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YEN-JIE LEE: So what are
we going to do today?

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00:00:26,040 --> 00:00:29,990
So today, we're going to
continue the discussion,

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based on what we have learned
from the diffraction and also

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00:00:35,080 --> 00:00:36,530
other interesting phenomena.

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00:00:36,530 --> 00:00:38,660
And we are going
to make connections

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00:00:38,660 --> 00:00:44,030
to quantum mechanics
and discuss in greater

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detail about this connection.

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00:00:46,730 --> 00:00:49,550
And also, if time
allows, we are going

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00:00:49,550 --> 00:00:58,650
to cover information about
gravitational waves as well.

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00:00:58,650 --> 00:01:02,750
So last time, we have
discussed diffraction pattern

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00:01:02,750 --> 00:01:04,790
coming from a laser beam.

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00:01:04,790 --> 00:01:08,540
And we discussed
about resolution.

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00:01:08,540 --> 00:01:11,940
And you can see that this is the
graph we see, last time already

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00:01:11,940 --> 00:01:13,190
in the lecture.

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00:01:13,190 --> 00:01:15,860
Basically, all the
point light source

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00:01:15,860 --> 00:01:23,300
coming through a single slit is
going to be doing interference

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00:01:23,300 --> 00:01:24,540
to each other.

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00:01:24,540 --> 00:01:27,530
So basically, you see
interesting pattern,

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00:01:27,530 --> 00:01:32,060
which you have a central peak.

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00:01:32,060 --> 00:01:35,780
And the total constructing
for interference

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00:01:35,780 --> 00:01:39,680
happens at the
center of the screen.

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00:01:39,680 --> 00:01:43,550
And at some point,
you have a deep--

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00:01:43,550 --> 00:01:48,330
which is actually where total
destructive interference

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00:01:48,330 --> 00:01:49,450
actually happened.

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00:01:49,450 --> 00:01:53,570
And we were able to understand
this with mathematics,

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00:01:53,570 --> 00:01:56,490
which we learned in 18.03.

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00:01:56,490 --> 00:01:58,550
Another interesting
result we find

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00:01:58,550 --> 00:02:02,780
is that, if we shoot a
laser beam to the moon--

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00:02:02,780 --> 00:02:06,290
by now, you should be able to
conclude that it's not going

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00:02:06,290 --> 00:02:09,650
to be a point on the moon.

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00:02:09,650 --> 00:02:15,140
Instead, it's going to be a spot
as large as the whole Missouri

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00:02:15,140 --> 00:02:16,460
state.

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00:02:16,460 --> 00:02:19,620
So that's actually
another interesting result

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00:02:19,620 --> 00:02:23,880
we found from that
discussion last time.

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00:02:23,880 --> 00:02:27,080
And finally, we are
able to put together

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00:02:27,080 --> 00:02:30,320
all the things we have learned
from the last few lectures.

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00:02:30,320 --> 00:02:34,200
Basically, you can
have, at the same time,

45
00:02:34,200 --> 00:02:38,910
the effect of multi-slit
interference and also

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00:02:38,910 --> 00:02:41,900
the effect of a single
slit diffraction--

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00:02:41,900 --> 00:02:43,760
all then put together.

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00:02:43,760 --> 00:02:47,960
Then you have this complicated
but also beautiful pattern,

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00:02:47,960 --> 00:02:50,510
which you will be able
to observe on the screen.

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00:02:50,510 --> 00:02:55,040
And basically, the point is
that you are going to have,

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00:02:55,040 --> 00:02:59,670
for example, in this case,
five-slit interference pattern.

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00:02:59,670 --> 00:03:02,110
But that is actually modulated.

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00:03:02,110 --> 00:03:05,660
The intensity is
modulated by the pattern

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00:03:05,660 --> 00:03:09,280
from a single-slit diffraction.

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00:03:09,280 --> 00:03:12,650
OK, so that is
actually what we have

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00:03:12,650 --> 00:03:16,070
learned from the last lecture.

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00:03:16,070 --> 00:03:25,370
Coming back to the original
question, why do we study 8.03?

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00:03:25,370 --> 00:03:30,890
The reason is that we
would like to understand--

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00:03:30,890 --> 00:03:35,250
we would like to hear
from that universe.

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00:03:35,250 --> 00:03:38,800
So we cannot even
recognize the universe,

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00:03:38,800 --> 00:03:42,090
without using waves
and vibrations.

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00:03:42,090 --> 00:03:46,460
So that's the course in which
we have been doing here.

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00:03:46,460 --> 00:03:50,010
And we have seen
waves of matter.

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So for example, here, we have
this water wave generator.

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You can see water waves.

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00:03:56,450 --> 00:03:59,120
We have this Bell Lab machine.

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Because you can see the
coupled oscillator--

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00:04:03,320 --> 00:04:05,540
a multiple coupled oscillator.

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00:04:05,540 --> 00:04:08,090
And they are doing
their job together

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00:04:08,090 --> 00:04:10,190
to form beautiful waves.

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00:04:10,190 --> 00:04:15,050
And you can see those
beautiful results from there.

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00:04:15,050 --> 00:04:19,980
Last time and also including
the last few lectures,

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we have been using
this laser to produce

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00:04:23,120 --> 00:04:27,110
interesting interference
patterns and the diffraction

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00:04:27,110 --> 00:04:28,910
pattern.

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00:04:28,910 --> 00:04:32,720
So that's the second kind
of wave, which we encounter.

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00:04:32,720 --> 00:04:36,600
The first kind is
the waves of matters.

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00:04:36,600 --> 00:04:39,660
The second kind
is waves of what?

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00:04:39,660 --> 00:04:42,930
Waves of vector fields.

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00:04:42,930 --> 00:04:44,570
It's not matter anymore.

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Because this field,
this oscillation field,

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can also travel through vacuum.

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00:04:51,630 --> 00:04:53,600
So that is actually
the second kind

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00:04:53,600 --> 00:04:59,660
of wave, which we
should learn for 8.03.

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00:04:59,660 --> 00:05:05,090
They provide a pretty
adequate description

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00:05:05,090 --> 00:05:08,270
of the nature, description
of the phenomenon, which

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00:05:08,270 --> 00:05:12,890
we can actually measure, and
see from the experiment we

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went over.

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00:05:15,120 --> 00:05:19,640
So what I would like to
say in the lecture today

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is that there are two kinds
of completely different waves,

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00:05:25,310 --> 00:05:27,750
which we haven't talked about.

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00:05:27,750 --> 00:05:32,450
The first one is the
probability density wave,

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00:05:32,450 --> 00:05:36,230
which I will cover
that in a few moments.

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00:05:36,230 --> 00:05:40,010
The second one is
gravitational waves.

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00:05:40,010 --> 00:05:43,940
This is actually a
space-time distortion

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00:05:43,940 --> 00:05:48,830
coming from the motion
of massive objects.

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00:05:48,830 --> 00:05:51,490
And we would like to
see what we can also

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00:05:51,490 --> 00:05:55,100
learn from there, using the
existing knowledge of which we

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00:05:55,100 --> 00:05:59,530
have learned from matter waves
and the vector-field waves.

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00:05:59,530 --> 00:06:02,970
And that they are, actually,
pretty similar to each other

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00:06:02,970 --> 00:06:06,210
if you look at their behavior.

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00:06:06,210 --> 00:06:12,220
So the first thing which I
would like to discuss is light.

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00:06:12,220 --> 00:06:16,260
So far, what is light?

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00:06:16,260 --> 00:06:20,630
Light is like
electromagnetic waves.

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00:06:20,630 --> 00:06:22,530
So that is actually
what we have learned

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00:06:22,530 --> 00:06:25,530
so far from 8.02 and 8.03.

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00:06:25,530 --> 00:06:27,210
So they are like waves.

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00:06:27,210 --> 00:06:29,670
They are waves, all right.

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00:06:29,670 --> 00:06:34,290
On the other hand,
in the 20th century,

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00:06:34,290 --> 00:06:38,050
there are many, many
crises going on.

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00:06:38,050 --> 00:06:40,260
So the first thing
which is happening

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00:06:40,260 --> 00:06:43,900
is photoelectric effect.

