1
00:00:13,080 --> 00:00:15,480
MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

2
00:00:15,480 --> 00:00:18,330
In this section and
also the next one,

3
00:00:18,330 --> 00:00:20,400
we're going to make a
case against aether.

4
00:00:20,400 --> 00:00:25,320
Aether was presumed to be the
medium in which light traveled.

5
00:00:25,320 --> 00:00:28,350
We do this-- we make
this case by studying

6
00:00:28,350 --> 00:00:30,820
the Michelson-Morley experiment.

7
00:00:30,820 --> 00:00:33,540
Michelson and Morley
went out to detect

8
00:00:33,540 --> 00:00:36,120
the motion of the Earth
relative to aether.

9
00:00:36,120 --> 00:00:38,290
And by not finding
the result, we

10
00:00:38,290 --> 00:00:40,440
can conclude that, at
least in this form,

11
00:00:40,440 --> 00:00:43,990
aether doesn't exist.

12
00:00:43,990 --> 00:00:46,030
So what is the
experimental setup?

13
00:00:46,030 --> 00:00:48,670
Also, it's shown in
the pictures above.

14
00:00:48,670 --> 00:00:52,840
We have a light source
here, through which

15
00:00:52,840 --> 00:00:55,010
the light travel to
some mirror which

16
00:00:55,010 --> 00:00:56,660
reflects about half the light.

17
00:00:56,660 --> 00:00:59,960
About half the light
goes through reflected

18
00:00:59,960 --> 00:01:03,420
on the second mirror and
then comes to a screen.

19
00:01:03,420 --> 00:01:07,080
The other part of the
light is up and back down.

20
00:01:07,080 --> 00:01:10,970
So the light either travels
against the aether wind

21
00:01:10,970 --> 00:01:13,790
or perpendicular
to the aether wind.

22
00:01:13,790 --> 00:01:17,390
If aether is the medium
in which light travels,

23
00:01:17,390 --> 00:01:19,820
then the velocity
needs to change.

24
00:01:19,820 --> 00:01:23,451
The velocity of light in
this medium will change.

25
00:01:23,451 --> 00:01:24,826
If there is no
aether wind, there

26
00:01:24,826 --> 00:01:27,650
is no change in the
velocity of the light.

27
00:01:27,650 --> 00:01:30,800
The result of the experiment
is an interference pattern

28
00:01:30,800 --> 00:01:32,930
on the screen.

29
00:01:32,930 --> 00:01:37,250
The experiment is called
an interferometer.

30
00:01:37,250 --> 00:01:42,870
So there are some systematic
uncertainties here.

31
00:01:42,870 --> 00:01:44,800
There are some unknowns.

32
00:01:44,800 --> 00:01:47,490
For example, if you're
building your table,

33
00:01:47,490 --> 00:01:50,460
it's not really clear in which
direction aether actually--

34
00:01:50,460 --> 00:01:53,610
which direction is actually the
direction of the aether flow.

35
00:01:53,610 --> 00:01:57,270
But you can get by this
by rotating the table

36
00:01:57,270 --> 00:01:59,950
and making various
sets of experiments.

37
00:01:59,950 --> 00:02:03,100
And that's what
Michelson and Morley did.

38
00:02:03,100 --> 00:02:09,830
I want you to show
that the effect they're

39
00:02:09,830 --> 00:02:11,039
about to observe--

40
00:02:11,039 --> 00:02:12,890
or they will not observe--

41
00:02:12,890 --> 00:02:15,800
is of the order of
v over c squared.

42
00:02:15,800 --> 00:02:22,430
And what you want
to do is compare

43
00:02:22,430 --> 00:02:27,410
the light as it travels on this
path number 1 to one mirror

44
00:02:27,410 --> 00:02:29,930
and on the second path
to the second mirror.

45
00:02:32,910 --> 00:02:34,850
So if you're
following the video,

46
00:02:34,850 --> 00:02:38,420
I ask you to just stop here
and figure out how long does it

47
00:02:38,420 --> 00:02:41,330
take for the light to
travel on this path

48
00:02:41,330 --> 00:02:45,710
here-- on the lower path, path
number 1, or path number 2.

49
00:02:48,770 --> 00:02:50,900
Well, obviously, I've
worked this out already.

