If I asked you to describe this apple, what would  you tell me?

You'd probably say something about   its size.

It's shape, color.

The fact that it has  a thin skin on the outside seeds in the middle,   you might tell me about the taste that it grows  on trees or that your uncle uses them to make   a fine pie.

Shout out to uncle Habib's apple  pie.

Even if I had never seen one in my life,   I have a pretty good sense of what one is now.

What if I asked you to tell me what an electron   is?

How would you describe its size, shape,  structure?

What does it look like?

What's it   made out of?

How does it interact with the  world around it?

How do we use it?

What is   it?

Except for how we use it, powering small  electronic devices to watch YouTube videos.

For example, we don't have easy answers to any  of those questions.

And the more you think about   them, the more confusing they seem to become.

Let's start with what seems like the simplest   question.

How big is an electron?

Now measuring  how big something is in our everyday world is   relatively easy, but you cannot measure the size  of an electron like this.

They're just too small.

Ironically, to measure the size of something super  small, you have to build something really big,   a particle accelerator.

Particle accelerators  shoot beams of particles at each other   at speeds very close to the speed of light, almost  300 million meters per second.

How those particles   interact with each other during and after the  collision can tell you roughly how big they are.

Here's an analogy.

These are small magnets  that I have super glued to the end of sticks,   but I want you to think of them as electrons being  shot at each other in a particle accelerator.

If I   bring together two low energy electrons, at some  point they will repel each other and deflect away   without touching.

Now, if I increase their energy,  the deflections will happen at smaller and smaller   distances until eventually I’m bringing them  together with enough energy that they'll actually   touch each other and bounce  off each other.

Ah!

Ah!

At this point, no matter how much extra  energy I add, they'll still bounce off   each other at exactly the same distance.

And  the same sort of thing happens in a particle   accelerator with electrons, or at least we think  it would happen.

If we were able to accelerate   the electrons enough.

Currently we've been able  to do some up to about 200,000 times the energy   they have just sitting around, but that's  not enough to detect any sort of hard core,   which is the dense hardball where the guts  of the electron would be concentrated.

So all we know for sure about the  size of an electron is that it's   smaller than 10 to the minus 18 centimeters.

That's about 170,000 times smaller than a helium   nucleus.

Some scientists think that if you  go down to 10 to the minus 20 centimeters,   you'll finally find the metaphorical center of  the Tootsie Pop.

Others think that you'd have   to get down to 10 of the minus 33 centimeters.

And  once you're there, you'd find that electrons don't   have a hardcore at all, but are strings.

That's  string theory.

And that's a whole other video.

Because we haven't figured  out how big electrons are,   theoretical chemists and physicists treat  them as point-like particles.

In other words,   as if they have no size, no diameter as  if they have zero volume.

Now electrons   do have mass.

one electron weighs about  nine times 10 of the minus 31 kilograms.

Now think about that for a second.

Nothing in  your everyday behaves like this; has mass, but   no volume.

Imagine saying I'm gonna treat this 200  gram apple as if it has zero volume.

That makes   no sense.

But with electrons it works.

It doesn't  break physics.

It doesn't break chemistry.

It just   breaks our brains.

Then there's something called  spin half.

Now let's start with the spin part.

First means that electrons behave as though they  are little spinning balls of charge.

The half part   means that you have to rotate an electron 720  degrees, two full turns to get it back to its   original spin state.

Now, given that we don't  know the exact size or shape of an electron and   treat them as though they have zero volume,  it can be hard to get your head around what   it means to rotate them 720 degrees.

This video  from Lloyd Watts shows a good visual analogy.

This strange looking gear thing is spin one half  in that you have to rotate it 720 degrees to get   it back to its starting point.

Obviously though,  electrons are not super small wooden gears.

One of the defining features of spin one half  particles like electrons, protons and neutrons   is that they take up space.

And the fact that  they do take up space, particularly the electron,   determines a lot of everything around us.

Now this is where things get philosophical.

Because I just told you that scientists treat  the electron as if it has zero volume, which   you'd think means that it takes up zero space,  but electrons do take up space and to see how   let's look at this hydrogen atom.

It has one  proton and one electron.

We can't say exactly   where the electron is at any given time, but we  can draw shapes around the nucleus that represent   regions with a high probability of finding the  electron.

These shapes are called orbitals.

So while the electron itself has zero volume,  in another sense, it takes up a relatively large   chunk of space within an atom.

There's one other  important piece to this puzzle.

All particles   with spin one half, including electrons, have  a fundamental property that says that only one   electron can be in an orbital in a given spin  state at a given time.

And electrons can either   be spin up or spin down.

