Hey Crazies.
Let’s talk a little more about quantum spin.
I mentioned it briefly in this video and some of you were still asking.
The short version is that it’s a little bit of angular momentum,
but that always brings up a question:
What is angular momentum?
Which I could answer, but, honestly, it’s not going to help you.
Electrons do not orbit.
Electrons do not spin.
We know not where they’re going.
We know not where they’ve been.
Particles like electrons can’t possibly be doing this.
Remember, in this video, we said the upper limit on the size of an electron is 10 to
the negative 18 meters, the smallest distance we’ve ever measured.
Let’s assume electrons are solid spheres, which isn’t necessarily as far-fetched as it
is for chickens or cows.
If those electrons have a diameter of 10 to the negative 18 meters, to be spinning with
an angular momentum of one half h-bar, the outer edge would be moving at almost 1,000,000
times the speed of light.
And the smaller the electron is, the faster it would have to be spinning.
The only possible conclusion is it’s not spinning.
Just.
Just think of it this way: Particles have all sorts of properties.
Mass, Charge, Position, Energy, etc.
Spin angular momentum or, just spin for short, is one of those properties.
We can sort these properties into two categories: Properties the particles have because of what
they are and properties they have because of what they’re doing.
Spin, as it turns out, falls into the first category.
It’s a type of angular momentum a particle has just because it’s that particle
and for no other reason.
It shouldn’t even be called spin.
Intrinsic angular momentum is more accurate, but not nearly as catchy.
Intrintum?
Intum?
Angtrinsic?
Tang?
The reality is just so unfamiliar, there isn’t a better word for it.
But how do we know it’s there?
Magnets!!
Any charge with any kind of momentum is going to have a magnetic field, which means
it's going to be affected by another magnetic field.
We’ll stick with electrons for now because, well, they’re easy.
EXPERIMENT TIME!!!
There was this experiment done in 1922 called the Stern-Gerlach Experiment.
Full-Disclosure: Otto Stern and Walter Gerlach did not use a beam of free electrons.
Because that isn’t going to work.
Charge is a bigger influencer than Spin, so they’ll all veer the same direction if they
get too close to a magnet.
Charge.
Such an attention hog.
Anyway, you need to make it neutral, like a whole atom instead.
Stern and Gerlach used silver.
Because reasons!
But I don’t want to get caught up in the details of the experiment.
All that matters is we now have an atom that we’re going to pretend is just a really
massive neutral electron.
I know.
It sounds silly.
But that’s how I feel about all experiments.
Theoretical physics is superior!
Next, we need something to control that electron.
Say, I don't know, two strong magnetic poles shaped like this.
Again, don’t get caught up in the details.
Think of it as just a spin separator.
If we send a bunch of these electrons through, we get two distinct groups, which we call
spin-up and spin-down.
Since the biggest possibility is plus one-half, we say they’re spin one-half particles,
but there’s nothing special about up and down.
We get two groups no matter how we orient this thing.
Each of the three main directions can only have two possible values: plus one half
and minus one half.
Never zero.
I wonder what that looks like.
If all the directions are plus one half, the spin arrow looks like this.
But this is quantum mechanics.
Only one of the directions can be definite at any one time.
What I mean is, if one of the directions is, say, definitely one half, like, for sure.
Then the other two directions are in a weird combination of both plus one half and minus
one half.
It’s called a Quantum Superposition.
So spin-up actually looks more like this.
There are only 4 possible directions for that arrow, all pointed up.
If we then tried to measure left and right, we might find that it’s pointed right.
Except now, it’s in this state.
We don’t know if it’s up or down anymore.
If you go back and measure up and down, you only have a 50% chance of getting up.
I shouldn’t have said that.
You only have a 50% of measuring up.
Ah, now it’s just depressing.
I just mean that, if you separate two groups in one direction.
Block one of those group.
Then separate into groups again in a different direction.
Block one of those groups.
And then re-measure in the original direction.
You get two groups, not one.
It forgot the original measurement.
There are always 4 possible directions to the spin arrow, so there is always quantum
weirdness.
Which is true of any spin one-half particle including protons and even neutrons.
Yes, neutrons!
They might be neutral, but they’re made of smaller particles that aren’t neutral,
so they’re still tiny magnets.
It gets even weirder with bigger spins.
Spin-one particles are separated into 3 groups.
So their spin arrows would look like this.
Spin-three-half particles are separated into 4 groups.
So their spin arrows would look like this.
Spin-two particles are separated into 5 groups and so on.
Of course, this only works if the particle has charge on a fundamental level.
If it doesn’t, like the photon, we have to be a little more creative.
If you have any questions, please ask in the comments.
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And until next time, remember, it’s okay to be a little crazy.
The featured comment comes from SteveMonkey6666 who asked:
Do neutron star shine?
Technically, yes.
They are hot, so they are emitting light from their surface.
But!
They’re not very bright.
There's just not enough surface area.
Thanks for watching!