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.