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- There's a law in physics that
has stood the test of time.

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Laws come and go.

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Sometimes we discover new things.

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We have to scrap them,
ammend them, adjust them,

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tweak them, throw them away,

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but there's one law that has
been around for a long time

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and no one has ever, ever
tried to damage this law

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or discovered any experiment
that has shown it to be wrong,

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and it's called the law
of conservation of charge.

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And this is electric charge,
is what we're talking about

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in this particular example.

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So what does this mean?

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Well, imagine you had a
box and inside of this box

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I'm gonna put some charges.

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So let's say we have a particle here

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and it's charge is positive two coulombs.

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And then we have another
charge flying around in here,

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and it has a charge of
negative three coulombs.

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And we have another charge over here

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that's got, I don't know,
positive five coulombs.

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These are flying around.

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What the law of
conservation of charge says

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is if this box is closed
up, in the sense that

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no charge can enter or exit.

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So I'm not going to let any charge come in

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and I'm not gonna let any charge go out.

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If that's the case,
the total charge inside

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of this region of space has to be constant

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when you add it all up.

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So if you want a mathematical statement,

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I like math, the mathematical
statement is that if you

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add up, the sigma is the
fancy letter for adding up,

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all the charges in a given region,

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as long as, here's the asterisk,

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as long as no charges
are incoming or outgoing,

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then the total amount of
charge in that region of space

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has to be a constant.

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This math looks complicated,
it's actually easy.

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All I'm saying is that if
you add up all this charge...

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Positive two coulombs plus five coulombs

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minus three coulombs, you'll get a number

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and what that number
represents is the total

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amount of charge in there.

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Which is going to be,
five plus two is seven,

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minus three is four.

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Positive four coulombs.

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You ever open up this box,
you're always going to

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find four coulombs in there.

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Now this sounds possibly obvious.

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You might be like, duh.

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If you don't let any of
these charges go in or out,

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of course you're only going
to find four coulombs in there

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because you've just got
these three charges.

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But not necessarily.

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Physicists know if you
collide two particles,

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these things don't have to
maintain their identity.

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I might end up with
eight particles in here

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at some later point in time.

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And if I add up all their
charges, I'll still get four.

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That's the key idea here.

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That's why this is not just a frivolous

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sort of meaningless trivial statement.

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This is actually saying something useful,

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because if these protons,
they're not because

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this is a positive two
coulomb and the proton

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has a very different charge,

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but for the sake of argument,
say this was a proton,

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runs into some other particle,
an electron, really fast.

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If there's enough energy,
you might not even end up

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with a proton and an electron.

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You might end up with
muons or top quarks

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or if this is another proton,

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you end up with Higgs
particles or whatever.

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And so at some later point in time,

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here's why this law is
important and not trivial,

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because if this really is closed up

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and the only stuff going
on in there is due to these

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and whatever descendants
particles they create,

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at some later point in time
I may end up with, like,

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say this one, it doesn't even
have to have the same charge.

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Maybe this one's positive one coulomb.

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And I end up with a
charge over here that has

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negative seven coulombs.

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If these were fundamental particles,

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they would have charges
much smaller than this,

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but to get the idea across,
big numbers are better.

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And let's say this is
negative four coulombs.

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And then you end up with
some other particle,

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some other particle you
didn't even have there.

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None of these particles were there before.

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And some charge q.

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Now we end up with these
four different particles.

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These combined, there
was some weird reaction

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and they created these particles.

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What is the charge of this q?

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This is a question we can answer now,

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and it's not even that hard.

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We know the charge of all the others.

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We know that if you add up all of these,

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you've got to add up to
the same amount of charge

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you had previously, because the law of

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conservation of charge says
is if you don't let any

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charge in or out, the total charge

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in here has to stay the same.

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So let's just do it.

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What do we do?

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We add them all up.

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We say that positive one
plus negative seven coulombs

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plus negative four coulombs
plus whatever charge

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this unknown, mystery particle is.

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We know what that has to equal.

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What does that have to equal?

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It has to equal the total charge,

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because this number does not change.

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This was the total charge
before, positive four coulombs.

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That means it has to be the
total charge afterward in there.

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That's what the law of
conservation of charge says.

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So that has to equal positive four.

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Well, negative seven and
negative four is negative 11,

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plus one is negative 10.

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So I get negative 10 coulombs, plus...

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Oh, you know what, these
q's look like nines,

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sorry about that.

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This is law of conservation of charge.

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I'm gonna add a little tail.

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This isn't the law of
conservation of nines.

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So this is a little q.

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This is a little q, not a nine.

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And so plus q equals four.

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Now we know that charge
has to have a charge of

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14 coulombs in order to
satisfy this equation.

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But you don't even really need a box.

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I mean, nobody really does
physics in cardboard box,

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so let's say we're doing an experiment

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and there was some
particle x, an x particle.

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And it had a certain amount of charge,

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it had, say, positive three coulombs.

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That would be enormous for a particle,

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but for the sake of argument,

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say it has positive three coulombs.

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Well, it decays.

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Sometimes particles decay,
they literally disappear,

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turn into other particles.

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Let's say it turns into y
particle and z particle.

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Just give them random names.

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And you discover that this y particle

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had a charge of positive two coulombs

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and this z particle had a
charge of negative one coulomb.

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Well, is this possible?

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No, this is not possible.

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If you discover this, something went wrong

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because this side over here,

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you started with positive three coulombs.

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Over here you've gotta end up,

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according to the law of
conservation of charge,

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with positive three coulombs,
but positive two coulombs

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minus one coulomb,
that's only one coulomb.

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You're missing two coulombs over here.

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Where'd the other two coulombs go?

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Well, there had to be some
sort of mystery particle

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over here that you missed.

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Something happened.

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Either your detector
messed up or it just didn't

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detect a particle that had
another amount of charge.

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How much charge should it have?

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This whole side's gotta add up to three.

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So if you started off with three,

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over here, these two together, y and z,

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are only one coulomb.

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That means that the
remainder, the two coulombs,

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the missing two coulombs, has to be here.

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So you must've had some particle or some

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missed charge that has
positive two coulombs.

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Is that another y particle?

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Maybe, that's why physics is fun.

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Maybe it is in there, maybe
you missed another one.

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Let me ask you this.

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So let's say we get rid
of all these charges.

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Here's one that freaks
people out sometimes.

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Take this.

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Let's say this had no charge.

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No charge, it was uncharged.

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You got some particle with zero coulombs.

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Is it possible to end up with
particles that have charge?

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Yeah, it can happen.

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In fact, if you have a
photon that has no charge,

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it's possible for this photon

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to turn into charged particles.

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How is that possible?

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Doesn't that break the law
of conservation of charge?

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No, but you've gotta make sure that

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whatever charge this gets,
say positive three coulombs,

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then this one's going to have to have

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negative three coulombs so
that the total amount of charge

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over here is zero coulombs
just like it was before.

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So this is weird, but yeah,
photon, a beam of light,

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can turn into an electron, but that means

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it has to also turn into an anti-electron

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because it has to have no
total charge over here.

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And an anti-electron has the
same charge as an electron,

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but positive instead of negative.

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Which is why it's called a positron.

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Anti-electrons are call positrons
because they're the same

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as electrons, just positive.

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You don't really need to know that.

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In fact, you don't need to know a lot

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about particle physics,
that's the whole point here.

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Just knowing conservation of charge

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lets you make statements
about particle physics

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because you know the
charge has to be conserved

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and that's a powerful tool
in analyzing these reactions

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in terms of what's possible
and what's not possible.