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MARKUS KLUTE: Welcome back
to 8.20, special relativity.

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In this section, we want
to talk and investigate

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a bit more length contraction.

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We have seen length
contraction a few times

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already in this class.

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We have derived it.

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We have seen it in application.

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But we want to get
some sort of feeling to

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how can we actually
understand what's

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happening to the objects.

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Later in this section,
in this video,

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we'll talk about another
paradox, spacecraft on a rope.

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So let's get to it.

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So the situation here is as we
have seen a few times already.

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We have Alice being
at rest, and Bob

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is moving with a velocity v.
And what we are interested in

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is this object here, which
might be a rod of some sort.

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You can think about a
spacecraft if you want,

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but a specific object, which,
at rest, has a length LB.

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For Alice, this object
is Lorentz contracted,

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and it appears shorter.

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So now what happens now if Bob
accelerates from his velocity v

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to a velocity v plus delta
v with respect to Alice?

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How does the acceleration occur?

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And how can we understand
then the further shrinking

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of the spacecraft?

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Bob tries really, really
hard to accelerate such

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that all elements of
this rod or spacecraft

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are being accelerated
simultaneously

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in his framework.

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You can think about
splitting up the spacecraft

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into small elements.

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They're all getting a
little bit of a kick,

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a little bit of an extra
momentum at the very same time.

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So, if now Alice observes
the same situation,

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we find that she looks
at the spacecraft.

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And, because the leading
clock in the spacecraft,

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in Bob's spacecraft,
lags, she observes

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that the spacecraft's back
is being accelerated first.

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And, because it's
accelerated first,

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she observes that the
spacecraft shrinks

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just a little bit because
of the additional velocity.

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Well, that's kind of
an interesting picture

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to think about how we can
understand length contraction

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and how we can understand
length contraction

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once there's
acceleration involved.

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OK, so the next question
now or the next topic

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here in this video is the
spacecraft on a rope paradox.

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This was phrased by Bell
in the 1950s and '60s.

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He was working at CERN at the
time and roaming the corridors,

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discussing with his colleagues.

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The situation here is related
to the one we just discussed,

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but slightly different.

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So let me explain.

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So again we have Alice
as an observer, observer

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in a reference frame A,
observing two spacecrafts.

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They are identical spacecrafts.

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They have the same engines.

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And they are separated
by distance D.

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So now Alice gives a
signal to both spacecrafts

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simultaneously in
her reference frame

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to accelerate at
the same time such

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that the distance between
B and C remains constant.

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So they're asked to accelerate
such that the distance remains

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constant.

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Well, the question now is,
when those two spacecrafts

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are connected with a rope,
will this rope break?

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So I'll let you think
about this a bit

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and come up with
your own answer.

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In the meantime, this is not
such a hard problem actually.

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In order to keep the
distance constant for A,

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the distance in the
BC reference frame,

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in the reference frame
of the two spacecrafts,

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needs to expand.

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So LA, so the distance as
observed by Alice or reference

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frame A, is equal
to 1 over gamma,

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the distance between
the two [? planes. ?]

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And for this to stay--
for LA to stay constant

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while there's acceleration
going on, LBC needs to increase.

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That's why the rope will break.