WEBVTT

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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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In this section and
also the next one,

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we're going to make a
case against aether.

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Aether was presumed to be the
medium in which light traveled.

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We do this-- we make
this case by studying

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the Michelson-Morley experiment.

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Michelson and Morley
went out to detect

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the motion of the Earth
relative to aether.

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And by not finding
the result, we

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can conclude that, at
least in this form,

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aether doesn't exist.

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So what is the
experimental setup?

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Also, it's shown in
the pictures above.

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We have a light source
here, through which

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the light travel to
some mirror which

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reflects about half the light.

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About half the light
goes through reflected

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on the second mirror and
then comes to a screen.

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The other part of the
light is up and back down.

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So the light either travels
against the aether wind

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or perpendicular
to the aether wind.

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If aether is the medium
in which light travels,

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then the velocity
needs to change.

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The velocity of light in
this medium will change.

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If there is no
aether wind, there

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is no change in the
velocity of the light.

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The result of the experiment
is an interference pattern

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on the screen.

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The experiment is called
an interferometer.

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So there are some systematic
uncertainties here.

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There are some unknowns.

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For example, if you're
building your table,

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it's not really clear in which
direction aether actually--

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which direction is actually the
direction of the aether flow.

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But you can get by this
by rotating the table

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and making various
sets of experiments.

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And that's what
Michelson and Morley did.

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I want you to show
that the effect they're

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about to observe--

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or they will not observe--

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is of the order of
v over c squared.

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And what you want
to do is compare

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the light as it travels on this
path number 1 to one mirror

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and on the second path
to the second mirror.

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So if you're
following the video,

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I ask you to just stop here
and figure out how long does it

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take for the light to
travel on this path

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here-- on the lower path, path
number 1, or path number 2.

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Well, obviously, I've
worked this out already.

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So we want to
calculate the time it

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takes light to
travel path 1 that

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is going up and coming down--

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going left and going right.

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So in the first
case, the velocity

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is reduced by the
velocity of aether.

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So the time it takes
is l1, the leg,

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divided by c minus v plus the
return leg, l1 over c plus v.

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And you work this out, and
you simplify a little bit,

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you get this first equation.

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For the second part,
the one up and down,

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you want to draw
this triangle here

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to figure out that t
is equal-- the time

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it takes is equal to the
square root of l square

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over c square minus v square.

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And then you simplify again,
you get this [INAUDIBLE]

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square root [INAUDIBLE].

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What's important is
the time difference

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for the light traveling
with two legs.

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And we find that the time
difference t1 or t2 minus t1

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is given by this bit
complicated looking equation.

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So now in the experiment, you
want to set up l1 equal to l2.

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To simplify, you might not be
able to do it very precisely.

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What you can do, however,
is rotate the table.

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If you rotate and then
compare the difference

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of the differences, you
find that here there's

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this v square over
c square dependence.

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I used a little trick to
simplify the square root

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as I use this 1 plus or
minus x to the nth power.

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It's about 1 plus minus
n times x for x plus 1.

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And since the
velocity of aether is

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presumed to be small compared
to the speed of light,

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that's a good approximation.

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The result of the experiment
was there was no effect.

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They tried-- they
improved the experiment.

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They tried to find
smaller effects.

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They didn't find any.

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The reason for this is
that there is no aether.

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But we can use this now to
make a case against the aether.

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But you could say
that maybe they

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didn't observe anything
because the aether is

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dragged with the Earth.

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So instead of the Earth
going through this aether,

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and therefore, we
experience aether winds,

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you could argue
that maybe aether is

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localized around the Earth,
moving with the Earth

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or maybe moving
with the universe.

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And so in the next video,
we'll look at a case

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against that scenario as well.