Where Does Electric Charge Come From?

thanks to brilliant for helping support this episode hey crazies in a previous video I explained that electric charge was a coupling property it measures how linked or coupled a particle is to the electromagnetic field this connection explains why electric charge is conserved and frankly why the electromagnetic field even works but to understand it we're gonna need a little quantum mechanics this episode was made possible by generous supporters on patreon okay so the ultimate question we're trying to answer what this video is why is charge conserved but we're gonna need to answer a few other questions first this video comes to you in four parts part 1 what do we mean by charge charge is a fundamental property of particles these are the elementary particles some of them have negative charge some of them have positive charge and some of them are electrically neutral they can combine to make composite particles which can also carry electric charge you just total up the charge of the elementary particles they're made of charge is just a number but aren't particles like electrons also called charges yes but that's just people being lazy I don't know if you knew this but humans are lazy when we call something like an electron a charge that's just short for charged particle I've ominously been guilty of it too but but for this video I'm gonna be more careful than that in this video the word charge will always refer to the number not the particle part two what does it mean for something to be conserved a conserved quantity is just a number that stays the same over time kind of like how environmental conservation is all about keeping the environment the same notice theorem tells us that all conserved quantities are the result of some invariance or symmetry in the universe if you can vary one condition like where or when an event takes place and that event plays out exactly the same way it's called an invariance neuters theorem says there must be a conserved quantity no exceptions linear momentum goes with location invariance energy goes with time invariance angular momentum goes with rotational invariance my stress goes with Quarantine invariance every in variance has a conserved quantity part three what invariance is causing charge to be conserved in invariance in the electromagnetic interaction charged particles interact electrically and magnetically they do this over seemingly empty space but not instantaneously this leads us to infer that maybe the space between them is filled with something something that carries the interaction between those particles whatever that something might be we have several ways of modeling it we could imagine it as some kind of field of forces the electric field exerts a force on charged particles the magnetic field does the same thing but only if the particles are moving however forces are not the only way to look at a situation sometimes energy and momentum can give you a deeper insight this is something called the electric potential it's a way for charged particles to provide energy to each other is there a magnetic potential yeah there is it fulfills a similar purpose but for momentum instead of energy it's a way for charged particles to exchange momentum with each other fields are fine if you're working with forces but potentials are better if you're working with energy and momentum you know things that tend to obey conservation principles and as it turns out the fields are invariant under certain changes in the potentials this is how they're related he is the electric field B is the magnetic field V is the electric potential and a is the magnetic potential the potentials determine the fields we're not uniquely say we take this electric potential and shift all the values by some constant the values might be different but the changes across space are still the same those changes are just the electric field it was unaffected by the shift in the potential that shift isn't even limited to constants it can vary across space and time it works as long as the shift is a rate of change across space in the magnetic potential and a rate of change across time in the electric potential these fields are defined by these potentials but also these potentials or these potentials this F could be any function of space and/or time that F is something we call a gauge so this invariance is called gauge invariance that gauge could be anything it's completely random or is it part 4 what does an invariance in a field have to do with charged particles this is where quantum mechanics becomes important little particles like electrons are inherently quantum mechanical they're not really tiny spheres we might not know exactly what they are but they're definitely not tiny versions of this their behavior is described by waves of probability like this one that describes location these waves are completely unobservable but we do get to see the square of those waves if the wave looks like this its square looks like this we call it a probability density because the area underneath tells us the probability that something will happen another nice feature of these waves is that they have something called global phase invariance what's a phase it's just what we call a shift in a wave it's not that big of a deal here's the basic sine wave it's exactly where it's supposed to be which means it has a phase of zero the size of any shift in that waves is called the phase if we're talking about a quantum wave for something like an electron then a phase shift will not affect the waves probability density the likelihood of finding the electron in any particular place is unaffected by the shift if that phase shift is the same everywhere in space and time we call it a global phase shift the real properties of all quantum particles are invariant under this kind of shift in the language of quantum mechanics we'd write that like this where fee is the phase angle inside is the quantum wave the complex squares of these two waves are the same which means the probabilities are the same so is there anything like that that only applies to charged particles yeah there is local phase invariants that's when a different phase shift occurs at different places in different times without some kind of control it would take a wave that looks like this and turn it into one that looks like this it's a complete mess but not if we can tweak Schrodinger's equation in just the right way that's the equation that governs what the particles wave looks like in space and how it evolves over time however this form of it the one that everybody knows only applies to electrically neutral spin zero particles luckily we can fix it with the electromagnetic potentials remember those the adjusted Schrodinger equation looks like this yes it's nastier but it finally applies to charged particles with nonzero spin it still doesn't apply to relativistic particles but that's a topic for another day though oddly enough this adjustment does fix our phase shift problem the local phase shift turned our particles wave into this but the electromagnetic interaction turns it back into this the electromagnetic potentials give charged particles local phase invariance if a particle has electric charge then it interacts with the electromagnetic field and has local phase invariance all three of these statements are 100% equivalent charge particles have local phase invariance neutral ones don't no exceptions but that middle statement that the one about interacting with the electromagnetic field it's the key to this whole thing do you remember that seemingly random gauge function from earlier well it's the same as the quantum phase of the particle the gauge shift in the field is the phase shift of the particle boom so wait why is charge conserved because of an invariance in the electromagnetic interaction charged particles are inextricably linked to the electromagnetic field quantum mechanics requires this that link is what it means to be electrically charged any invariance in the field we'll be coupled with an invariance in the particles and according to neuters theorem any invariance results in a conserved quantity that conserved quantity is electric charge so hopefully that ties up all the loose ends I'm sure you'll let me know in the comments if I forgot to mention something thanks for liking and sharing this video don't forget to subscribe if you'd like to keep up with us and until next time remember it's okay to be a little crazy many people are on the lookout for online math and science resources right now if you are - you should check out brilliant brilliant is a problem-solving based website and app with a hands-on approach with over 60 interactive courses in math science and computer science whether you're a student looking to get ahead a professional brushing up on cutting-edge topics or someone who just wants to use this time to understand the world better brilliant could be the resource you're looking for check out their trigonometry course with quizzes on waves and phase shifts or go back to the basics with their mathematical fundamentals course brilliant helps you achieve your goals in stem starting with one small commitment to learning and building up to long term challenge and growth if this sounds like a service you'd like to use go to brilliant org slash science asylum today the first 200 subscribers will get 20% off an annual subscription Feinstein 100 brought up an old quote time is what keeps everything from happening at once yes wheeler said that but technically he was quoting an old short story from 1921 called the time professor the more you know anyway thanks for watching

Channel: The Science Asylum

Views: 163,486

Keywords: quantum mechanics, conservation principles, noether, nother, electromagnetism, electric charge, charge, gauge invariance, gauge, phase invariance, phase

Id: LbJJFnf-NWM

Length: 10min 36sec (636 seconds)

Published: Fri May 15 2020