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  • Spin In this video, we're going to start looking

  • at something called Spin. Spin was something that was only discovered when people started

  • experimenting on very small things like electrons. I'm going to tell you about some of the experimental

  • facts that they found.

  • Firstly, what is it? We know that normal objects can have all kinds

  • of measureable properties like Position,

  • Speed, Temperature

  • etc

  • Spin is another one of these properties that you can measure of a particle. And in the

  • same way that a particle can have different positions and can change it's position, the

  • spin of an object can take different values and change over time.

  • But unlike those other properties, it's hard to describe what it actually is intuitively.

  • The best I can do is say that the spin of an particle measures how magnetic it is, and

  • decides which direction the magnetic field is pointing. The problem with this statement

  • is that it makes particles seem like they act like tiny little bar magnets. Actually

  • they don't, because as we'll see, spin is a very strange thing.

  • From here on in we're going look at the spin of electrons. Whenever we measure spin, we

  • have to pick a direction, aka an axis, to measure it in. Let's call the direction pointing

  • east the x axis, and the direction pointing north the y axis. Then say I happen to know

  • that an electron has spin of some strength that I'll call s, in the x direction. It's

  • tempting to say the electron is like a bar magnet pointing in the x direction. But if

  • that was the case, how much spin would you expect the electron to have in the y direction?

  • Well the y direction is perpendicular to x, so you normally we wouldn't expect there to

  • be any magnetic field that way at all. However if you measure the spin in the y direction

  • you will get a very weird result. Say we do this experiment record the results, then do

  • it again using a new electron and keep repeating. Half the time you will find that the particle

  • not only does have spin in that direction, its strength is still s. The other half of

  • the time? It will still have strength s but this time in the negative direction of y!

  • This is completely unexpected. But notice something. If we take the average of the results,

  • we get 0, which was the result we thought we'd get. Hm, let's try another example

  • Let's say we have a particle with spin s in the x direction again. We'll pick the 45 degree

  • axis to measure spin in. What would we normally expect? Well the 45 degree angle axis is still

  • somewhat pointing in the x direction, so we'd expect there to be some spin in that direction

  • but a smaller amount than s. We can calculate how strong we think it would be using vectors

  • and get that the new spin should be s on root 2. But what happens when I measure it? Again,

  • every single time I repeat this experiment, the electron will have spin of strength s,

  • but this time, it will be slightly more likely to be in the positive direction than the negative,

  • so that when I take the average of all my results I get s on root 2. Again, though each

  • individual trial was unexpected, the average result is what I thought I'd get.

  • Let me summarize the two things we can learn about the spin of an electron from these kinds

  • of experiments Firstly, no matter what direction we measure

  • the spin in, its value will always be positive s or negative s where s is equal to this number.

  • We'll give these two possibilities some convenient names: up and down. So you can for example

  • say that an electron is spin down in the y direction.

  • The second weird thing is that, where ever you'd normally expect an electron to have

  • a certain spin in a direction, let's say spin equal to k, you will instead find that each

  • time you measure you only get spin up or down but when you average the spin of each trial

  • you get the right result, Ie averaging your data will give you k.

  • So you see, its possible to say which direction an electrons spin is in and its strength but

  • it's not really like the classical situation with a bar magnet. With a bar magnet, knowing

  • how strong the magnet is, and in what direction, allows you to find its strength in every other

  • direction. That's not the case with spin. When there's lots of particles, on average

  • they act just like bar magnets, but individually they act like they're equally strong in all

  • directions they're measured in and act randomly. We still don't know if that randomness is

  • true randomness though, and we still don't know what spin really is.

Spin In this video, we're going to start looking

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スピン (Spin)

  • 60 11
    Cheng-Hong Liu に公開 2021 年 01 月 14 日
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