1
00:00:13,020 --> 00:00:15,390
PROFESSOR: Welcome back to
8.20, special relativity.

2
00:00:15,390 --> 00:00:16,950
In the last section,
we discussed

3
00:00:16,950 --> 00:00:20,250
that moving clocks
tick differently

4
00:00:20,250 --> 00:00:22,440
than those which are at rest.

5
00:00:22,440 --> 00:00:24,310
And here, I would
like to discuss

6
00:00:24,310 --> 00:00:26,430
real life example of this.

7
00:00:26,430 --> 00:00:29,400
The muon is an
elementary particle

8
00:00:29,400 --> 00:00:31,110
very similar to the electron.

9
00:00:31,110 --> 00:00:36,000
It's mass is about
200 times as heavy.

10
00:00:36,000 --> 00:00:38,340
The muon was
discovered in the 1930s

11
00:00:38,340 --> 00:00:41,760
by Anderson and
Neddermeyer at Caltech.

12
00:00:41,760 --> 00:00:45,150
And it's really one of
my favorite particles

13
00:00:45,150 --> 00:00:46,200
because you can--

14
00:00:46,200 --> 00:00:47,130
they are abundant.

15
00:00:47,130 --> 00:00:50,490
There's many of them
in cosmic air showers.

16
00:00:50,490 --> 00:00:53,040
You can study them, you
can study their lifetime.

17
00:00:53,040 --> 00:00:58,080
You can even calculate the
lifetime on a piece of paper.

18
00:00:58,080 --> 00:00:59,580
So what Anderson
and Neddermeyer did

19
00:00:59,580 --> 00:01:03,390
is they just basically
went outside and discovered

20
00:01:03,390 --> 00:01:05,620
a particle which
comes from the sky.

21
00:01:05,620 --> 00:01:09,270
And so they studied
cosmic radiation.

22
00:01:09,270 --> 00:01:11,490
Muons are produced in
cosmic air showers,

23
00:01:11,490 --> 00:01:14,820
and we look at one of
those a little later.

24
00:01:14,820 --> 00:01:17,400
Basically, protons hits
the upper atmosphere,

25
00:01:17,400 --> 00:01:21,120
and in a shower of
various particles,

26
00:01:21,120 --> 00:01:22,980
muons are being produced.

27
00:01:22,980 --> 00:01:25,410
And then those muons are
not stable particles,

28
00:01:25,410 --> 00:01:28,530
but they are stable
enough to reach us.

29
00:01:28,530 --> 00:01:31,890
On average, if you hold
out your hand right now,

30
00:01:31,890 --> 00:01:37,210
about one muon travels through
your hand every second.

31
00:01:37,210 --> 00:01:38,710
How is this possible?

32
00:01:38,710 --> 00:01:40,560
So if you look at this
muon, it gives you

33
00:01:40,560 --> 00:01:43,320
a little bit of particle
physics explanation here.

34
00:01:43,320 --> 00:01:45,260
Again, the muon is
not a stable particle.

35
00:01:45,260 --> 00:01:48,180
They decay via the
weak interaction.

36
00:01:48,180 --> 00:01:50,280
For those who are
interested, this

37
00:01:50,280 --> 00:01:53,070
is a Feynman diagram
for this decay.

38
00:01:53,070 --> 00:01:57,300
The muon couples to the w,
and as a result of the decay,

39
00:01:57,300 --> 00:02:00,450
you find an electron, an
anti-electron neutrino,

40
00:02:00,450 --> 00:02:02,430
and the muon [INAUDIBLE].

41
00:02:02,430 --> 00:02:07,230
The lifetime is about
2.2 microseconds--

42
00:02:07,230 --> 00:02:10,110
2.2 times 10 to the
minus 6 seconds.

43
00:02:10,110 --> 00:02:14,580
And I just taught 8.701
which is introductory class

44
00:02:14,580 --> 00:02:16,440
into particle and
nuclear physics,

45
00:02:16,440 --> 00:02:18,810
and the students
calculated the lifetime

46
00:02:18,810 --> 00:02:20,230
of a muon in that class.

