What is Quantum Mechanical Spin?

so what happens is that this electron like every electron has a charge but it also has a magnetic dipole is like a tiny tiny tiny magnet called the spin the word spin is a bit of historical misfortune so to some degree in a classical word you can think of a electrically charged particle so something that has a negative charge and if you make it spin literally spin like a gyroscope around an axis it will in fact produce a magnetic field okay so it would be like you know this magnetic dipole and so you can describe this object as a magnetic dipole that points in some direction in reality the spin is a purely quantum mechanical property that actually comes from solving some relativistic equations of quantum mechanics the Dirac equation and the the most striking example to explain why you cannot think of the spin as actually the electron spinning on itself is when you think of the neutron the neutron also has a spin but it has no charge so how can you say oh the neutron is spinning on itself therefore it produces a magnetic dipole well the neutron has no charge and yet it has a spin just like the electron and the proton so imagine a solenoid where you have wires so on this side you have current going in and on this side you have current coming out so you have the current going this way that produces a big magnetic field in this direction okay so that's what we call the B 0 that is the static magnetic field that is produced by us by connecting a large current source and running a current down this solenoid okay so in our laboratory we work with fields of about 1.5 Tesla which is a strong field in fact we have superconducting magnets to do this in this magnetic field the magnetic dipole that is associated with the spin with the particle we'll have its lowest energy when it's pointing along the field okay think of the needle of a compass literally okay the Earth's magnetic field is oriented towards the north so when you take your compass you will see the needle pointing towards the north because that is the direction where the magnetic needle has its lowest energy okay but the point is the spin is not just the needle of a compass is not just a switch the spin is a quantum mechanical object that can be in 0 and 1 at the same time so you can create what's called a quantum superposition of 0 and 1 so at the single spin level it's often hard to see where the quantum mechanical you know speciality comes in it's much more striking when you put two of them then it goes completely out of your classical intuition let's do it ok they could be in the two electrons that are bound to two different phosphorous atoms now when you have two electrons interacting like this what you'll find is that there are four i mean intuitively you think there are four possible states right that's what you have electronic electron up electron up electron down down up and down down right you think that those are the four possible combination of those two spins in reality what you'll find is that you have the up up and down down that's fine but up down and down up are not the natural quantum states of those electrons those electrons will find themselves in what we call a quantum superposition of down-up and up-down but that quantum superposition has absolutely no classical intuitive picture to it in this case this quantum superposition of up down and down up is what we call an entangled state the two electrons no longer have a direction of their own okay so you cannot say this electron is down and this electron is up the two electrons are in a state where they have the opposite direction but they do not have a direction of their own so it's only when you measure one of them and you find okay this is down that this one ends up being up but until you measure them they are in a state where their only property is being opposite to each other why is this so powerful it's powerful because now you have these four quantum states right you have the down down then you have this thing that we call the singlet state which is one over square root of two down up - up down then you have this theme it's called T zero state which is 1 over square root of 2 down up plus up down and then you have the up up okay.i is it that the simple up down and down up are not the natural states of the two qubits that is really where the whole fundamental issue lies up down and down up are not the natural state it's because they are coupled ok we said we have these two spins they're coupled to each other now it's exactly like this double pendulum you have two pendulums and they're coupled to each other by the string so let's say I now set one pendulum emotion look at what happens you see now the other one starts to move as well and at some point which is about to happen you see this one has actually stopped and all the energy is in that one and then it's going to come back now this one was slowed down and the other one would start moving again so you see this configuration of the double pendulum is not a stable one right so if you just put one pendulum in motion and the other one not in motion it doesn't stay that way it kind of swaps so you can think as pendulum moving and pendulum not moving as the spin-up and spin-down so if you've prepared up-down it doesn't stay there the up will eventually turn into down and the down into op like the pendulum the moves will stop and then the other one will start to move okay so then what is the stable configuration for the coupled double pendulum well there is one possibility which is to put both pendulums in motion at the same time like this these will persist unchanged for well not forever because the pendulum has dissipation but if we had a perfect pendulum this would persist for them so this is one possibility the second possibility is to do it this way this configuration will also persist forever but is different from the previous one here the two pendulums are going in opposite phase whereas before they were going with the same phase so that is the meaning of that minus sign that we saw in the two superposition so you can think of this as the superposition of pendulum left moving pendulum right not moving and the other way around but you need to distinguish this one from this one and that minus sign is what distinguishes about 311 which is as many particles and variety so we are really reaching the eternal circle often well not now on exotic labora hundred

Channel: 2veritasium

Views: 502,111

Rating: 4.932621 out of 5

Keywords: Qubit, spin, quantum mechanics, electron, superposition, entanglement, entangled, Spinning, coupled, pendulum, quantum bit, quantum computer, magnet, magnetic field, dipole, quantum, bit, spins

Id: v1_-LsQLwkA

Length: 8min 43sec (523 seconds)

Published: Mon Jun 17 2013