1
00:00:00,000 --> 00:00:02,440
[SQUEAKING]

2
00:00:02,440 --> 00:00:03,904
[RUSTLING]

3
00:00:03,904 --> 00:00:05,368
[CLICKING]

4
00:00:19,070 --> 00:00:22,240
MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

5
00:00:22,240 --> 00:00:25,500
So in this section,
we're going to review

6
00:00:25,500 --> 00:00:28,500
the content of the
material, but underlined

7
00:00:28,500 --> 00:00:31,500
with a few questions and
examples, very similar

8
00:00:31,500 --> 00:00:32,940
to the previous section.

9
00:00:32,940 --> 00:00:37,550
It's just this one is
interleaved with activities.

10
00:00:37,550 --> 00:00:42,320
So let me start by bringing
back two of those Einstein

11
00:00:42,320 --> 00:00:45,490
quotes, which nicely relate
to each other in a sense

12
00:00:45,490 --> 00:00:48,210
that they feed off each other.

13
00:00:48,210 --> 00:00:51,110
The first one is, "I
have no special talent.

14
00:00:51,110 --> 00:00:54,140
I'm only passionately curious."

15
00:00:54,140 --> 00:00:55,460
Albert Einstein.

16
00:00:55,460 --> 00:00:59,210
And the second one, "It is
a miracle that curiosity

17
00:00:59,210 --> 00:01:01,190
survives formal education."

18
00:01:01,190 --> 00:01:03,680
And I [LAUGHS] sincerely
hope that I didn't stop

19
00:01:03,680 --> 00:01:06,590
your curiosity
with this lecture--

20
00:01:06,590 --> 00:01:08,353
quite the opposite.

21
00:01:08,353 --> 00:01:10,520
Like we discussed here,
it's just the starting point

22
00:01:10,520 --> 00:01:13,070
of a wider discussion
of general relativity

23
00:01:13,070 --> 00:01:16,160
in your education at MIT
in the Physics Department.

24
00:01:16,160 --> 00:01:18,980
You could learn about quantum
mechanics, quantum field

25
00:01:18,980 --> 00:01:19,760
theories.

26
00:01:19,760 --> 00:01:22,290
And a lot of physics
is out there,

27
00:01:22,290 --> 00:01:28,040
which is super exciting
and interesting.

28
00:01:28,040 --> 00:01:30,500
So it basically
needs your curiosity

29
00:01:30,500 --> 00:01:34,370
in order to tackle challenging
questions in physics today.

30
00:01:37,100 --> 00:01:39,200
We started the
discussion looking

31
00:01:39,200 --> 00:01:42,050
at the background
which led Einstein

32
00:01:42,050 --> 00:01:44,360
to make his discoveries.

33
00:01:44,360 --> 00:01:47,420
And specifically the
year 1905, in which

34
00:01:47,420 --> 00:01:53,870
he was able to come out with
five papers, all breakthrough

35
00:01:53,870 --> 00:01:58,550
papers, including the theory
of special relativity.

36
00:01:58,550 --> 00:02:00,670
His career didn't stop there.

37
00:02:00,670 --> 00:02:05,310
He developed the general
theory of relativity

38
00:02:05,310 --> 00:02:09,259
and published a paper
on this in 1915.

39
00:02:09,259 --> 00:02:11,570
And his fame as a
physicist really

40
00:02:11,570 --> 00:02:15,380
comes out of the predictions
he made at that time.

41
00:02:17,890 --> 00:02:20,310
So we set the context
of this class,

42
00:02:20,310 --> 00:02:25,740
and we started with a question
of Galilean transformation and

43
00:02:25,740 --> 00:02:32,160
whether or not you can
tell in a moving train car

44
00:02:32,160 --> 00:02:35,460
whether or not this is
actually moving or stationary.

45
00:02:35,460 --> 00:02:39,000
And we demonstrated that
time and acceleration

46
00:02:39,000 --> 00:02:41,940
is invariant in the
Galilean transformation.

47
00:02:41,940 --> 00:02:47,820
And then, therefore, since you
cannot distinguish the strength

48
00:02:47,820 --> 00:02:51,990
of a force in two reference
frames which move to each other

49
00:02:51,990 --> 00:02:56,620
with moderate velocity, you
cannot tell whether or not

50
00:02:56,620 --> 00:02:59,360
the train car is moving or not.