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00:06:43,900 --> 00:06:48,270
So this experimental
result was actually

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00:06:48,270 --> 00:06:52,290
first discovered by Hertz.

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00:06:52,290 --> 00:06:57,390
So he found that, if you
want to kick one electron out

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00:06:57,390 --> 00:07:01,960
of some material or
some charged material,

117
00:07:01,960 --> 00:07:08,160
it is easier if you use a
high-frequency light compared

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00:07:08,160 --> 00:07:10,470
to low-frequency light.

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00:07:10,470 --> 00:07:11,430
So that's the issue--

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00:07:11,430 --> 00:07:12,840
really strange.

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00:07:12,840 --> 00:07:17,880
Because based on waves and
also the intensity formula--

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00:07:17,880 --> 00:07:21,270
while we really
care, intensity is

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00:07:21,270 --> 00:07:25,580
proportional to the square of
the electric field amplitude.

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00:07:25,580 --> 00:07:28,110
So that's actually
what we learned

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00:07:28,110 --> 00:07:30,070
from the previous lectures.

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00:07:30,070 --> 00:07:35,100
But what Hertz was saying
is that the frequency also

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00:07:35,100 --> 00:07:36,300
matters.

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00:07:36,300 --> 00:07:40,710
OK, so that's really
a bit strange.

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00:07:40,710 --> 00:07:44,780
And Einstein actually
came in and explained

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00:07:44,780 --> 00:07:48,120
this photoelectric effect.

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00:07:48,120 --> 00:07:51,510
So what we found
is that this effect

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00:07:51,510 --> 00:08:01,950
can be explained by viewing
the light of small quantas.

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00:08:01,950 --> 00:08:07,780
And light is actually
not like waves any more,

134
00:08:07,780 --> 00:08:09,950
but like quantas--

135
00:08:09,950 --> 00:08:12,540
the small quantas--
discrete ones--

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00:08:12,540 --> 00:08:18,470
with energy proportional
to the frequency.

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00:08:18,470 --> 00:08:20,020
All right?

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00:08:20,020 --> 00:08:25,380
And basically, the energy
of those little quanta--

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00:08:25,380 --> 00:08:28,440
or we now call them photons--

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00:08:28,440 --> 00:08:35,370
is actually equal to h,
which is some constant--

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00:08:35,370 --> 00:08:41,100
relate the frequency and
the energy of the quanta.

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00:08:41,100 --> 00:08:45,570
And with this
explanation, the view

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00:08:45,570 --> 00:08:50,250
is that the photons
are like particles.

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00:08:50,250 --> 00:08:53,940
And therefore, he can
actually explain that, OK,

145
00:08:53,940 --> 00:09:02,530
if I measure the kinetic energy,
the maxima kinetic energy

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00:09:02,530 --> 00:09:09,900
of the electrons,
which are kicked out

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00:09:09,900 --> 00:09:14,820
from this photoelectric
effect experiment.

148
00:09:14,820 --> 00:09:16,255
I call it K-max.

149
00:09:19,420 --> 00:09:23,230
What you are going to get
is a formula like this.

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00:09:23,230 --> 00:09:26,850
The maxima kinetic
energy of electrons

151
00:09:26,850 --> 00:09:34,120
will be equal to h
bar mu minus phi.

152
00:09:34,120 --> 00:09:37,110
Phi is actually some
kind of threshold,

153
00:09:37,110 --> 00:09:39,450
which you need
or, say, some kind

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00:09:39,450 --> 00:09:42,420
of energy, which you need
to overcome to kick one

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00:09:42,420 --> 00:09:47,070
electron out of the material.

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00:09:47,070 --> 00:09:52,860
So you can see from here that,
if the frequency of the light

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00:09:52,860 --> 00:09:56,660
is too low, then
this will never work.

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00:09:56,660 --> 00:10:01,460
Because the maximum kinetic
energy will be below 0.

159
00:10:01,460 --> 00:10:06,170
Therefore, you cannot
kick out a electron.

160
00:10:06,170 --> 00:10:12,950
But if the frequency is high,
as shown by Hertz experiment,

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00:10:12,950 --> 00:10:13,982
it is possible.

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00:10:13,982 --> 00:10:20,300
And also, you can create
energetic electron,

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00:10:20,300 --> 00:10:23,240
have them kicked
out of the material.

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00:10:23,240 --> 00:10:26,730
And this is actually
verified by experiment.

165
00:10:26,730 --> 00:10:29,990
And that's essentially
why Einstein should

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00:10:29,990 --> 00:10:33,860
get the Nobel Prize in 1921.

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00:10:33,860 --> 00:10:38,260
So let me tell you
what the feeling here--

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00:10:38,260 --> 00:10:42,340
the feeling here is that, now,
things are really becoming

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00:10:42,340 --> 00:10:43,570
more and more interesting.

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00:10:43,570 --> 00:10:46,330
Because first of
all, we see really

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00:10:46,330 --> 00:10:51,310
well that the electromagnetic
wave describes

172
00:10:51,310 --> 00:10:53,240
the behavior of the light.

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00:10:53,240 --> 00:10:54,270
We see diffraction.

174
00:10:54,270 --> 00:10:56,190
We see interference.

175
00:10:56,190 --> 00:10:57,910
All those things
can be explained

176
00:10:57,910 --> 00:11:02,380
by the beautiful mathematics,
which we have been employing

177
00:11:02,380 --> 00:11:04,270
to explain all those results.

178
00:11:04,270 --> 00:11:07,870
But here, you can see
that, at the same time,

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00:11:07,870 --> 00:11:15,730
the photons are very good
tool or very good viewpoint

180
00:11:15,730 --> 00:11:18,280
to explain the
photoelectric effect.

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00:11:18,280 --> 00:11:24,130
So that's actually
really surprising.

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00:11:24,130 --> 00:11:27,430
Because that means
you have, suddenly,

183
00:11:27,430 --> 00:11:30,860
both kinds of explanation
of light, which should

184
00:11:30,860 --> 00:11:34,240
be describing the same thing.

185
00:11:34,240 --> 00:11:39,050
So now, one idea is to
describe them by waves.

186
00:11:39,050 --> 00:11:43,390
The other idea is to
describe them by particles.

187
00:11:43,390 --> 00:11:45,740
And also, at the same
time, as we actually

188
00:11:45,740 --> 00:11:48,820
discussed in the
previous lecture,

189
00:11:48,820 --> 00:11:55,930
we can do a two-slit
experiment with billiard balls

190
00:11:55,930 --> 00:11:58,720
or with bullets.

191
00:11:58,720 --> 00:12:01,530
Suppose we do this experiment.

192
00:12:01,530 --> 00:12:08,900
We fire the balls or
bullets through some source.

193
00:12:08,900 --> 00:12:16,100
And we have some kind
of two-slit set up here,

194
00:12:16,100 --> 00:12:20,060
so that the bullets or balls
can actually pass through.

195
00:12:20,060 --> 00:12:21,880
And then we were
wondering, what will

196
00:12:21,880 --> 00:12:25,270
be the pattern which we
see from the detector

197
00:12:25,270 --> 00:12:27,230
in the right-hand side.

198
00:12:27,230 --> 00:12:29,610
And basically, what we
see is the following.

199
00:12:29,610 --> 00:12:31,910
So basically, we
have a distribution

200
00:12:31,910 --> 00:12:39,800
of the balls coming
from slit number one.

201
00:12:39,800 --> 00:12:44,750
And we have another distribution
of balls, which is actually

202
00:12:44,750 --> 00:12:48,230
coming from slit number two.

203
00:12:48,230 --> 00:12:52,220
And I can call it P-1 and
P-2, which is actually

204
00:12:52,220 --> 00:12:55,940
the probability
density distribution

205
00:12:55,940 --> 00:12:58,350
of the experimental result.

206
00:12:58,350 --> 00:13:03,350
And the final result,
or say, if you just

207
00:13:03,350 --> 00:13:05,920
look at the
distribution of balls

208
00:13:05,920 --> 00:13:11,990
without separating the
balls from slit number

209
00:13:11,990 --> 00:13:14,810
one and slit number
two, basically you

210
00:13:14,810 --> 00:13:18,320
get some distribution
like this, which

211
00:13:18,320 --> 00:13:23,750
is a superpositional P-1
and the P-2 distributions.

