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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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In this section, we're
going to build on--

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we just learned about
the relativistic Doppler

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effect and redshift.

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So we take on traveling
through the galaxy

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from here, from Earth, towards
the center of the galaxy.

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The situation is as follows.

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We have Bob, who's
stationary on our planet,

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Earth, and Alice, who makes
use of a new spacecraft.

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This spacecraft
is able to travel

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with a velocity of 0.99999998
times the speed of light.

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So that's really fast.

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It corresponds to a
gamma factor of 15,000.

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Now, the center of the galaxy is
about 30,000 light years away.

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And in Bob's reference
frame, this journey

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will take about 30,000
years, because velocity

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is about the speed of light.

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For Alice, however, the journey
will only take two years.

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So it's quite doable.

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The question, now, is
what does Alice see?

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Literally, what is
she going to see

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while she is looking out of
the windows of the spacecraft?

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Is the picture
similar to the one

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we see in some of the
movies, where on the horizon,

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there's lots of stars, and once
the spacecraft accelerates,

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you see those dots
kind of blurry, coming

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towards us, right?

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Or is the situation
somehow different?

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The starlight has a wavelength
of about 600 nanometers,

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and the cosmic microwave
background a wavelength

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of 1.06 millimeters.

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So how is Alice going
to observe those two

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light sources in her travel?

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So I invite you
to work this out,

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but also think about
the next question.

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How long does it take for
Alice to accelerate from 0

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to her velocity with
an acceleration of 10

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meters per second
squared, which is

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1g, which is very, very doable?

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OK.

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So I invite you to
stop the video here

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and work out those
numbers to get a feel

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and speculate a little bit about
how this journey is actually

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going to look like.

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So here's the solution.

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So the light's
moving towards us,

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so it's going to be blueshifted.

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The velocity is given here.

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And with beta, we have seen
that redshift or 1 plus

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redshift is equal to the
emitted wavelength divided

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by the observed wavelength.

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And you find that
that factor is 10,000.

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So we just have to divide our
emitted wavelength by 10,000

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and find that the
observed starlight has

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a wavelength of 0.06
nanometers, which is X-ray.

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So she's going to be
flooded by X-rays of light

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coming from the stars.

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And similarly, the observed
cosmic microwave background

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is going to be about
106 nanometers, which

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is ultraviolet light.

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The ultraviolet light--
there's a spectrum to this.

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So what she's going to see is
X-rays, which she can actually

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not see with her eyes.

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But she will be able to see
the ultraviolet, or some part

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of the spectrum, as kind
of a blurry, fuzzy kind

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of background all
over the place.

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So the situation is actually
different from what we just

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saw in this picture.

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A few more fun facts about the
cosmic microwave background.

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It's actually at a temperature.

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So the spectrum of cosmic
microwave background, those

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photons, they correspond
to a spectrum emitted

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by [INAUDIBLE] which corresponds
to a specific temperature

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of 2.7 kelvin.

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That is the temperature
of our universe.

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This temperature was about
3,000 kelvin about 380,000 years

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after the Big Bang, the age
of the universe at the time.

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And so then at that time, this
corresponds to visible light.

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But at that moment, the light
stopped interacting-- well,

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stopped--

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The likelihood for the light
to interact with something

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out there in the
universe became so low

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that it just
stopped interacting.

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And then the frequency
changed, because the universe

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was expanding.

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So what we are
seeing today is kind

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of a relic of the universe
at that time, at 380,000

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years after the Big Bang.

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And if you study the
cosmic microwave background

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with some more
precision, you see

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that there are
actually fluctuations

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which can be analyzed.

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It turns out that you can
correlate those fluctuations--

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the fluctuations of the
energy density 380,000 years

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after the Big Bang--

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to this, the present of
today's stars and galaxies

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and galaxy clusters.

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So those energy
fluctuations, they

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served as seeds for the
formation of galaxies

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and galaxy clusters.

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Quite interesting.

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Today, we have about
400 of those photons--

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microwave photons-- per
square cubic centimeter.

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So there's quite a busy
environment around here.

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So like, this little cube has
about 400 of those photons.

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Now, this is a spectrum as well.

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It's not just a
monochromatic background,

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but it's a spectrum
which corresponds

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to these temperature
[INAUDIBLE] All right.