WEBVTT

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MARKUS KLUTE: Welcome
back to [INAUDIBLE],,

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special relativity.

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So moving from
special relativity

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to general relativity,
we relax the requirement

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that reference
frames can only have

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a constant relative
velocity to each other.

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So we are looking
at what happens now

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if you have accelerating
reference frame,

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and the first example is that
of rotational time dilation.

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So I mentioned you have a
device which has two clocks.

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And so the first block
sends it ticks up

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in terms of light beams, beams
with some specific frequency.

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So there is a
transmission going on,

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and there is a receiver
on the other side.

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And the clock, the
upper clock, u clock,

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submits the same things.

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They both have the
same frequency,

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let's say 10 pulses per tick.

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We also assume now
that we don't have

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to consider special relativity
effects, yes, so the velocity

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of the thing is very small.

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OK so relativistic
effects are small.

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But when I now
accelerate this device,

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there is an interesting effect.

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The lower clock will receive
more than 10 pulses per tick,

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so it is perceived as running
slow from the upper clock,

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right.

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So the lower clock is expecting
10 ticks, but it's seeing 12,

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so you think that your
clock is running slow.

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Similarly you can
discuss the upper clock,

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which because it's
accelerating upwards,

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it only receives
8 pulses per tick.

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So it's expecting 10, so
it's perceived to be faster.

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Now, this acceleration
as in this example,

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as I've discussed previously,
is equivalent to being

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in a gravitational field.

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So we have a time
dilation effect on us.

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We already discussed
the consequence

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in the discussion
of GPS systems.

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Here is a summary of this
plot, and just showing you

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the effect of changing
gravitational fields

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as a function of the distance
of the center of the Earth.

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And you see that the rotational
speed-up, 0 on the Earth's

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surface, becomes rather
large the further away

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you get from Earth,
while if you consider

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that the object, a a satellite,
in an orbital motion, the speed

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of this object is kind of
compensating partially.

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But there is this net effect,
as we discussed earlier,

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on the GPS system.