212
00:13:23,750 --> 00:13:28,530
All of these things
doesn't surprise anybody.

213
00:13:28,530 --> 00:13:34,540
The experiment one,
which we perform--

214
00:13:34,540 --> 00:13:41,130
now, instead of billiard balls,
we perform the same experiment

215
00:13:41,130 --> 00:13:44,380
with electrons.

216
00:13:44,380 --> 00:13:47,230
And again, we have
all those electrons

217
00:13:47,230 --> 00:13:53,790
pass through this two-slit
two-slit experiment.

218
00:13:53,790 --> 00:13:58,390
As we see before,
basically, again, we

219
00:13:58,390 --> 00:14:04,060
can actually separate electrons
from the first slit, which

220
00:14:04,060 --> 00:14:12,220
I called I-1, and the
intensity of electrons

221
00:14:12,220 --> 00:14:16,840
coming from the second
slit, which I called I-2.

222
00:14:16,840 --> 00:14:20,510
Then, basically, if you
can identify and make sure

223
00:14:20,510 --> 00:14:22,990
that the electron is coming
from one of the slits,

224
00:14:22,990 --> 00:14:26,910
you are going to get
distribution like this.

225
00:14:26,910 --> 00:14:28,000
OK?

226
00:14:28,000 --> 00:14:33,790
And of course, I can always
write these I-1 as a sine wave

227
00:14:33,790 --> 00:14:37,480
function, psi-1 squared.

228
00:14:37,480 --> 00:14:41,280
And I can always write this
I-2, which is the intensity

229
00:14:41,280 --> 00:14:45,610
as a function of position of the
electron coming from the second

230
00:14:45,610 --> 00:14:46,870
slit--

231
00:14:46,870 --> 00:14:50,580
I can always write
it as psi-2 squared.

232
00:14:53,660 --> 00:14:56,980
In the case of
light, it's actually

233
00:14:56,980 --> 00:15:02,380
just proportional to
the electric field.

234
00:15:02,380 --> 00:15:06,520
So if you accept this,
and now you actually

235
00:15:06,520 --> 00:15:10,620
don't measure where
the electron actually

236
00:15:10,620 --> 00:15:14,050
pass through when the
electron from the source

237
00:15:14,050 --> 00:15:15,910
passed through this experiment--

238
00:15:15,910 --> 00:15:20,650
we now don't measure if it
passed through one or two.

239
00:15:20,650 --> 00:15:23,850
Then, the pattern
becomes like this.

240
00:15:23,850 --> 00:15:29,690
You have something like
this which, essentially,

241
00:15:29,690 --> 00:15:35,860
is very, very similar to
the two-slit interference

242
00:15:35,860 --> 00:15:42,190
experimental result of
the laser experiment.

243
00:15:42,190 --> 00:15:46,570
As you see from this
experimental result,

244
00:15:46,570 --> 00:15:50,480
you see some kind of pattern.

245
00:15:50,480 --> 00:15:52,300
You have the peak.

246
00:15:52,300 --> 00:15:54,570
You have the valley,
as a function

247
00:15:54,570 --> 00:15:57,470
of position in the detector.

248
00:15:57,470 --> 00:16:02,590
And we can actually call
this I-1-2, which is actually

249
00:16:02,590 --> 00:16:08,320
when you don't measure
or you don't identify

250
00:16:08,320 --> 00:16:11,600
which slit the
electron goes through,

251
00:16:11,600 --> 00:16:14,740
then you have the intensity,
which is actually called I-1-2.

252
00:16:17,330 --> 00:16:22,400
And what we actually found
is that I-1-2 is actually

253
00:16:22,400 --> 00:16:26,890
not I-1 plus I-2.

254
00:16:26,890 --> 00:16:32,020
What we found is that
I-1-2 is actually psi-1

255
00:16:32,020 --> 00:16:34,045
plus psi-2 squared.

256
00:16:36,730 --> 00:16:43,000
So basically, we see
interference pattern.

257
00:16:43,000 --> 00:16:49,952
And this will be equal to I-1
plus I-2 plus 2 squared root

258
00:16:49,952 --> 00:16:55,840
of I-1 plus I-2 and
the cosine delta,

259
00:16:55,840 --> 00:17:03,170
where the delta is coming from
the path length difference.

260
00:17:03,170 --> 00:17:07,490
So based on this
experimental result,

261
00:17:07,490 --> 00:17:10,609
this is actually
really surprising.

262
00:17:10,609 --> 00:17:16,829
First of all, electrons are
arriving like a particle,

263
00:17:16,829 --> 00:17:17,329
right?

264
00:17:17,329 --> 00:17:20,869
Because we can see
from this slide,

265
00:17:20,869 --> 00:17:26,662
if you look at the upper left
figure, you see doo-doo-doo.

266
00:17:26,662 --> 00:17:31,010
Every time, you have
something hitting the screen.

267
00:17:31,010 --> 00:17:33,160
And what is actually left over?

268
00:17:33,160 --> 00:17:37,260
It's a single hit on the screen.

269
00:17:37,260 --> 00:17:43,190
Therefore, the electrons are
arriving like a particle,

270
00:17:43,190 --> 00:17:46,250
producing a hit in the detector.

271
00:17:46,250 --> 00:17:49,760
On the other hand,
what we are saying here

272
00:17:49,760 --> 00:17:56,420
is that, before
they hit the screen,

273
00:17:56,420 --> 00:17:59,800
they are behaving like a wave.

274
00:17:59,800 --> 00:18:03,940
It has interference with
itself, like a wave.

275
00:18:03,940 --> 00:18:07,310
All right, so is
electron a particle?

276
00:18:07,310 --> 00:18:09,845
Or is the electron a wave?

277
00:18:15,120 --> 00:18:17,130
Strange.

278
00:18:17,130 --> 00:18:20,490
The answer is
electron is actually

279
00:18:20,490 --> 00:18:22,225
neither of them in reality.

280
00:18:27,790 --> 00:18:31,240
So how about we actually
do some more experiments

281
00:18:31,240 --> 00:18:36,110
to convince ourselves what
is actually really going on.

282
00:18:36,110 --> 00:18:37,550
So what we could do--

283
00:18:37,550 --> 00:18:39,730
as I actually mentioned.

284
00:18:39,730 --> 00:18:41,620
I can still have
the electronic gun.

285
00:18:44,368 --> 00:18:49,740
I have electron source
in the left-hand side.

286
00:18:49,740 --> 00:18:52,980
Again, I have this
two-slit experiment here.

287
00:18:59,620 --> 00:19:07,170
Then what I'm going to do is
to produce a light source here.

288
00:19:07,170 --> 00:19:13,590
OK, I put a light source there
to shine the whole experiment.

289
00:19:13,590 --> 00:19:16,040
Then, I was wondering
what is going

290
00:19:16,040 --> 00:19:21,350
to happen to the distribution.

291
00:19:21,350 --> 00:19:28,930
So if I first close the
lower slit, slit number two,

292
00:19:28,930 --> 00:19:32,880
and only measure the intensity
coming front slit number 1,

293
00:19:32,880 --> 00:19:36,116
then this is the distribution
I get, which is I-1.

294
00:19:36,116 --> 00:19:41,030
If I close the upper one
and open only the lower one,

295
00:19:41,030 --> 00:19:45,410
I get a distribution
which is I-2.

296
00:19:45,410 --> 00:19:49,480
And this light
source, essentially

297
00:19:49,480 --> 00:19:53,780
interacting with the
electron-- when electrons

298
00:19:53,780 --> 00:19:58,270
pass through this slit,
what is going to happen

299
00:19:58,270 --> 00:20:02,000
is that you'll see some
scattered light coming

300
00:20:02,000 --> 00:20:03,410
from the slit.

301
00:20:03,410 --> 00:20:07,690
Therefore, you can know which
slit the electron actually

302
00:20:07,690 --> 00:20:09,770
passed through.