51
00:02:59,360 --> 00:03:02,690
Very important are the
development of clocks and times

52
00:03:02,690 --> 00:03:05,390
and signal processing
of the time.

53
00:03:05,390 --> 00:03:08,210
And we discussed this in the
context of trains and train

54
00:03:08,210 --> 00:03:12,140
lines, but also in Einstein
living in the city of Bern,

55
00:03:12,140 --> 00:03:15,200
with a large number
of clock towers

56
00:03:15,200 --> 00:03:16,640
which needed synchronization.

57
00:03:16,640 --> 00:03:20,630
And even working in
the patent office

58
00:03:20,630 --> 00:03:24,810
certainly confronted him with
those questions all the time.

59
00:03:24,810 --> 00:03:25,850
So time is suspect.

60
00:03:25,850 --> 00:03:30,230
That is really the
key to moving out

61
00:03:30,230 --> 00:03:33,620
from Galilean transformation
into Newtonian mechanics

62
00:03:33,620 --> 00:03:38,420
to special relativity.

63
00:03:38,420 --> 00:03:43,460
When we classify or when
we look at specific series,

64
00:03:43,460 --> 00:03:46,100
we have to understand that
they live within a context,

65
00:03:46,100 --> 00:03:48,480
within a range of validity.

66
00:03:48,480 --> 00:03:50,540
And so classical
mechanics is not wrong

67
00:03:50,540 --> 00:03:54,500
because it breaks down
at large velocities.

68
00:03:54,500 --> 00:03:58,670
It's just only correct in
the frame of slow velocities.

69
00:03:58,670 --> 00:04:03,350
And special relativity
also has its limitations,

70
00:04:03,350 --> 00:04:08,120
as in it only describes
reference frames or scenarios

71
00:04:08,120 --> 00:04:11,030
in which there is no
acceleration between two

72
00:04:11,030 --> 00:04:11,960
reference frames.

73
00:04:14,570 --> 00:04:18,980
Going back to the question
of the time, Michelson--

74
00:04:18,980 --> 00:04:21,440
and a number of other
experiments leading to the very

75
00:04:21,440 --> 00:04:23,330
same direction--

76
00:04:23,330 --> 00:04:25,775
was trying to
establish that there

77
00:04:25,775 --> 00:04:28,910
is an ether wind, a medium
in which light is moving.

78
00:04:28,910 --> 00:04:31,670
And his experiment,
at the time, failed

79
00:04:31,670 --> 00:04:35,060
to demonstrate that
ether actually exists.

80
00:04:35,060 --> 00:04:37,940
His experiment used a light
source and a couple of mirrors

81
00:04:37,940 --> 00:04:42,050
in order to show
interference patterns.

82
00:04:42,050 --> 00:04:45,330
And those interference patterns
didn't manifest themselves.

83
00:04:45,330 --> 00:04:48,950
So he thought for a long time
that his experiment is limited

84
00:04:48,950 --> 00:04:51,330
or that he has made a mistake.

85
00:04:51,330 --> 00:04:55,370
But it turns out that
ether indeed doesn't exist.

86
00:04:55,370 --> 00:04:58,610
Einstein tackled this problem
by making two postulates.

87
00:04:58,610 --> 00:05:03,770
The first one is the
principle of relativity,

88
00:05:03,770 --> 00:05:06,830
that there is no preferred
reference frame if you want;

89
00:05:06,830 --> 00:05:10,440
and the second, that the
speed of light is constant--

90
00:05:10,440 --> 00:05:13,470
and constant and the same
in all reference frames.

91
00:05:13,470 --> 00:05:16,160
And in this class we use
those two postulates in order

92
00:05:16,160 --> 00:05:19,700
to derive everything we know
about special relativity.

93
00:05:22,485 --> 00:05:23,860
So we looked at
the implications.

94
00:05:23,860 --> 00:05:25,990
And the implications
started from time dilation,

95
00:05:25,990 --> 00:05:26,890
length contractions.

96
00:05:26,890 --> 00:05:30,250
We were able to derive the
Lorentz factor and Lorentz

97
00:05:30,250 --> 00:05:31,600
transformation.

