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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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In this section, we want to
study space-time diagrams

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a little bit more in detail,
and also define certain regions

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in space-time diagrams.

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So let's start again with
Alice's space-time diagram here

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in which we plot or draw
Bob's space-time diagram.

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The relative velocity difference
is 0.5 times the speed

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of light, and that leads
to a gamma effect of 1.2.

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We also plotted the world line
of light in here in yellow.

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Light is the speed
of light equal to c.

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I want to discuss
two specific events.

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The first one here,
event number 1,

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is the one where tA, the
time for Alice's [INAUDIBLE],,

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and xB, the space for
Bob, is equal to 0.

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So this event lies
on Bob's timeline.

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If we read off the
time on Bob's clock,

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we see it's 0.83, 1 over gamma.

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And here, we can
immediately [? read of ?]

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time dilation for this event.

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Note that while xB Bob is equal
to 0, xA for Alice is not 0.

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Similarly, we can look
at the second event here,

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where we read off xA equals 1.

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[INAUDIBLE] 1, in this
case, light year for Alice.

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And so now we want to
investigate this length

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in Bob's reference frame.

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For him, time is equal to 0.

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So tB equals 0.

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We can immediately again
read off xB equals 0.83,

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and that indicates
length contraction as

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of the [INAUDIBLE].

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Important to note here is
that those two, Alice and Bob,

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will not agree when the time
and the measurement was made.

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All right.

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So let's zoom out
here a little bit

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and look at another
space-time diagram.

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So in this space-time
diagram, again, I drew light--

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blurred lines, or
blurred lines for light--

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in yellow.

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And I [? wrote ?] a total
of 12 different events.

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Now we want to
characterize those events.

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And we want to characterize
them based on whether or not

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they are time-like,
light-like, or space-like.

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As time-like, we
define those events.

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We have c squared, t
squared, minus x squared,

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is greater than 0.

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Light-like are those which are
like light in a blurred line.

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[? ct, ?] c squared, t squared,
minus x squared, equal to 0.

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And space-like, those
were c squared, t squared,

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minus x squared, smaller than 0.

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The first task is now to find
to which of those regions

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the individual
events correspond.

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And so again, stop
the video, and try

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to figure out whether or not
you can find the solutions.

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Because the solutions
are given here.

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Time-like are
events 2, 5, and 6.

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Light-like are the ones which
lay on the yellow lines.

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1, 7, 4, and 9.

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And space-like are
8, 12, 11, 10, and 2.

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One of the things you can
find, if you are starting here

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in the origin, and you're
going to correspond

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to any event in the
future, you can only

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do that if the
events are time-like.

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If the events are
space-like, you

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will not be able to correspond
between those two events.

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That's one of the
ways to read this kind

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of space-time diagram.

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And in the next section,
in the next video,

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we'll talk about causality,
meaning can a specific event

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cause something to
happen, another event?

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Again, this can only happen
if the events are actually

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time-like.