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MARKUS KLUTE:
Welcome back to 8.20.

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In this section, we're going
to talk about cause and effect

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and causality.

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And we do this with
an example which

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talks about the good
guys and the bad guys.

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There's always good guys and
bad guys in the universe.

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In this example,
those two groups,

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they were fighting a war.

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And after some very
long and grueling time,

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they were able to
sign a peace treaty.

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So this happens in this
story at year number 0.

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So in year 0, a peace
treaty is signed.

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And the good guys, they
go back to their families.

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They go back home
to their planet.

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There's a spacecraft,
which is able to go

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with a velocity of 0.6
times the speed of light.

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The bad guys.

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That's the bad guys.

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And so they develop a
faster-than-the-speed-of-light

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spacecraft to follow
the good guys.

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And they succeed with the
development of the spacecraft

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after four years.

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So they do.

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They follow the good guys.

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And in year number
5, the bad guys

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attack and destroy
the good guys.

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The challenge for you now
is to explain the story

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and answer the
following question.

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When and where does the attack
happen, from the good guys'

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perspective?

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And when did the bad guys
invent the spacecraft,

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from the good guys' perspective?

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You will see some surprising
results in this analysis.

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So please stop the video
and try to work this out.

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I recommend drawing a
space-time diagram in order

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to get to a good picture of
what is actually happening here.

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If you do this, you find
the space-time diagram

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here for the bad guys.

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So again, there's a number
of important events.

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In year number 0, the
peace treaty is signed.

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And then the good
guys, they start

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traveling away at 0.6
times the speed of light.

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So what you see here is a
world line of the good guys.

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In year number 4, in
the reference frame

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of the bad guys, they
developed a spacecraft,

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and they keep following
the good guys.

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And here in year number 5,
the attack actually happens.

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So if you analyze this
for the good guys,

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you find that the exposition,
the position of the attack,

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is in their spacecraft.

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So let's figure out whether
or not this is correct.

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You find gamma and
xB minus v times tB.

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If you put in the
numbers, you find,

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luckily, the exposition
is equal to 0.

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At what time did
this event happen?

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Here, for the good guys, you
find gamma times tB minus v

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over c xB.

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And again, if you
put the numbers in,

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the attack for the good guys
happens in year number 4.

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But then the question
is, when did the bad guys

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invent the spacecraft
in the reference

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frame of the good guys?

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And if you put in
the numbers, you

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find the invention actually
happens in year number 5.

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So the attack happens
before the spacecraft

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is invented in the reference
frame of the good guys.

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And this clearly
violates causality.

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You cannot use a device which
is not invented yet unless you

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travel faster than
the speed of light.

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You travel in time.

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All right.

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I find this a really
funny and geeky example.

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And the reason why this doesn't
work out, why it's geeky,

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is that they travel faster
than the speed of light.

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So let me conclude this
part of the section

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here with a concept question.

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We have an event A,
and ask ourselves,

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can event A cause other events?

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So event A might be the
invention of a spacecraft.

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Can event A cause event C,
event D, or more than one event,

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like B and C or B and D?

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Note that the time access
here has units years

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and the x-axis has
units light years.

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Again, stop your video here.

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Think about your answer.

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Maybe you draw in the
space-time diagram

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in order to find the answer.

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And the answer, the correct
answer, is C. Only event C

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can be caused, because
only C lies within what we

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call the light cone of event A.

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In order to impact, in
order to cause an effect

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on any other event,
the message needs

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to be traveling
with speed smaller

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than the speed of light.

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So that means that, in
order to reach event C,

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we can design a
spacecraft, or we

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can send a light beam to this
event or in this direction.

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And then just wait a little
bit, in order to make any sort

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of impact on event C. We cannot
travel faster than the speed

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of light, which would be
necessary in order to reach

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event D. And you can also
not go backwards in time,

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this message is, in
order to reach event D.