98
00:05:31,600 --> 00:05:35,020
And we did this by showing
this light clock here,

99
00:05:35,020 --> 00:05:38,920
where you observe a ticking
clock in which there

100
00:05:38,920 --> 00:05:41,290
is two mirrors and
light bouncing back.

101
00:05:41,290 --> 00:05:43,450
And each time there
is a bounce, we

102
00:05:43,450 --> 00:05:46,430
count this as one
tick of the clock.

103
00:05:46,430 --> 00:05:48,160
So if the clock is
moving, the light

104
00:05:48,160 --> 00:05:49,810
has to travel a longer distance.

105
00:05:49,810 --> 00:05:53,860
And hence time is delayed.

106
00:05:53,860 --> 00:05:56,530
And from just the
geometry of this problem,

107
00:05:56,530 --> 00:06:00,100
we were able to derive
this gamma factor here--

108
00:06:00,100 --> 00:06:02,470
1 over square root of
1 minus beta squared.

109
00:06:02,470 --> 00:06:05,876
The beta is velocity
over the speed of light.

110
00:06:05,876 --> 00:06:08,300
So as the first activity
in today's class,

111
00:06:08,300 --> 00:06:11,350
I want you to think
about a clock which

112
00:06:11,350 --> 00:06:13,990
is moving with a
photon, a clock which is

113
00:06:13,990 --> 00:06:15,640
moving with the speed of light.

114
00:06:15,640 --> 00:06:19,030
And also discuss why isn't
it possible to go faster

115
00:06:19,030 --> 00:06:20,110
than the speed of light.

116
00:06:20,110 --> 00:06:23,410
And why can you not
just keep accelerating?

117
00:06:23,410 --> 00:06:25,060
So think about
this a little bit.

118
00:06:25,060 --> 00:06:27,760
In the live class we
will have a discussion.

119
00:06:27,760 --> 00:06:30,730
But just come up with
some sort of answer

120
00:06:30,730 --> 00:06:32,363
of why this is the case.

121
00:06:36,440 --> 00:06:38,750
So here we have, in
the class, actually

122
00:06:38,750 --> 00:06:40,130
showed that there
is a real speed

123
00:06:40,130 --> 00:06:42,980
limit, that if you
try to go faster,

124
00:06:42,980 --> 00:06:44,570
past [INAUDIBLE]
velocity, you run

125
00:06:44,570 --> 00:06:48,870
against a boundary,
a real speed limit.

126
00:06:48,870 --> 00:06:50,900
If you think about keeping
accelerating, giving

127
00:06:50,900 --> 00:06:53,060
more energy, you
find that the amount

128
00:06:53,060 --> 00:06:56,900
of energy you need in order to
go faster and faster, faster,

129
00:06:56,900 --> 00:06:59,990
doesn't get you to velocities
which are faster and faster.

130
00:06:59,990 --> 00:07:04,010
And again, you enter a speed
limit-- the speed of light.

131
00:07:09,280 --> 00:07:11,140
An important topic
in understanding

132
00:07:11,140 --> 00:07:13,510
some of the paradoxes
in special relativity,

133
00:07:13,510 --> 00:07:15,850
and some of the
confusion, is the concept

134
00:07:15,850 --> 00:07:18,625
of the relativity
of simultaneity.

135
00:07:18,625 --> 00:07:21,790
Now, it can be illustrated quite
nicely in this example here,

136
00:07:21,790 --> 00:07:26,920
where you have a carriage train
car with light being emitted

137
00:07:26,920 --> 00:07:32,470
and clocks which record those
events at each end of the train

138
00:07:32,470 --> 00:07:33,520
car.

139
00:07:33,520 --> 00:07:37,640
For the stationary person,
those clocks will tick in sync.

140
00:07:37,640 --> 00:07:41,890
They will always show the
same tick and the same time.

141
00:07:41,890 --> 00:07:46,780
But for somebody who's observing
this train from a platform,

142
00:07:46,780 --> 00:07:49,390
or somebody who's moving
with a relative velocity

143
00:07:49,390 --> 00:07:52,750
towards this train car, you
will see those clocks not

144
00:07:52,750 --> 00:07:54,990
ticking at the same time.