303
00:20:09,770 --> 00:20:13,370
And if I do this
experiment result--

304
00:20:13,370 --> 00:20:17,730
if I block one of the slits,
this is the distribution, I-1

305
00:20:17,730 --> 00:20:22,400
and I-2 and now I'm
going to open both slits,

306
00:20:22,400 --> 00:20:26,090
and you will see light
coming out of the slit

307
00:20:26,090 --> 00:20:31,160
when the electron pass slit
number one or slit number two.

308
00:20:31,160 --> 00:20:35,190
You can identify which slit
fora all the electrons passing

309
00:20:35,190 --> 00:20:37,160
through this experiment.

310
00:20:37,160 --> 00:20:44,900
And the resulting distribution
of electrons on the screen

311
00:20:44,900 --> 00:20:46,500
is actually like this.

312
00:20:46,500 --> 00:20:49,370
It's actually like I-1 plus I-2.

313
00:20:49,370 --> 00:20:53,870
There will be no interference.

314
00:20:53,870 --> 00:20:55,850
Why is that?

315
00:20:55,850 --> 00:21:00,360
Now, this because you
know very precisely which

316
00:21:00,360 --> 00:21:03,190
slit the electron
actually passed through,

317
00:21:03,190 --> 00:21:06,070
this experiment.

318
00:21:06,070 --> 00:21:11,520
And also, we can say that,
huh, the electrons are actually

319
00:21:11,520 --> 00:21:13,420
disturbed.

320
00:21:13,420 --> 00:21:18,580
Therefore, they now behave like
bullets or like billiard balls.

321
00:21:21,100 --> 00:21:24,160
So this is actually
a bit strange.

322
00:21:27,100 --> 00:21:32,020
Maybe it is because the
intensity of the light

323
00:21:32,020 --> 00:21:33,860
is too large.

324
00:21:33,860 --> 00:21:38,380
Therefore, it's changing the
behavior of the electron.

325
00:21:38,380 --> 00:21:41,890
So what are we going to do now?

326
00:21:41,890 --> 00:21:45,040
Experimental result
number three is

327
00:21:45,040 --> 00:21:53,000
to lower the intensity
of the light.

328
00:21:56,210 --> 00:22:00,580
So what will happen if
I lower the intensity

329
00:22:00,580 --> 00:22:06,040
of the light source so that we
would like to see the behavior,

330
00:22:06,040 --> 00:22:08,020
as a function of intensity?

331
00:22:10,970 --> 00:22:18,060
So at some point, we will find
that some of the electrons

332
00:22:18,060 --> 00:22:21,420
are not heated by a photon.

333
00:22:21,420 --> 00:22:26,520
Or say, there will be no
scattered light of the electron

334
00:22:26,520 --> 00:22:29,730
when it passes through
the experiment.

335
00:22:29,730 --> 00:22:34,710
Because the intensity of
the light is too small.

336
00:22:34,710 --> 00:22:40,410
And we already know, from
photoelectric experiments,

337
00:22:40,410 --> 00:22:43,800
light is, essentially,
also like quanta.

338
00:22:43,800 --> 00:22:47,580
So when the intensity
is low enough,

339
00:22:47,580 --> 00:22:54,210
the effectiveness of the
light source decreases.

340
00:22:54,210 --> 00:22:57,890
Then the experimental
result would be like what?

341
00:22:57,890 --> 00:23:01,570
Can somebody actually
give a guess?

342
00:23:01,570 --> 00:23:06,840
Is that going to be like
experimental result number one?

343
00:23:06,840 --> 00:23:11,570
Or is that going to be like
experimental result number two?

344
00:23:14,460 --> 00:23:16,165
Anybody want to get--

345
00:23:16,165 --> 00:23:18,812
AUDIENCE: [INAUDIBLE]

346
00:23:18,812 --> 00:23:19,770
YEN-JIE LEE: Very good.

347
00:23:19,770 --> 00:23:26,130
So the result-- as I mentioned
before, sometimes the electrons

348
00:23:26,130 --> 00:23:30,490
are detected by
the light source.

349
00:23:30,490 --> 00:23:34,860
Sometimes the
electrons are lucky.

350
00:23:34,860 --> 00:23:38,610
They pass through without
getting heated by a photon.

351
00:23:38,610 --> 00:23:41,430
Therefore, you cannot
know which slit, actually,

352
00:23:41,430 --> 00:23:44,110
this electron went through.

353
00:23:44,110 --> 00:23:46,170
Therefore, the
experimental result

354
00:23:46,170 --> 00:23:51,180
is that, if I just lower the
intensity of the light source,

355
00:23:51,180 --> 00:23:55,760
then what I'm going to get is a
mixture of experimental result

356
00:23:55,760 --> 00:24:02,310
number one and the
experimental result number two.

357
00:24:02,310 --> 00:24:05,910
When I have the
intensity low enough--

358
00:24:05,910 --> 00:24:09,200
going to really, really
low intensity limit--

359
00:24:09,200 --> 00:24:14,280
the result will become
experimental result number one.

360
00:24:14,280 --> 00:24:17,520
Because then you are
not really impacting

361
00:24:17,520 --> 00:24:20,120
the position of the electrons.

362
00:24:23,000 --> 00:24:26,990
Finally, you can actually
suggest something else.

363
00:24:26,990 --> 00:24:33,110
So OK, now I have low
intensity of light.

364
00:24:33,110 --> 00:24:37,190
One way to lower the intensity
is like what I was saying.

365
00:24:37,190 --> 00:24:39,410
The rate of the
photon emission--

366
00:24:39,410 --> 00:24:42,470
I can make it lower and lower.

367
00:24:42,470 --> 00:24:43,590
All right?

368
00:24:43,590 --> 00:24:47,690
There's another way to do this.

369
00:24:51,430 --> 00:24:53,870
Experimental result
number four--

370
00:24:53,870 --> 00:24:57,980
so what will happen
if I use this formula

371
00:24:57,980 --> 00:25:04,100
E equal to h bar mu equal
to hc divided by lambda?

372
00:25:04,100 --> 00:25:08,470
Because mu is actually
just c over lambda.

373
00:25:08,470 --> 00:25:14,690
What will happen if
I, instead of lowering

374
00:25:14,690 --> 00:25:20,830
the rate of photon
emission, I lower the energy

375
00:25:20,830 --> 00:25:23,410
of individual photons?

376
00:25:23,410 --> 00:25:25,610
How do I do that?

377
00:25:25,610 --> 00:25:31,440
What I could do is to
lower the frequency

378
00:25:31,440 --> 00:25:35,700
of the electromagnetic
wave of the light source

379
00:25:35,700 --> 00:25:40,380
or, say, increase
the wavelengths

380
00:25:40,380 --> 00:25:41,850
of the light source.

381
00:25:41,850 --> 00:25:45,090
OK, this is very nice.

382
00:25:45,090 --> 00:25:47,640
Because now, I can
keep this in, right?

383
00:25:47,640 --> 00:25:50,340
So that I make sure
all the electrons

384
00:25:50,340 --> 00:25:54,660
are bothered by the photon.

385
00:25:54,660 --> 00:25:57,310
Because I can emit
very high rate.

386
00:25:57,310 --> 00:26:00,850
But at the same time, I can
also lower the intensity,

387
00:26:00,850 --> 00:26:04,920
so that the intensity
is very, very low.

388
00:26:04,920 --> 00:26:07,620
Can anybody guess what
is going to happen?

389
00:26:10,940 --> 00:26:14,670
With a result like
experimental result number one,

390
00:26:14,670 --> 00:26:18,870
when I go to extremely
low intensity?

391
00:26:18,870 --> 00:26:24,330
Or my result will be like
experimental result number two?

392
00:26:24,330 --> 00:26:29,620
Because each electrons
are bothered,

393
00:26:29,620 --> 00:26:37,170
are heated, by the emission
from the light source.

394
00:26:37,170 --> 00:26:40,330
Anybody want to try?

395
00:26:40,330 --> 00:26:42,180
Just guess, no?

396
00:26:42,180 --> 00:26:43,796
One or two?

397
00:26:43,796 --> 00:26:47,325
Or a mixture of them?

398
00:26:47,325 --> 00:26:49,200
AUDIENCE: Be like two.

399
00:26:49,200 --> 00:26:50,940
YEN-JIE LEE: The
guess is that it's

400
00:26:50,940 --> 00:26:54,450
going to be like two, which
was actually well-motivated.

