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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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In this section, we talk
about the famous twin paradox.

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It's probably the most famous
paradox in special relativity.

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I want to get to
the bottom of this,

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and understand
really where there

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is a conflicting or
contradictory statement

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in this story.

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Let me just first say that
this is personal to me.

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I do have a twin
brother, and you

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can see three pictures of
myself and my twin brother here.

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We were very little on our
first day of school in Germany.

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You get a little
box of candy when

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you go to schools to make it
more attractive to actually

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learn and study.

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And then a picture,
which is probably already

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about 10 years old.

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What you can take away
from here is clearly

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moving clocks are slow.

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It turns out that
my twin brother

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lives in the very same
village in Germany

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where I grew up,
where we both grew up,

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while I traveled the world
constantly and constantly

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on the road between
France and Geneva

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and Switzerland and
the United States.

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And again, I think there
is no dispute here.

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It can be seen from this picture
that your professor looks

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much younger.

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I even have a more
recent picture.

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This is two years ago.

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The German Kris Kringle Market,
where I asked my brother

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to take this picture for
this class, for 8.20.

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And again, I think the answer
to the question is clear.

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Professor Klute has aged less.

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All right.

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On a more serious
note, we're going

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to quantitatively understand
and analyze the situation.

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And we use Bob and Alice again.

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In this situation,
here Bob stays local.

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Alice has a spacecraft, and she
moves with the velocity of 0.6,

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six times the speed of light,
a gamma factor of 1.25.

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The travel takes her
to a distant star,

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which is in this example
It's three light years away

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from Bob, measured by Bob.

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The journey takes her, on
Bob's clock, five years,

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and the return takes
another five years.

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She doesn't spend much time.

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She wants to go home
as quickly as possible.

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If you analyze this,
from Alice's perspective,

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we see that for Alice, the
journey takes four years,

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and the distance traveled
for her in a spacecraft is 0.

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From Bob's perspective, the
journey, as seen by Alice,

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is only 3.2 years long.

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And so we find that
there's already a conflict.

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If you add the times together,
both ways, the inbound

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and the outbound ways, 6.4
years is not equal to 10 years.

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So there's already a
contradictory statement

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in this story.

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But the key to the
understanding of this problem

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is that Alice, in
order to return,

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has to change reference points.

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And there, we do have to
resynchronize the clocks,

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if you want, or add a
specific extra factor.

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And we'll go back
to this when we

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look at space and [INAUDIBLE].

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So the time, as seen
by Bob, is 3.2 years

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for the outbound journey,
and then 3.6 years

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in order to resynchronize
the clocks on the return,

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on the turning around.

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And then 3.2 years on the
return, which makes 10 years.

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And so that observation
of Bob, of Alice,

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is in agreement with
Bob's own clock.

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All right.

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So we saved the day here.

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Let's look at
space-time diagrams.

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The outbound journey
is shown here.

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You see I've got it--

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in addition to Bob's
reference frame,

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I've plotted Alice's reference,
and it makes it easier

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to understand what's going on.

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So we see in Alice's
reference frame,

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the journey takes four years.

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If you then go back to the
position in which Bob is,

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3.2 years have passed.

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So this is iffy.

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At the time when Alice
arrives we go back

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to the position of Bob,
3.2 years have passed.

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We then turn around and
ask the very same question.

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At that time-- it's
still four years--

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we go back the other
direction now to Bob,

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we are already
much further ahead,

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3.2 years plus 3.6 years.

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And then the journey continues,
and we add another 3.2 years

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to the journey.

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When Alice and
Bob reunite, Alice

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aged by eight years, 2 times
4, and Bob aged by 10 years.

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So the question now is,
there may be a paradox here.

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Is it possible that we
missed somehow that by--

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and try to understand why this
is a probably not symmetric.

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Why can I not just use
the other reference frame,

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and just declare that
Alice stayed stationary

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in her spacecraft while
Bob moved away with Earth

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and then came back?

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Why are those two
things not consistent?

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The answer is that
it's not Bob who

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has to change reference
frame, but Alice.

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It's Alice who has to do this.

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There is where the asymmetry is.

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You can argue if you want that,
in order for Alice to do that,

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she actually has to accelerate.

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But we don't have any
sort of discussion

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of how the acceleration
actually went about.

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It's really the change
in reference frame

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which is crucial
in this discussion,

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and causes the asymmetry
between Bob and Alice.