145
00:07:54,990 --> 00:07:58,610
So the clear evidence
is given in this picture

146
00:07:58,610 --> 00:08:01,115
again, where you see that
the light's being emitted

147
00:08:01,115 --> 00:08:04,520
in the center, but one side
of the train car is hit first

148
00:08:04,520 --> 00:08:07,350
and the second side
is hit afterwards.

149
00:08:07,350 --> 00:08:10,190
So you see that the
leading clock lags.

150
00:08:10,190 --> 00:08:13,560
The leading clock in
this example lags behind.

151
00:08:13,560 --> 00:08:15,710
And so what you find
here is that events which

152
00:08:15,710 --> 00:08:19,130
are observed simultaneously
for one observer--

153
00:08:19,130 --> 00:08:24,200
in this case, the person
inside the carriage--

154
00:08:24,200 --> 00:08:28,760
they will not be simultaneous
for an observer who's moving

155
00:08:28,760 --> 00:08:30,990
with a relative velocity.

156
00:08:30,990 --> 00:08:34,669
And that led us to the
understanding of the pole

157
00:08:34,669 --> 00:08:40,730
in the barn paradox, where,
in one example, the event

158
00:08:40,730 --> 00:08:44,750
of the front of the pole
hitting the back of the barn

159
00:08:44,750 --> 00:08:47,270
and the event of the
back of the pole hitting

160
00:08:47,270 --> 00:08:49,880
the front of the barn,
they are simultaneously

161
00:08:49,880 --> 00:08:51,170
for the barn owner.

162
00:08:51,170 --> 00:08:54,980
But they're not simultaneously
happening for the person

163
00:08:54,980 --> 00:08:58,580
who's carrying the pole.

164
00:08:58,580 --> 00:09:05,660
In this case, the event of
hitting the back of the barn

165
00:09:05,660 --> 00:09:08,600
is simultaneous to an event
where the back of the pole

166
00:09:08,600 --> 00:09:10,220
is still sticking
out of the barn.

167
00:09:10,220 --> 00:09:11,750
So there is a
clear disagreement.

168
00:09:11,750 --> 00:09:13,790
But the disagreement
can be resolved

169
00:09:13,790 --> 00:09:17,540
by understanding that
simultaneous events are not

170
00:09:17,540 --> 00:09:23,130
necessarily simultaneous
to two observers.

171
00:09:23,130 --> 00:09:28,140
Then we moved on to a
variety of other paradoxes

172
00:09:28,140 --> 00:09:29,640
in special relativity.

173
00:09:29,640 --> 00:09:33,120
And the most famous likely
is the twin paradox,

174
00:09:33,120 --> 00:09:38,970
where we discussed that a person
moving away and then returning

175
00:09:38,970 --> 00:09:42,930
is younger than the person
who actually stayed at rest.

176
00:09:42,930 --> 00:09:47,910
And we discussed that we were
able to use time dilation

177
00:09:47,910 --> 00:09:51,270
or length contraction in order
to quantitatively figure out

178
00:09:51,270 --> 00:09:53,170
the difference in time.

179
00:09:53,170 --> 00:09:54,910
But we also discussed
that the person

180
00:09:54,910 --> 00:10:00,110
who is moving away
and then coming back

181
00:10:00,110 --> 00:10:04,920
needs to describe the journey in
two different reference frames.

182
00:10:04,920 --> 00:10:07,170
And from the fact that
you don't consistently can

183
00:10:07,170 --> 00:10:10,370
describe this sequence
of events as two

184
00:10:10,370 --> 00:10:13,700
reference frames
can see the paradox

185
00:10:13,700 --> 00:10:18,710
and the extra confusion.

186
00:10:18,710 --> 00:10:21,080
So here we have
another activity--

187
00:10:21,080 --> 00:10:22,820
an asymmetric travel.

188
00:10:22,820 --> 00:10:26,750
So we discussed also the example
where two people move away

189
00:10:26,750 --> 00:10:29,190
and then they come back
in a symmetric fashion.

190
00:10:29,190 --> 00:10:30,830
But here we want
to discuss the case

191
00:10:30,830 --> 00:10:32,390
where there are three trends.

192
00:10:32,390 --> 00:10:33,800
Carol stays on Earth.