401
00:26:54,450 --> 00:26:57,120
Very good try.

402
00:26:57,120 --> 00:26:59,400
What essentially,
happens is that--

403
00:26:59,400 --> 00:27:00,580
OK, I can say, oh!

404
00:27:00,580 --> 00:27:05,280
Each electron are bothered
by many, many photons.

405
00:27:05,280 --> 00:27:08,160
So those are disturbed.

406
00:27:08,160 --> 00:27:15,480
Therefore, it has to look like
experimental result number two.

407
00:27:15,480 --> 00:27:18,360
The answer may surprise you.

408
00:27:18,360 --> 00:27:22,290
The answer is that,
if I have the limit

409
00:27:22,290 --> 00:27:28,370
lambda goes to
infinity, mu goes to 0,

410
00:27:28,370 --> 00:27:32,170
what is going to happen
is that, no matter how

411
00:27:32,170 --> 00:27:37,330
high frequency of
photon emission I have,

412
00:27:37,330 --> 00:27:44,700
I am going to get the result
of experimental number one.

413
00:27:44,700 --> 00:27:46,651
Why is that?

414
00:27:46,651 --> 00:27:51,190
Now, this is because
when the wavelengths

415
00:27:51,190 --> 00:27:55,840
of the electromagnetic
wave or the photon is going

416
00:27:55,840 --> 00:28:07,370
to infinity, that means you
cannot resolve which slit,

417
00:28:07,370 --> 00:28:10,780
actually, the
electron goes through.

418
00:28:10,780 --> 00:28:15,790
Because if I draw
the wavelengths here,

419
00:28:15,790 --> 00:28:17,770
it's going to be like this.

420
00:28:17,770 --> 00:28:22,450
If you observe some
kind of scattered light

421
00:28:22,450 --> 00:28:31,190
from the electron, it
could come from both slits,

422
00:28:31,190 --> 00:28:33,620
because the wavelength
is too long.

423
00:28:33,620 --> 00:28:35,780
So if you go to
infinity, then it's

424
00:28:35,780 --> 00:28:39,640
like you have a constant
electric field there.

425
00:28:39,640 --> 00:28:41,690
It doesn't really
actually help you

426
00:28:41,690 --> 00:28:45,480
to identify which slit
the electron actually

427
00:28:45,480 --> 00:28:47,150
passed through.

428
00:28:47,150 --> 00:28:52,490
So therefore, the interference
pattern reappears.

429
00:28:52,490 --> 00:28:58,430
So this is really crazy thing,
if you look at all these four

430
00:28:58,430 --> 00:29:01,870
experimental results.

431
00:29:01,870 --> 00:29:07,090
The conclusion from these
four imaginary experiments

432
00:29:07,090 --> 00:29:11,830
is that it is not
yet possible to tell

433
00:29:11,830 --> 00:29:17,320
the position of the electron
and also, at the same time,

434
00:29:17,320 --> 00:29:20,830
do not disturb it.

435
00:29:20,830 --> 00:29:26,470
If you were able to tell the
position of the electron,

436
00:29:26,470 --> 00:29:29,950
then there would be no
interference pattern.

437
00:29:29,950 --> 00:29:33,700
On the other hand, if
your experimental set-up

438
00:29:33,700 --> 00:29:38,810
have no ability at all to
tell if the electron's coming

439
00:29:38,810 --> 00:29:42,550
from slit number one
compared to slit number two,

440
00:29:42,550 --> 00:29:49,310
then you are going to
get interference pattern.

441
00:29:49,310 --> 00:29:53,470
There's another thing which I
would like to make connection

442
00:29:53,470 --> 00:29:57,490
to the Uncertainty Principle,
which we actually learn

443
00:29:57,490 --> 00:30:01,210
from waves and vibrations.

444
00:30:01,210 --> 00:30:12,170
So we have learned that
Heisenberg's Uncertainty

445
00:30:12,170 --> 00:30:12,860
Principle--

446
00:30:21,100 --> 00:30:23,420
this is essentially
purity coming

447
00:30:23,420 --> 00:30:28,760
from the property of the
wave, if you actually

448
00:30:28,760 --> 00:30:31,700
remember the deviation
which we have

449
00:30:31,700 --> 00:30:33,830
done in the previous lecture.

450
00:30:33,830 --> 00:30:38,690
So what is this uncertainty
principle telling us?

451
00:30:38,690 --> 00:30:44,595
Is that the standard
deviation of the position

452
00:30:44,595 --> 00:30:50,840
times the standard
deviation of the momentum

453
00:30:50,840 --> 00:30:57,560
is going to be greater or equal
to h bar over 2 some constant.

454
00:30:57,560 --> 00:31:00,710
And how do we actually
understand this

455
00:31:00,710 --> 00:31:05,430
from the electron experiment.

456
00:31:05,430 --> 00:31:10,220
That is actually highly related
to the single-slit experiment

457
00:31:10,220 --> 00:31:11,810
with electrons.

458
00:31:11,810 --> 00:31:17,810
So what we could do now is
to have a fifth experiment.

459
00:31:17,810 --> 00:31:21,470
I have electron source here.

460
00:31:21,470 --> 00:31:25,820
And I have a single slit.

461
00:31:25,820 --> 00:31:32,000
And the width of the
slit is capital D.

462
00:31:32,000 --> 00:31:35,780
And we were wondering,
what is going to happen?

463
00:31:35,780 --> 00:31:39,250
What will be recorded
by the smoke detector

464
00:31:39,250 --> 00:31:40,880
in the right-hand side?

465
00:31:40,880 --> 00:31:43,610
And by now, it should
not surprise you

466
00:31:43,610 --> 00:31:49,250
that this would give you some
kind of diffraction pattern,

467
00:31:49,250 --> 00:31:51,990
which you say should be very
similar to what we actually

468
00:31:51,990 --> 00:31:56,740
observe with laser experiments.

469
00:31:56,740 --> 00:31:58,390
So you can see that.

470
00:31:58,390 --> 00:32:02,590
The electron-- the momentum--

471
00:32:02,590 --> 00:32:06,950
now, I would like to actually
define my coordinate system.

472
00:32:06,950 --> 00:32:14,050
The vertical direction, pointing
upward, is my x direction.

473
00:32:14,050 --> 00:32:19,060
So now, take a look at
this experimental result.

474
00:32:19,060 --> 00:32:23,530
So what this is actually
telling us is the following.

475
00:32:23,530 --> 00:32:28,030
We know the position
of the electron

476
00:32:28,030 --> 00:32:35,870
to a accuracy of the
width of this slit, which

477
00:32:35,870 --> 00:32:39,700
is D. So that is
actually telling you

478
00:32:39,700 --> 00:32:49,300
about the uncertainty over the
position in the x direction.

479
00:32:49,300 --> 00:32:53,710
Now, this electron goes through.

480
00:32:53,710 --> 00:32:58,910
And they actually
hit the screen.

481
00:32:58,910 --> 00:33:06,070
And each electron is
having a single path.

482
00:33:06,070 --> 00:33:11,770
If I look at one of the paths,
the upper one, what I'm getting

483
00:33:11,770 --> 00:33:17,496
is that there must be a
momentum quintessentially

484
00:33:17,496 --> 00:33:22,820
in the x direction, when
this electronic goes

485
00:33:22,820 --> 00:33:28,440
through the slit
and hits the screen.

486
00:33:32,060 --> 00:33:35,180
One interesting thing we
learned from the deviation

487
00:33:35,180 --> 00:33:40,790
from last time is that, if I
just look at the slide here--

488
00:33:40,790 --> 00:33:43,910
if I look at the
left-hand side slide--

489
00:33:43,910 --> 00:33:49,150
if I have a very small slit--

490
00:33:49,150 --> 00:33:53,180
D is small-- what does
that correspond to?

491
00:33:53,180 --> 00:34:01,820
That corresponds to delta x
goes to very small value case.

492
00:34:01,820 --> 00:34:04,250
We have a small delta x value.

493
00:34:04,250 --> 00:34:08,360
You are really sure
where is the electron

494
00:34:08,360 --> 00:34:15,940
at some instant of time, when it
passed through the experiment.

