is stunningly successful at describing the small scales of reality Britt's equations are also stunningly complex a lot of the genius in QF T's development was in finding brilliant hacks to make these equations workable the most famous of these are the incredible Fineman diagrams the equations of quantum field theory allow us to calculate the behavior of subatomic particles by expressing them as vibrations in quantum fields but even the most elegant and complete formulations of quantum field theory like the Dirac equation or finance path integral become impossibly complicated when we try to use them on anything but the most simple systems but physicists tend to interpret that's impossible as I'd a to try and try they did first they express these impossible equations in approximate but solvable forms then they tackle the pesky infinities that kept appearing in these new approximate equations finally the entire mess was ordered into a system that mere humans could deal with using the famous Feynman diagrams to give you an idea of how messy quantum field theory can be let's look at what should be a simple phenomenon electron scattering when two electrons repel each other in old-fashioned classical electrodynamics we think of each electron as producing an electromagnetic field that field then exerts a repulsive force on the other electron at least in the simplest cases the Coulomb equation governing this subatomic billiard shot is really easy to solve but in quantum field theory specifically quantum electrodynamics or QED the story is very different we think of the electromagnetic field as existing everywhere in space whether or not there's an electron present vibrations in the e/m field are called photons what we experience is light the electron itself is just an excitation of vibration in a different field the electron field and the electron and e/m fields are connected vibrations in one can cause vibrations in the other this is how QED describes electrons scattering one electron excites a photon and that photon delivers a bit of the first electrons momentum to the second electron it's arguable exactly how real that exchange photon is in fact we call it a virtual photon and it only exists long enough to communicate this force there are other types of virtual particle whose existence is similarly ambiguous we'll get back to those in another episode this is a good time to introduce our first Fineman diagram the brilliant Richard Fineman developed these pictorial tools to organize the painful mathematics of quantum field theory but they also serve to give a general idea of what these interactions look like in a Fineman diagram one direction is the time in this case up the other axis represents space although the actual distances aren't relevant here we see two electrons entering in the beginning and moving towards each other they exchange a virtual photon this squiggly line here and the two electrons move apart at the end but Feynman diagrams aren't really just drawings of the interaction they're actually equations in disguise each part of the Feynman diagram represents a chunk of the math incoming lines are associated with the initial electron States and outgoing lines represent the final electron States the squiggle represents the quantized fueled excitation of the photon and the connecting points the vertices represent the absorption and emission of the photon the equation you string together through this one diagram represents all the ways the two electrons can deflect involving only a single virtual photon and from that equation it's possible to perfectly calculate the effect of that simple exchange unfortunately real electrons scattering at a quantum level is a good deal more complicated than this for that reason the simple calculation gives the wrong repulsive effect between two electrons if we observe two electrons bouncing off each other all we really see is two electrons going in and two electrons going out the quantum event around the scattering is a mystery there are literally infinite ways that scattering could have occurred in fact according to some interpretations all infinite intermediate events that lead to the same final result actually do happen sort of we talked about this weirdness when we discussed the Fineman path integral recently just as with the path integrals to perfectly calculate the scattering of two electrons we need to add up all of the ways the electrons can be scattered and this is where Fineman diagrams start to come in handy because they keep track with the different families of possibilities for example the electrons might exchange just a single virtual Photon but they might also exchange two or three or more the electrons might also emit and reabsorb a virtual Photon or any of those photons might do something crazy like momentarily split into a virtual antiparticle particle pair those last two events are actually hugely complicating as we'll see we have infinite possible interactions behind this one simple process a perfectly complete quantum field theory mnek solution is impossible but if you can't do something perfectly may be near enough is good enough this is the philosophy behind perturbation theory and absolutely essential tool to solving quantum field theory problems the idea is that if the correct equation is unsolvable just find a similar equation that you can solve then make small modifications to it perturb so it's a bit closer to the equation that you want it'll never be exact but it might get you pretty close in the case of electron scattering the most likely interaction is the exchange of a single photon every other way to scatter the electrons contributes less to the probability of the event in fact the more complicated the interaction the less it contributes here Fineman diagrams are indispensable it turns out that the probability amplitude of a particular interaction depends on the number of connections or vertices in the diagram every additional vertex in an interaction reduces its contribution to the probability by a factor of around 100 so the most probable interaction for electron scattering is the simple case of one photon exchange with its two vertices a three vertex interaction would contribute about one percent of the probability of the main to vertex interaction however it turns out that for electron scattering there are no three vertex interactions however there are several interactions that include four vertices and each contributes about 1% of 1% of the to vertex interaction and this is true even though those complex interactions are very different to each other they include exchanging 2 virtual photons or one electron emitting and reabsorbing a virtual photon or the exchange photon momentarily exciting a virtual electron-positron pair and more complicated interactions add even less to the probability so with find the diagrams you very quickly get an idea of which are the important additions to your equation and which you can ignore perturbation theory with the help of Fineman diagrams make the calculation possible but that doesn't mean we're done including all of these weird intermediate States really opens up a can of worms this is especially true for so called loop interactions so like when a photon momentarily becomes a virtual particle antiparticle pair and then reverts to a photon again or when a single electron emits and reabsorbs the same photon this latter case can be thought of as the electron causing a constant disturbance in the e/m field electrons are constantly interacting with virtual photons this impedes the electrons motion and actually increases effective mass the effect is called self energy but if you try to calculate the self energy correction to an electrons mass using quantum electrodynamics you get that the electron has infinite extra mass this sounds like a problem to calculate the mass correction due to one of these self energy loops you need to add up all possible fertile energies but those energies can be arbitrarily large sending the self energy enhance the mass to infinity in reality something must limit the maximum energy of these photons do we don't know what that limit is the answer probably lies within a theory of quantum gravity which we don't yet have but just as with perturbation Theory physicists found a cunning trick to get around this mathematical inconvenience it's called renormalization obviously electrons do not have infinite mass and we know that because we've measured that mass although any measurement we make actually includes some of this self energy so our measurements are never of the fundamental or bare mass of the electron and that is where the trick lies instead of trying to start with the unmeasurable fundamental mass of the electron and solve the equations from there you fold in a term for the self energy corrected mass based on your measurements in a sense you capture the theoretical infinite terms within an experimental finite number this renormalization trick can be used to eliminate many of the infinities that arise in quantum field theory for example the infinite shielding of electric charge due to virtual particle antiparticle pairs popping into and out of existence however you pay a price for renormalization for every infinity you want to get rid of you have to measure some property in the lab that means the theory can't predict that particular property from scratch it can only make predictions of other properties relative to your and measurements nonetheless renormalization saved quantum field theory from this plague of infinities Feynman diagrams successfully describe everything from particle scattering self-energy interactions matter antimatter creation and annihilation to all sorts of decay processes we'll go further into the nuts and bolts of Fineman diagrams in an upcoming challenge episode a set of relatively straightforward rules governs what diagrams are possible and these rules make fineman's doodles an incredibly powerful tool for using quantum field theory to predict the behavior of the subatomic world the results led to the standard model of particle physics in future episodes we'll talk more about what is now the most complete description we have for the smaller