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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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So if there is a
time dilation effect

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due to gravitational
fields, then there's

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also a redshift which is
of gravitational fields.

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So a consequence
of time dilation

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is a change in the
light frequency.

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And I asked you to estimate
the magnitude of this effect.

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And the example you want to
use is the one shown here.

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So you have a tower just--

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not randomly, but 22
and 1/2 meters tall.

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And a light beam is sent down.

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Basically, the tower is
built on this planet,

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and there's gravity
that's acting.

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So this is basically an
accelerating reference frame.

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The length of the tower
is, again, 22 meters.

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And I would like you
to just get a feeling.

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How big can this effect be,
the effect of redshift here?

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So please, try to work this out.

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The way to think about
this is first to say, OK,

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now the light--

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the delta t equals
the light to travel--

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is l divided by c.

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The speed of light is c.

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The length is l.

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The change in velocity
is g, acceleration,

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times l divided by c.

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So the Doppler shift then is the
frequency, the new frequency,

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divided by the
initial frequency.

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And that can be approximated
by 1 plus delta v over c.

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So we find that it's 1 plus
g times l over c square.

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Now the speed of
light is pretty fast,

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3 times 10 to the
9 meter per second.

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And this distance is
only 22 and 1/2 meters.

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So we find that this is a
tiny, tiny, tiny effect.

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But nevertheless,
experimentalists at Harvard

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tested this effect.

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So Pound, Rebka, and Snider
in the 1950s and '60s

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were able to show
this very tiny effect.

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You want to know
more about this,

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you can, for example, look up a
small description in Wikipedia

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here.

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But there's quite
some literature

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on those experimental
tests [INAUDIBLE]