495
00:34:15,940 --> 00:34:17,179
Then what is going to happen?

496
00:34:17,179 --> 00:34:19,429
If you look at the
right-hand side,

497
00:34:19,429 --> 00:34:25,810
the distribution on the screen,
you have a wide distribution.

498
00:34:25,810 --> 00:34:29,570
The central maximum
peak will be very wide.

499
00:34:29,570 --> 00:34:30,830
So what does that mean?

500
00:34:30,830 --> 00:34:34,250
That means you have
a wide distribution

501
00:34:34,250 --> 00:34:37,957
of momentum in the x direction.

502
00:34:40,889 --> 00:34:45,759
Therefore, that
will give you that

503
00:34:45,759 --> 00:34:48,860
is actually consistent with what
we've actually written here,

504
00:34:48,860 --> 00:34:50,460
Heisenberg's Principle.

505
00:34:50,460 --> 00:34:55,239
Delta x times delta p will be
greater or equal to some value.

506
00:34:55,239 --> 00:35:01,410
On the other hand, if I
increase the width of the slit,

507
00:35:01,410 --> 00:35:03,735
the D is now large.

508
00:35:03,735 --> 00:35:08,460
As you are making a D larger
and larger, what is happening

509
00:35:08,460 --> 00:35:13,550
is that the central
peak, the width,

510
00:35:13,550 --> 00:35:18,120
is actually going to be
narrower and narrower.

511
00:35:18,120 --> 00:35:20,130
Now, this is actually
also consistent with what

512
00:35:20,130 --> 00:35:23,250
we have learned from
Heisenberg's Uncertainty

513
00:35:23,250 --> 00:35:24,030
Principle.

514
00:35:24,030 --> 00:35:29,990
When delta x become even larger,
then the uncertainty or, say,

515
00:35:29,990 --> 00:35:35,320
the distribution of the
momentum in the x direction,

516
00:35:35,320 --> 00:35:38,310
becomes smaller.

517
00:35:38,310 --> 00:35:41,940
So now, we actually also
understand a little bit more

518
00:35:41,940 --> 00:35:46,200
about what the single
diffraction actually means.

519
00:35:46,200 --> 00:35:51,720
And this issue is really closely
connected to the Uncertainty

520
00:35:51,720 --> 00:35:55,500
Principle Heisenberg
actually proposed.

521
00:35:55,500 --> 00:35:58,530
And if we use the
mathematics which

522
00:35:58,530 --> 00:36:01,780
we learned from last
time, the C function

523
00:36:01,780 --> 00:36:06,060
is going to be proportional
to integration from minus D

524
00:36:06,060 --> 00:36:09,150
over 2 to D over 2.

525
00:36:09,150 --> 00:36:15,990
dx exponential as ikx times x.

526
00:36:15,990 --> 00:36:19,870
And if I have D
goes to infinity,

527
00:36:19,870 --> 00:36:24,240
which means that you have
an infinitely wide slit--

528
00:36:24,240 --> 00:36:28,530
based on the formula which
we have derived last time--

529
00:36:28,530 --> 00:36:34,680
basically, we will see that C
function is a function of kx.

530
00:36:34,680 --> 00:36:37,380
It's going to become
a delta function.

531
00:36:41,250 --> 00:36:47,270
And this delta
function is delta kx.

532
00:36:47,270 --> 00:36:51,720
So that means, if you
have absolutely no idea

533
00:36:51,720 --> 00:36:56,670
about the position
of the electron,

534
00:36:56,670 --> 00:37:03,950
you are going to get very, very
precise information about--

535
00:37:03,950 --> 00:37:07,200
the momentum in the x
direction is actually

536
00:37:07,200 --> 00:37:10,620
going to be equal to 0.

537
00:37:10,620 --> 00:37:12,160
Because it's a delta function.

538
00:37:12,160 --> 00:37:19,820
It's only nonzero at kx, which
is the directional propagation

539
00:37:19,820 --> 00:37:23,050
equal to 0.

540
00:37:23,050 --> 00:37:24,090
Any questions so far?

541
00:37:27,760 --> 00:37:31,930
OK, so from those
experimental results,

542
00:37:31,930 --> 00:37:40,900
we've found that the probability
of getting heat on the screen

543
00:37:40,900 --> 00:37:45,850
is proportional to
psi-1 square, if I only

544
00:37:45,850 --> 00:37:49,550
have the first lead there.

545
00:37:49,550 --> 00:37:56,430
That means the probability, p,
is proportional to psi squared.

546
00:37:59,330 --> 00:38:03,650
And this is actually
probably one

547
00:38:03,650 --> 00:38:11,420
of the most crazy results in
the physics we learned so far.

548
00:38:11,420 --> 00:38:15,550
In some sense, it's
kind of sad as well.

549
00:38:15,550 --> 00:38:18,020
Why sad?

550
00:38:18,020 --> 00:38:24,680
This means that, OK, I can
calculate those wave functions.

551
00:38:24,680 --> 00:38:28,220
And the probability
of getting an outcome

552
00:38:28,220 --> 00:38:32,910
at a specific position is
proportional to this wave

553
00:38:32,910 --> 00:38:33,685
function squared.

554
00:38:37,400 --> 00:38:40,990
But I feel, maybe,
demotivated, right?

555
00:38:40,990 --> 00:38:44,150
Because originally,
we are like god.

556
00:38:44,150 --> 00:38:45,520
You can predict--

557
00:38:45,520 --> 00:38:48,440
OK, I have this
thing, this object.

558
00:38:48,440 --> 00:38:50,150
And I have force.

559
00:38:50,150 --> 00:38:52,790
And then it goes like--
oh-- like this way.

560
00:38:52,790 --> 00:38:58,510
I can calculate the
trajectory of this chalk thing

561
00:38:58,510 --> 00:39:00,530
all over the place,
as a function of time.

562
00:39:00,530 --> 00:39:02,930
And I know what is
going to happen.

563
00:39:02,930 --> 00:39:07,490
I have the full control
of all the objects

564
00:39:07,490 --> 00:39:12,160
which I have in my
hand in my experiment.

565
00:39:12,160 --> 00:39:18,560
But now, quantum mechanics
or this experimental result

566
00:39:18,560 --> 00:39:23,360
tells me that we
can only predict

567
00:39:23,360 --> 00:39:29,350
the probability, the odd,
instead of the outcome.

568
00:39:29,350 --> 00:39:31,460
You see my point?

569
00:39:31,460 --> 00:39:35,110
I can only pretend the wave
function, the distribution

570
00:39:35,110 --> 00:39:36,730
of the wave function.

571
00:39:36,730 --> 00:39:40,660
And the probability of
getting a result here

572
00:39:40,660 --> 00:39:43,810
is proportional to the
wave function squared.

573
00:39:43,810 --> 00:39:48,600
But I cannot predict the outcome
before I do the experiment.

574
00:39:51,600 --> 00:39:58,180
That's really a big
change in your view

575
00:39:58,180 --> 00:40:03,105
or, they say, in our current
understanding of the physics.

576
00:40:06,130 --> 00:40:11,080
You can say that, well,
maybe Yen-Jie's not

577
00:40:11,080 --> 00:40:14,800
working hard enough.

578
00:40:14,800 --> 00:40:22,840
Maybe all those electrons which
are emitted from the electron

579
00:40:22,840 --> 00:40:26,830
source already
made up their mind

580
00:40:26,830 --> 00:40:30,520
where this electron is going to.

581
00:40:30,520 --> 00:40:35,444
For example, electron number
one is doing this-- rrrrr--

582
00:40:35,444 --> 00:40:36,760
and going to here.

583
00:40:36,760 --> 00:40:39,820
And electron number two
already made up his mind.

584
00:40:39,820 --> 00:40:41,560
He's just going to do this.

585
00:40:41,560 --> 00:40:43,940
And the electron
number three is-- uh--

586
00:40:43,940 --> 00:40:47,630
maybe do this--
vwooo-do-do-do-do.

587
00:40:47,630 --> 00:40:53,410
And then all those trajectories
are already determined.

588
00:40:53,410 --> 00:40:59,960
And they are heating variables
which Yen-Jie doesn't know.