50
00:02:50,900 --> 00:02:52,580
So we want to
calculate the time it

51
00:02:52,580 --> 00:02:56,150
takes light to
travel path 1 that

52
00:02:56,150 --> 00:02:59,652
is going up and coming down--

53
00:02:59,652 --> 00:03:01,670
going left and going right.

54
00:03:01,670 --> 00:03:03,980
So in the first
case, the velocity

55
00:03:03,980 --> 00:03:06,470
is reduced by the
velocity of aether.

56
00:03:06,470 --> 00:03:10,370
So the time it takes
is l1, the leg,

57
00:03:10,370 --> 00:03:18,040
divided by c minus v plus the
return leg, l1 over c plus v.

58
00:03:18,040 --> 00:03:20,810
And you work this out, and
you simplify a little bit,

59
00:03:20,810 --> 00:03:24,820
you get this first equation.

60
00:03:24,820 --> 00:03:28,150
For the second part,
the one up and down,

61
00:03:28,150 --> 00:03:30,970
you want to draw
this triangle here

62
00:03:30,970 --> 00:03:33,970
to figure out that t
is equal-- the time

63
00:03:33,970 --> 00:03:36,880
it takes is equal to the
square root of l square

64
00:03:36,880 --> 00:03:38,830
over c square minus v square.

65
00:03:38,830 --> 00:03:42,880
And then you simplify again,
you get this [INAUDIBLE]

66
00:03:42,880 --> 00:03:44,525
square root [INAUDIBLE].

67
00:03:44,525 --> 00:03:46,150
What's important is
the time difference

68
00:03:46,150 --> 00:03:48,910
for the light traveling
with two legs.

69
00:03:48,910 --> 00:03:52,840
And we find that the time
difference t1 or t2 minus t1

70
00:03:52,840 --> 00:03:57,190
is given by this bit
complicated looking equation.

71
00:03:57,190 --> 00:04:00,480
So now in the experiment, you
want to set up l1 equal to l2.

72
00:04:00,480 --> 00:04:04,620
To simplify, you might not be
able to do it very precisely.

73
00:04:04,620 --> 00:04:07,560
What you can do, however,
is rotate the table.

74
00:04:07,560 --> 00:04:09,840
If you rotate and then
compare the difference

75
00:04:09,840 --> 00:04:16,380
of the differences, you
find that here there's

76
00:04:16,380 --> 00:04:21,089
this v square over
c square dependence.

77
00:04:21,089 --> 00:04:24,840
I used a little trick to
simplify the square root

78
00:04:24,840 --> 00:04:29,980
as I use this 1 plus or
minus x to the nth power.

79
00:04:29,980 --> 00:04:34,840
It's about 1 plus minus
n times x for x plus 1.

80
00:04:34,840 --> 00:04:36,550
And since the
velocity of aether is

81
00:04:36,550 --> 00:04:39,640
presumed to be small compared
to the speed of light,

82
00:04:39,640 --> 00:04:44,330
that's a good approximation.

83
00:04:44,330 --> 00:04:46,850
The result of the experiment
was there was no effect.

84
00:04:46,850 --> 00:04:48,860
They tried-- they
improved the experiment.

85
00:04:48,860 --> 00:04:50,450
They tried to find
smaller effects.

86
00:04:50,450 --> 00:04:52,100
They didn't find any.

87
00:04:52,100 --> 00:04:55,670
The reason for this is
that there is no aether.

88
00:04:55,670 --> 00:05:00,300
But we can use this now to
make a case against the aether.

89
00:05:00,300 --> 00:05:02,190
But you could say
that maybe they

90
00:05:02,190 --> 00:05:04,380
didn't observe anything
because the aether is

91
00:05:04,380 --> 00:05:05,830
dragged with the Earth.

92
00:05:05,830 --> 00:05:09,360
So instead of the Earth
going through this aether,

93
00:05:09,360 --> 00:05:12,600
and therefore, we
experience aether winds,

94
00:05:12,600 --> 00:05:15,360
you could argue
that maybe aether is

95
00:05:15,360 --> 00:05:18,630
localized around the Earth,
moving with the Earth

96
00:05:18,630 --> 00:05:20,920
or maybe moving
with the universe.

97
00:05:20,920 --> 00:05:22,980
And so in the next video,
we'll look at a case

98
00:05:22,980 --> 00:05:25,400
against that scenario as well.