So each orbital can hold  one spin up electron and one spin down electron.

And that is it.

This means there is a fundamental  limit on the number of electrons that can fit   into a given space in an atom.

Each electron  takes up space and pushes other electrons away.

Even though each electron itself  has zero volume.

By the way,   you probably learned this concept in high school  chemistry as the Pauli Exclusion Principle.

It's why you filled atomic orbitals with only  two electrons, one spin up and the other spin   down.

But it also applies when electrons from two  different atoms approach each other.

And that's   when the definition of taking up space starts  really making sense to show you I'm gonna need   a book.

And I just so happen to have one.

Oh I  think this one should do it.

When I hit this book,   why doesn't my hand go through it?

More  specifically, why doesn't the cloud of electrons   on the out's surface of my fingers go through  the cloud of electrons on the cover of the book.

Now you might think you know the answer  to this question and yes, electrons are   negatively charged and like charges do repel each  other.

So the electrons on the very outermost   surface of your hand, repel the electrons  on the very outermost surface of the book   before my hand even makes contact with the book.

But that's not the only thing happening here to  see what's really going on.

Let's assume that   my hand and the book are both made of neutral  helium atoms.

Now I'm choosing helium because   it's one atomic orbital is full of electrons.

It's what your high school chem teacher called   happy.

Even though your skin and the book  are definitely not made of helium, they're   both made of long and complicated molecules.

The  vast majority of the atoms in those molecules are   happy, meaning they have their full compliment of  electrons.

So helium gives a reasonable picture.

Okay.

So each helium atom has two electrons in  its one S orbital.

If these two orbitals were to   overlap in space, in other words, if my hand and  the book were to take up the same space, then we'd   have two, two spin up electrons and two spin down  electrons in the same orbital in this same space.

And here's the thing.

The universe literally  does not allow that to happen.

Why not?

We   don't exactly know.

All we know is that if we  allow, for example, two spin up electrons to   occupy the same orbital, we'd end up with things  like negative probabilities affect not following   causes and other deeply, deeply weird behavior.

So when the book is taking up this space, my hand   cannot also take up this space because identical  electrons cannot overlap.

You shall not PASS!

This is so fundamental that it sounds obvious,  but let's consider something that is in many ways,   the opposite of an electron, a particle  of light, a photon.

Photons and electrons   can be described by the same fundamental  equations.

The difference between them is   that while electrons are spin half, photons are  spin one.

So instead of needing to turn them   two full turns to them back to the same spin  state, you only need to turn them one full turn.

Just like literally everything you see around  us.

If I turn this apple 360 degrees, it comes   back to the same place that it started at.

Now in  that sense, photons are not as weird as electrons,   but in other ways they're less intuitive.

Look at  these two lasers.

They're both shooting out red   photons.

Laser on the left is way more intense.

Meaning it's shooting out way more photons than   the one on the right, which you can clearly see  because it's much brighter.

Now look at the width   of the beams.

It's the same.

Identical.

And yet the beam on the left is brighter.

What does that tell you?

And it tells you  that say 300 photons can take up the exact   same amount of space as 100 photons.

How is  that possible?

Well, photons are spin one   particles and spin one particles are not  subject to the Pauli Exclusion Principle.

Why not?

We have no idea.

The universe is  just cool with letting hundreds, thousands,   trillions of spin one particles, hang out in the  same space.

There's actually no upper limit to   the number of photons that can occupy the same  space.

We can cram as much light as we want   into as small a space as we want.

In fact, with  light, the word cram has no meaning since adding   additional photons doesn't reduce available  space for more photons until you add so many   that the system collapses into a black hole.

At that point, you've got bigger problems.

Here's a thought.

Imagine if somehow we were  made of photons instead of protons, neutrons   and electrons.

Now that statement is fundamentally  weird on many different levels, but just roll with   it here.

Two humans or five or a thousand could  take up the exact same space.

But of course,   if we were made of photons, we wouldn't be, well,  human.

The fact that spin one half particles like   electrons, protons, and neutrons take up space  is literally the reason that matter, all stuff,   as we know it exists.

If these particles were spin  one, they'd have a wispy existence passing through   each other like ghosts, no rocks, no floor, no  earth, no animals, no plants, no us.

So to get   back to where we started, what is an electron?

Well, it's a particle with charge and spin.

It may or may not have any volume, but we treat it  as if it has none.

And despite having no volume,   it definitely takes up space to the extent  that it's one of the fun building blocks of   all matter in our universe.

So to summarize an  electron is, well, I mean, it's kind of like a,   well, if you, if you took a, if you took  a tiger and uh, no, that's not right.