589
00:40:59,960 --> 00:41:03,280
Therefore, he screwed this
up and said, oh, come on.

590
00:41:03,280 --> 00:41:07,898
We can only predict
the probability.

591
00:41:07,898 --> 00:41:15,400
But the thing is that, from the
experimental result number two,

592
00:41:15,400 --> 00:41:19,660
experimental result number
three and number four,

593
00:41:19,660 --> 00:41:26,560
you can see that the electrons
cannot make up their mind when

594
00:41:26,560 --> 00:41:28,210
they are emitted.

595
00:41:28,210 --> 00:41:32,620
Because when they got
heated by that light--

596
00:41:32,620 --> 00:41:36,370
electrons cannot know in advance
that it is going to be heated

597
00:41:36,370 --> 00:41:38,830
by a light.

598
00:41:38,830 --> 00:41:43,690
And the light can be a very,
very mild, very, very small

599
00:41:43,690 --> 00:41:44,300
energy.

600
00:41:44,300 --> 00:41:50,410
So that it should not
affect the predetermined

601
00:41:50,410 --> 00:41:53,760
path of the electron.

602
00:41:53,760 --> 00:41:56,420
Do you get this?

603
00:41:56,420 --> 00:41:57,790
So that doesn't makes sense.

604
00:41:57,790 --> 00:42:03,050
So it is not because
Yen-Jie is not trying hard.

605
00:42:03,050 --> 00:42:07,580
It is really because
nobody can really

606
00:42:07,580 --> 00:42:14,720
tell before the experimental
result is actually shown

607
00:42:14,720 --> 00:42:18,200
or the measurement
is already done.

608
00:42:18,200 --> 00:42:23,970
If you can find
any case, maybe you

609
00:42:23,970 --> 00:42:27,430
will win another
100 Nobel Prize.

610
00:42:27,430 --> 00:42:32,170
Because you are showing that the
whole understanding of quantum

611
00:42:32,170 --> 00:42:37,820
mechanics is not
correct, really.

612
00:42:37,820 --> 00:42:40,900
Please tell me when you actually
have done this experiment.

613
00:42:40,900 --> 00:42:46,290
I will be very proud
of you, for sure.

614
00:42:46,290 --> 00:42:49,170
So now, we are
entering a position

615
00:42:49,170 --> 00:42:53,370
to discuss this result.
So now, actually, we

616
00:42:53,370 --> 00:42:57,540
can also make use of
this understanding

617
00:42:57,540 --> 00:43:01,560
and predict what would be
the particle probability

618
00:43:01,560 --> 00:43:05,370
distribution in
a potential well.

619
00:43:05,370 --> 00:43:12,240
Suppose I have an experiment,
which I have a well,

620
00:43:12,240 --> 00:43:16,140
where I have potential
goes to infinity

621
00:43:16,140 --> 00:43:18,060
in the left-hand side
or right-hand side

622
00:43:18,060 --> 00:43:21,010
edge of this well.

623
00:43:21,010 --> 00:43:23,740
And I will define
my coordinate system

624
00:43:23,740 --> 00:43:27,750
so that the well is
actually equal to 0,

625
00:43:27,750 --> 00:43:35,140
or x equal to L. So by
now, when you see this,

626
00:43:35,140 --> 00:43:37,980
this looks really
familiar to you.

627
00:43:37,980 --> 00:43:40,320
In the center part,
you have some kind

628
00:43:40,320 --> 00:43:42,630
of translation symmetry.

629
00:43:42,630 --> 00:43:45,780
And the boundary-- those
are forbidden regions.

630
00:43:45,780 --> 00:43:48,540
You cannot actually
have particles there,

631
00:43:48,540 --> 00:43:52,290
because the potential
is infinity.

632
00:43:52,290 --> 00:43:55,530
Therefore, this is
actually giving you

633
00:43:55,530 --> 00:44:04,250
boundary conditions
of the wave function,

634
00:44:04,250 --> 00:44:11,920
describing the state of the
particle inside this box.

635
00:44:11,920 --> 00:44:15,000
So the boundary
condition would be psi 0.

636
00:44:15,000 --> 00:44:18,340
It will be equal to 0,
because it's actually

637
00:44:18,340 --> 00:44:22,080
at the left-hand side
edge of the well,

638
00:44:22,080 --> 00:44:26,070
where you have
infinite potential.

639
00:44:26,070 --> 00:44:31,880
And also, you can have psi
L. This will be equal to 0,

640
00:44:31,880 --> 00:44:34,380
because the
right-hand side edge,

641
00:44:34,380 --> 00:44:43,890
you also have infinitely
high potential.

642
00:44:43,890 --> 00:44:49,620
Therefore, when you see
this, your immediate reaction

643
00:44:49,620 --> 00:44:52,485
will be, how do I
know what is this?

644
00:44:52,485 --> 00:44:54,560
This is actually psi m.

645
00:44:54,560 --> 00:44:56,430
The solution to
this problem must

646
00:44:56,430 --> 00:44:59,810
be something like
psi m of x should be

647
00:44:59,810 --> 00:45:02,580
the normal mode of this system.

648
00:45:02,580 --> 00:45:09,330
And it's going to
be A-m sin km-x,

649
00:45:09,330 --> 00:45:16,095
where km will be equal
to m-pi divided by L,

650
00:45:16,095 --> 00:45:17,880
where m is a number.

651
00:45:17,880 --> 00:45:21,660
It can be 1, 2, 3-- it
goes to infinity, right?

652
00:45:21,660 --> 00:45:23,730
By far, you have
actually learned

653
00:45:23,730 --> 00:45:28,900
all these practical calculations
from the previous examples

654
00:45:28,900 --> 00:45:31,100
we had.

655
00:45:31,100 --> 00:45:38,510
Therefore, what would be the
psi m, x as a function of time?

656
00:45:38,510 --> 00:45:44,410
Then what I am going
to get is A-m sin km

657
00:45:44,410 --> 00:45:48,570
x exponential minus i omega-m t.

658
00:45:52,900 --> 00:45:59,350
Of course, we can also really
plot all those results.

659
00:45:59,350 --> 00:46:02,990
So for example, n is equal to 1.

660
00:46:02,990 --> 00:46:07,360
Basically, what you are
getting is like this.

661
00:46:07,360 --> 00:46:09,730
Doesn't surprise you.

662
00:46:09,730 --> 00:46:14,250
This is actually psi
as a function of x.

663
00:46:14,250 --> 00:46:17,050
And n equal to 2--

664
00:46:17,050 --> 00:46:19,480
this will correspond
to the situation

665
00:46:19,480 --> 00:46:29,680
where you have one node in the
middle, et cetera, et cetera.

666
00:46:29,680 --> 00:46:36,780
You can't have many, many
higher m value solutions.

667
00:46:36,780 --> 00:46:40,180
And what would be
the probability

668
00:46:40,180 --> 00:46:45,160
to find the particle
in a specific location?

669
00:46:45,160 --> 00:46:48,460
That's why we mentioned
before, the probability is

670
00:46:48,460 --> 00:46:52,390
proportional to a
wave function squared.

671
00:46:52,390 --> 00:47:01,540
Therefore, the probability will
be proportional to sin squared

672
00:47:01,540 --> 00:47:04,470
k-m x.

673
00:47:04,470 --> 00:47:06,630
And what we are going
to get is like this.

674
00:47:06,630 --> 00:47:12,150
If I plot m equal to 1,
using P as a function of x,

675
00:47:12,150 --> 00:47:19,720
the probability of getting a
particle at a specific place,

676
00:47:19,720 --> 00:47:24,670
if we are looking at the
situation in normal mode number

677
00:47:24,670 --> 00:47:27,400
one, that is like this.

678
00:47:27,400 --> 00:47:31,210
You are much more likely
to find a particle

679
00:47:31,210 --> 00:47:34,620
in the middle of the box.

680
00:47:34,620 --> 00:47:39,600
On the other hand, we can
also plot the probability

681
00:47:39,600 --> 00:47:43,870
as function of x, where
m equals to 2 k's.

682
00:47:43,870 --> 00:47:48,850
If we are actually operating
in a second normal mode,

683
00:47:48,850 --> 00:47:53,080
then basically you have some
distribution-- looks like this.