47
00:02:20,230 --> 00:02:21,390
So you can calculate this.

48
00:02:21,390 --> 00:02:25,460
And you need a few tools, but
it's not that hard after all.

49
00:02:25,460 --> 00:02:27,290
The average velocity
of the muons

50
00:02:27,290 --> 00:02:30,830
when they're being produced is
close to the speed of light,

51
00:02:30,830 --> 00:02:33,900
or 0.998 times the
speed of light.

52
00:02:33,900 --> 00:02:35,790
And if you do a
classical calculation,

53
00:02:35,790 --> 00:02:37,820
and you want to figure
out how long do the muons

54
00:02:37,820 --> 00:02:39,440
on average live--

55
00:02:39,440 --> 00:02:43,550
fly, you find that this
is about 660 meters.

56
00:02:43,550 --> 00:02:45,920
Now they are produced
in the upper atmosphere,

57
00:02:45,920 --> 00:02:50,270
and nevertheless, we can
find them down here on Earth.

58
00:02:50,270 --> 00:02:52,207
So something is not quite right.

59
00:02:52,207 --> 00:02:54,290
What is not quite right--
you can already assume--

60
00:02:54,290 --> 00:02:58,940
is that the clock in the
muon as observed by us

61
00:02:58,940 --> 00:03:05,610
ticks much, much slower
than for the muon at rest.

62
00:03:05,610 --> 00:03:08,790
And so the lifetime of the
muon of 2.2 microseconds

63
00:03:08,790 --> 00:03:11,540
is basically extended.

64
00:03:11,540 --> 00:03:14,180
If you calculate this--
this is average velocity--

65
00:03:14,180 --> 00:03:17,360
we find gamma factor of 15.

66
00:03:17,360 --> 00:03:19,760
Using the equation we--

67
00:03:19,760 --> 00:03:23,090
[? of ?] time dilation, you
just simply multiply 15 times

68
00:03:23,090 --> 00:03:26,270
2.2 microseconds, and you
find that muons, indeed,

69
00:03:26,270 --> 00:03:31,450
reach our hand on
the surface of Earth.

70
00:03:31,450 --> 00:03:33,250
This is a really fun example.

71
00:03:33,250 --> 00:03:36,010
Again, you can study
those cosmic showers,

72
00:03:36,010 --> 00:03:39,070
those muons, and
learn about the muons

73
00:03:39,070 --> 00:03:41,365
in very simple experiments.

74
00:03:41,365 --> 00:03:43,990
This picture here shows you one
of those air shower formations.

75
00:03:43,990 --> 00:03:45,740
So the story is a
little bit more complex.

76
00:03:45,740 --> 00:03:48,970
As I explain, this is a
spectacular air shower,

77
00:03:48,970 --> 00:03:51,490
or a picture of
one, where you have

78
00:03:51,490 --> 00:03:53,290
an [INAUDIBLE] coming
in at an energy

79
00:03:53,290 --> 00:03:55,900
of 10 to 15 electronvolts.

80
00:03:55,900 --> 00:04:01,030
And so even its lower energies
show us look like the one here.

81
00:04:01,030 --> 00:04:05,690
It produces, in collision
with the atmosphere,

82
00:04:05,690 --> 00:04:09,320
many, many particles-- pions,
protons, additional protons,

83
00:04:09,320 --> 00:04:10,540
neutrons, and pions again.

84
00:04:10,540 --> 00:04:13,840
And those pions then,
they decay into muons.

85
00:04:13,840 --> 00:04:16,570
And this all happens in
the upper atmosphere,

86
00:04:16,570 --> 00:04:19,000
but also in some
cases, further down.

87
00:04:22,710 --> 00:04:25,490
So here, we have
seen now an example

88
00:04:25,490 --> 00:04:27,380
which you can actually
see and observe

89
00:04:27,380 --> 00:04:30,410
in nature, where particles
travel with high speed.

90
00:04:30,410 --> 00:04:32,090
And there are
relativistic effects

91
00:04:32,090 --> 00:04:34,990
we can measure and observe.