# Things we know about spin in quantum mechanics

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.