193
00:10:33,800 --> 00:10:35,390
Bob moves to Star 1.

194
00:10:35,390 --> 00:10:37,730
And Alice moves to Star 2.

195
00:10:37,730 --> 00:10:44,420
The distance to Star 1 is longer
than the distance to Star 2.

196
00:10:44,420 --> 00:10:49,580
So the question is, in this
journey, they both start

197
00:10:49,580 --> 00:10:53,210
and they both return at
the same time for Carol.

198
00:10:53,210 --> 00:10:57,090
But which of the
twins is the youngest?

199
00:10:57,090 --> 00:10:59,580
So again, I invite you
to just work this out.

200
00:10:59,580 --> 00:11:03,780
You can use some numbers if
you want a quantitative answer.

201
00:11:03,780 --> 00:11:06,300
Or you can just reason
about [INAUDIBLE]..

202
00:11:10,070 --> 00:11:16,880
The answer here is that Bob
is the youngest of the three

203
00:11:16,880 --> 00:11:20,150
once they return to Earth.

204
00:11:20,150 --> 00:11:23,280
And the reason for this is
the distance he has to travel

205
00:11:23,280 --> 00:11:24,080
is the longest.

206
00:11:24,080 --> 00:11:27,890
Hence the velocity he has
to travel in is the largest.

207
00:11:27,890 --> 00:11:30,590
And hence the effect of
time dilation for him

208
00:11:30,590 --> 00:11:31,610
is the biggest.

209
00:11:31,610 --> 00:11:34,730
And therefore he's going to
be the youngest of the three.

210
00:11:40,670 --> 00:11:41,630
All right.

211
00:11:41,630 --> 00:11:46,400
We had a rather long discussion
about waves and light, Doppler

212
00:11:46,400 --> 00:11:50,060
effect, and relativistic
Doppler effect.

213
00:11:50,060 --> 00:11:52,070
Here, just as a
reminder, the wave

214
00:11:52,070 --> 00:11:54,440
equation for an electric
field in a vacuum.

215
00:11:54,440 --> 00:11:56,930
And the solution to
the wave equation

216
00:11:56,930 --> 00:12:02,880
is use the second derivative
with space and time.

217
00:12:02,880 --> 00:12:04,910
And the solution
simply can be expressed

218
00:12:04,910 --> 00:12:09,130
as a cosine, which is a
function of space and time.

219
00:12:09,130 --> 00:12:11,630
We have talked about
light quite a bit.

220
00:12:11,630 --> 00:12:13,480
And just as
reminder, [INAUDIBLE]

221
00:12:13,480 --> 00:12:17,290
the energy of photon is
related via the Planck-Einstein

222
00:12:17,290 --> 00:12:20,110
relation to the frequency.

223
00:12:20,110 --> 00:12:26,115
So the higher the frequency,
the higher the energy.

224
00:12:26,115 --> 00:12:28,600
The higher the frequency,
the higher the energy.

225
00:12:28,600 --> 00:12:31,630
And here, in this
picture, you can

226
00:12:31,630 --> 00:12:34,495
see the effect of
the Doppler effect,

227
00:12:34,495 --> 00:12:37,570
where, when you have
a moving source,

228
00:12:37,570 --> 00:12:40,300
the observer sees the
waveline modified.

229
00:12:43,440 --> 00:12:46,260
Objects which move
towards us are

230
00:12:46,260 --> 00:12:49,770
blueshifted, starting
from white light,

231
00:12:49,770 --> 00:12:51,630
or green light in this example.

232
00:12:51,630 --> 00:12:55,080
And objects that move away
from us are redshifted.

233
00:12:55,080 --> 00:12:58,200
The effect can be
used, for example,

234
00:12:58,200 --> 00:13:01,650
in speed measurements of cars.

235
00:13:01,650 --> 00:13:04,680
It can also be used in order
to measure speed or distances

236
00:13:04,680 --> 00:13:07,260
of stars moving away from us.

237
00:13:07,260 --> 00:13:09,330
And so that defines,
then, the concept

238
00:13:09,330 --> 00:13:16,380
of redshift, which is simply
the ratio of the difference

239
00:13:16,380 --> 00:13:19,860
in wavelength divided
by the wavelength as

240
00:13:19,860 --> 00:13:22,260
observed by the observer.

