Here's how Quantum Physics predicts the existence of Bosons and Fermions - but we also discuss what those words even mean!
Hey everyone! I'm back with a new video, filmed a few weeks before we hit 50k subscribers! Thanks so much for all your support. In this video, I wanted to talk to you about two different kinds of particles, known as Bosons and Fermions. You may have heard of these two classes of particle. For example, a few years ago the Higgs Boson was in the news a lot. This, naturally, is a kind of boson. And you may have heard of a particular kind of fermion known as the electron.
Well the existence of bosons and fermions is predicted by quantum mechanics, if we consider a simple system consisting of two (or more) indistinguishable particles. These particles in our system are not only identical in every way (same mass, same charge, etc.), but they are indistinguishable from each other. This means we cannot label them as particle A, particle B, etc., and track them over time. If we leave our system alone for a while and then come back to it, then we have no way of knowing which particle is which. All we know is that the number of particles in the system beforehand is equal to the number of particles in the system afterwards.
This assumption that our system consists of indistinguishable particles can actually be encoded mathematically. If our particles are to be indistinguishable, then we can imagine labelling them particle A and particle B. But this is only for the purposes of our own calculations. If the particles are really to be indistinguishable, then our system must look the same regardless of whether we have particle A on the left and particle B on the right, or if the two particles have swapped positions - we must have no way of knowing. And if that is the case, then the probability distribution of our system (the probability of finding two particles in two given locations in space) must be the same regardless of whether we have particle A on the left and B on the right, or if they are swapped around. I've made videos in the past about indistinguishable particles, so please do check them out on my channel.
As we see in the video, the probability distribution of our system is very closely linked to the wave function of our system. Specifically, it's linked to the square of the wave function. And so we can equate the squares of the wave functions for a scenario where we have particle A on the left and B on the right, and when they are swapped around.
When we do this, we can then follow some simple mathematics to tell us that for a system like this, we can see two different kinds of wave functions. One where the wave function is unchanged when the two particles are swapped, and the other where the wave function becomes negative when the two particles are swapped. These are two different classes of particle. The system of particles that has its wave function unchanged when particles are exchanged, is known to contain bosons. The system that has its wave function become negative under particle exchange is known to contain fermions.
As it turns out, we have seen many particles that display either bosonic or fermionic behaviour. Bosons can display special behaviours such as Bose-Einstein condensation, while Fermions must obey the Pauli Exclusion Principle. I will make videos about both of these topics in the future, so keep an eye out for them.
Until then, I hope you enjoyed this video. If you did, please leave a thumbs up and subscribe, and head over to my second channel "Parth G's Shenanigans" (here / @_parthmusic ) for some of my original music! Follow me on Instagram @parthvlogs.
4 окт 2024