241
00:13:22,260 --> 00:13:24,220
So here there's two
concept questions.

242
00:13:24,220 --> 00:13:27,490
The first one is, is
the wave equation,

243
00:13:27,490 --> 00:13:29,100
which you can see
there as an example,

244
00:13:29,100 --> 00:13:32,250
invariant under
Lorentz transformation?

245
00:13:32,250 --> 00:13:34,920
And the second question is,
how about the solutions?

246
00:13:34,920 --> 00:13:36,930
Are the solutions
to the wave equation

247
00:13:36,930 --> 00:13:39,830
invariant under
Lorentz transformation?

248
00:13:39,830 --> 00:13:42,100
So I'll have you
work this out again.

249
00:13:42,100 --> 00:13:48,800
And the answers are yes and no.

250
00:13:48,800 --> 00:13:50,840
The wave equation is invariant.

251
00:13:50,840 --> 00:13:54,490
The wave equation
describes the physics.

252
00:13:54,490 --> 00:13:58,130
It explains how electric
and magnetic fields change.

253
00:13:58,130 --> 00:14:01,580
And the laws of physics
need to be invariant

254
00:14:01,580 --> 00:14:02,870
under Lorentz transformation.

255
00:14:02,870 --> 00:14:04,610
Otherwise they
will not be valid.

256
00:14:04,610 --> 00:14:08,420
They will violate the postulate
we just made that all reference

257
00:14:08,420 --> 00:14:10,970
frames are equal to each other.

258
00:14:10,970 --> 00:14:14,140
However, the solutions of the
wave equation-- light itself--

259
00:14:14,140 --> 00:14:16,900
is not invariant under
Lorentz transformation.

260
00:14:16,900 --> 00:14:19,870
We've just discussed
redshift and blueshift,

261
00:14:19,870 --> 00:14:22,120
which means that the wavelength
and frequency of light

262
00:14:22,120 --> 00:14:26,290
changes with respect to the
observer, or for each observer.

263
00:14:26,290 --> 00:14:28,120
So the solutions-- light--

264
00:14:28,120 --> 00:14:32,613
are not invariant under
Lorentz transformation.

265
00:14:32,613 --> 00:14:34,780
And then we went a little
bit into particle physics.

266
00:14:34,780 --> 00:14:37,660
And I have to apologize
for my own preference.

267
00:14:37,660 --> 00:14:39,630
But elementary
particles, as they

268
00:14:39,630 --> 00:14:41,080
have been reproduced
or observed,

269
00:14:41,080 --> 00:14:43,970
are typically moving at
rather large velocities.

270
00:14:43,970 --> 00:14:45,850
So they are very good
examples to study

271
00:14:45,850 --> 00:14:48,310
effects of special relativity.

272
00:14:48,310 --> 00:14:51,520
We looked at energy, the
total energy m0 gamma c

273
00:14:51,520 --> 00:14:54,010
squared, which also
can be expressed

274
00:14:54,010 --> 00:14:57,280
as the energy of the rest
energy of the particle,

275
00:14:57,280 --> 00:15:00,100
m0 c squared, plus
the kinetic energy.

276
00:15:00,100 --> 00:15:01,930
And we looked at
the total energy

277
00:15:01,930 --> 00:15:05,680
as being invariant, one
of those invariants,

278
00:15:05,680 --> 00:15:08,900
as equal to the total
momenta squared.

279
00:15:08,900 --> 00:15:11,350
The total energy squared is
equal to the total momentum

280
00:15:11,350 --> 00:15:14,560
squared times c squared
plus the rest mass squared

281
00:15:14,560 --> 00:15:16,610
times c to the fourth power.

282
00:15:16,610 --> 00:15:19,980
And then we went through a
larger number of examples,

283
00:15:19,980 --> 00:15:23,340
from accelerating electrons
to composite particles.

284
00:15:23,340 --> 00:15:27,490
We talked about deuteron
photon absorption and emission,

285
00:15:27,490 --> 00:15:31,350
the creation of particle, the
creation of antiparticles,

286
00:15:31,350 --> 00:15:33,520
and the scattering of particles.

287
00:15:33,520 --> 00:15:35,580
So here we had another example.

288
00:15:35,580 --> 00:15:39,270
Oops-- without the solution.

289
00:15:39,270 --> 00:15:43,710
In 1995, at Fermilab, a
proton-antiproton collider,

290
00:15:43,710 --> 00:15:47,130
the Tevatron, top
quarks were discovered.

291
00:15:47,130 --> 00:15:51,960
And we measured the top
quark mass to 175 GeV.

292
00:15:51,960 --> 00:15:54,120
The center of mass
energy at the Tevatron

293
00:15:54,120 --> 00:15:58,740
was 1.8, and later almost
2 tera-electronvolt,

294
00:15:58,740 --> 00:16:02,730
and clearly sufficient for the
production of top and antitop.

295
00:16:02,730 --> 00:16:05,640
But what is the minimal energy
in order for this process

296
00:16:05,640 --> 00:16:07,270
to occur?

297
00:16:07,270 --> 00:16:10,950
And here we went through
a number of examples.

298
00:16:10,950 --> 00:16:12,420
The minimal energy-- sorry.

299
00:16:12,420 --> 00:16:14,580
I have to work this out again.

300
00:16:14,580 --> 00:16:20,070
The minimal energy required
can be derived or extracted

301
00:16:20,070 --> 00:16:23,340
in the center of mass frame,
where the top and antitop are

302
00:16:23,340 --> 00:16:25,000
produced at rest.

303
00:16:25,000 --> 00:16:26,560
And if you do this--
in this example,

304
00:16:26,560 --> 00:16:29,530
the proton in this
collider experiment--

305
00:16:29,530 --> 00:16:31,320
the experiment is
already conducted

306
00:16:31,320 --> 00:16:32,760
in the center of mass frame.

307
00:16:32,760 --> 00:16:35,760
So the minimal energy
is simply 2 times

308
00:16:35,760 --> 00:16:39,210
the top mass times c square,
or 2 times gamma times the mass

309
00:16:39,210 --> 00:16:41,310
of the proton times c
square, which gives you

310
00:16:41,310 --> 00:16:44,380
a gamma factor of 175.

311
00:16:44,380 --> 00:16:47,310
But the likelihood
to actually observe

312
00:16:47,310 --> 00:16:54,070
a top quark and a antitop
quark at that energy, 175 GeV

313
00:16:54,070 --> 00:16:58,840
proton or antiproton
energy, is rather 0.

314
00:16:58,840 --> 00:17:01,540
And the reason for this has
to do with the structure

315
00:17:01,540 --> 00:17:02,620
of the proton.

316
00:17:02,620 --> 00:17:05,619
The actual interaction between
the proton and the antiproton

317
00:17:05,619 --> 00:17:10,869
is such that the quarks and
antiquarks inside the proton,

318
00:17:10,869 --> 00:17:12,730
and also the gluons, interact.

319
00:17:12,730 --> 00:17:15,040
And they only carry a
fraction of the momentum

320
00:17:15,040 --> 00:17:16,390
and the energy of the proton.

321
00:17:16,390 --> 00:17:18,640
And hence this
minimal calculation

322
00:17:18,640 --> 00:17:21,430
is insufficient to get a
sufficient cross-section

323
00:17:21,430 --> 00:17:25,359
likelihood for top quarks and
antiquarks to be produced.

324
00:17:25,359 --> 00:17:28,420
But that is particle physics
and goes beyond the scope

325
00:17:28,420 --> 00:17:30,640
of this lecture.

326
00:17:30,640 --> 00:17:33,700
One last point, which leads
sometimes to confusion,

327
00:17:33,700 --> 00:17:38,660
is the concept of conserved
and invariant properties.

328
00:17:38,660 --> 00:17:41,260
When we look at the
meaning of the word,

329
00:17:41,260 --> 00:17:43,630
invariant means never-changing.

330
00:17:43,630 --> 00:17:46,060
And in the concept of
special relativity,

331
00:17:46,060 --> 00:17:48,550
properties are invariant
when they do not

332
00:17:48,550 --> 00:17:52,540
change under Lorentz
transformation or Galilean

333
00:17:52,540 --> 00:17:56,170
transformation, as we
discussed earlier in the class.