684
00:47:53,080 --> 00:47:56,410
In this situation, it
is forbidden-- or say,

685
00:47:56,410 --> 00:47:58,780
there's zero
probability you will

686
00:47:58,780 --> 00:48:02,820
find the particle in
the middle of the box,

687
00:48:02,820 --> 00:48:04,010
et cetera, et cetera.

688
00:48:04,010 --> 00:48:09,850
You can actually calculate all
those corresponding probability

689
00:48:09,850 --> 00:48:14,170
distributions as a
function of m value

690
00:48:14,170 --> 00:48:17,630
and as a function of position.

691
00:48:17,630 --> 00:48:18,680
OK?

692
00:48:18,680 --> 00:48:21,560
Sounds like a very good story.

693
00:48:21,560 --> 00:48:24,660
But there's something
missing, right?

694
00:48:24,660 --> 00:48:27,630
What is actually missing?

695
00:48:27,630 --> 00:48:29,710
You have the normal modes.

696
00:48:29,710 --> 00:48:31,680
You have the k-m.

697
00:48:31,680 --> 00:48:37,320
What is missing is
the wave equation.

698
00:48:37,320 --> 00:48:40,920
The wave equation
is missing, right?

699
00:48:40,920 --> 00:48:44,070
You don't have the
dispersion relation.

700
00:48:44,070 --> 00:48:47,250
This solution is incomplete.

701
00:48:47,250 --> 00:48:50,370
You don't know what is
actually the omega value.

702
00:48:54,120 --> 00:48:56,650
Because you don't have
dispersion relation.

703
00:48:56,650 --> 00:49:03,750
So what is actually
the wave equation

704
00:49:03,750 --> 00:49:06,820
for the quantum mechanics?

705
00:49:06,820 --> 00:49:11,170
So it is actually
Schrodinger's equation.

706
00:49:11,170 --> 00:49:14,890
So Feynman once
commented on the origin

707
00:49:14,890 --> 00:49:17,590
of the Schrodinger's Equation.

708
00:49:17,590 --> 00:49:18,910
It's from where?

709
00:49:18,910 --> 00:49:25,360
It's not possible to derive
it from anything you know.

710
00:49:25,360 --> 00:49:30,050
It's just coming out of the
might Schrodinger, actually.

711
00:49:30,050 --> 00:49:31,540
So there's no reason.

712
00:49:31,540 --> 00:49:33,970
And it works.

713
00:49:33,970 --> 00:49:36,280
That's the beautiful part.

714
00:49:36,280 --> 00:49:38,840
So what is, actually,
this equation?

715
00:49:38,840 --> 00:49:41,700
So this is the equation
Schrodinger actually

716
00:49:41,700 --> 00:49:43,450
writes down.

717
00:49:43,450 --> 00:49:47,410
It's like i h-bar--

718
00:49:47,410 --> 00:49:53,170
Plank's constant,
partial/partial t, psi xt.

719
00:49:53,170 --> 00:49:57,840
And this will be equal
to minus h bar squared

720
00:49:57,840 --> 00:50:08,672
over 2m partial square, partial
x square, plus v xt, psi xt.

721
00:50:11,470 --> 00:50:14,140
So this is really nice.

722
00:50:14,140 --> 00:50:19,060
And it works and matches
with experimental results.

723
00:50:19,060 --> 00:50:22,010
And now, I have already
the normal mode.

724
00:50:22,010 --> 00:50:24,460
I can plug that
into this equation

725
00:50:24,460 --> 00:50:27,070
to see what I can
actually learn from there.

726
00:50:27,070 --> 00:50:31,780
So what I am going to do
is to plug in psi-m xt

727
00:50:31,780 --> 00:50:36,220
into this equation, to get
the dispersion relation.

728
00:50:36,220 --> 00:50:38,290
So what this issue, the
dispersion relation.

729
00:50:38,290 --> 00:50:40,450
So here, I have
partial/partial t.

730
00:50:40,450 --> 00:50:46,000
So I extract one omega
minus i omega out of this.

731
00:50:46,000 --> 00:50:52,935
Then, basically, I get
h bar omega-m psi-m xt

732
00:50:52,935 --> 00:50:54,310
in the lambda psi.

733
00:50:54,310 --> 00:51:00,470
OK, plugging in psi-m into this
equation and see what happens.

734
00:51:00,470 --> 00:51:03,070
Then this will be equal to--

735
00:51:03,070 --> 00:51:09,550
I also know that, in the middle
of the box, v, essentially,

736
00:51:09,550 --> 00:51:11,700
the potential--

737
00:51:11,700 --> 00:51:14,500
the potential is
0 inside the box.

738
00:51:14,500 --> 00:51:19,180
The potential is infinity
at the edge of the box.

739
00:51:19,180 --> 00:51:23,800
Therefore, I can safely ignore
this term, to be equal to 0.

740
00:51:23,800 --> 00:51:27,760
So you have a free path
to go inside the box.

741
00:51:27,760 --> 00:51:31,330
And what, essentially,
this term--

742
00:51:31,330 --> 00:51:36,560
this term will give you
minus h-bar square over 2m.

743
00:51:36,560 --> 00:51:38,950
OK, I have a double
differential of x.

744
00:51:38,950 --> 00:51:45,680
And therefore, I get, basically,
minus km squared, right?

745
00:51:45,680 --> 00:51:47,320
Because it's psi zeta, right?

746
00:51:47,320 --> 00:51:50,240
So basically, I get
minus k squared.

747
00:51:50,240 --> 00:51:53,890
So therefore, I cancel
this minus sign.

748
00:51:53,890 --> 00:51:59,530
I have km squared out
of this calculation.

749
00:51:59,530 --> 00:52:02,650
And I still have psi-m xt.

750
00:52:06,310 --> 00:52:08,050
I can cancel this too.

751
00:52:08,050 --> 00:52:16,850
Then, what I'm getting is that
omega-m is equal to km squared,

752
00:52:16,850 --> 00:52:17,820
h-bar--

753
00:52:17,820 --> 00:52:22,360
I cancel one of the h-bar here--

754
00:52:22,360 --> 00:52:23,620
divided by 2m.

755
00:52:26,320 --> 00:52:33,132
This-- essentially, dispersion
relation of the wave function.

756
00:52:37,950 --> 00:52:54,850
De Broglie proposed that
wavelengths of the matter wave,

757
00:52:54,850 --> 00:53:01,690
essentially, highly related
to the momentum of the matter.

758
00:53:01,690 --> 00:53:07,000
So basically, he propose that
p, the momentum of the particle

759
00:53:07,000 --> 00:53:11,140
is actually equal to h-bar
k, where k is the wave

760
00:53:11,140 --> 00:53:14,680
number of the matter wave.

761
00:53:14,680 --> 00:53:20,950
If you accept de Broglie's
interpretation, basically what

762
00:53:20,950 --> 00:53:24,340
we are getting is something
really, really interesting.

763
00:53:24,340 --> 00:53:29,510
If we put together this
dispersion relation

764
00:53:29,510 --> 00:53:35,730
and the de Broglie's
interpretation of matter wave--

765
00:53:35,730 --> 00:53:44,100
what I am going to do is to
calculate the group velocity

766
00:53:44,100 --> 00:53:46,350
of this dispersion relation.

767
00:53:46,350 --> 00:53:48,600
So I can now calculate--

768
00:53:48,600 --> 00:53:55,500
group velocity, V-g, will
be equal to d omega, dk.

769
00:53:55,500 --> 00:54:00,090
And I know that omega is equal
to h-bar k squared divided

770
00:54:00,090 --> 00:54:01,730
by 2m.

771
00:54:01,730 --> 00:54:09,420
This is essentially equal
to h-bar k divided by m.

772
00:54:09,420 --> 00:54:12,350
Everybody is following?

773
00:54:12,350 --> 00:54:13,800
OK.

774
00:54:13,800 --> 00:54:16,050
And this is equal to what?

775
00:54:16,050 --> 00:54:21,710
This is equal to p divided by
m, if I use de Broglie's matter

776
00:54:21,710 --> 00:54:23,670
wave.

777
00:54:23,670 --> 00:54:29,910
Therefore, you have p
equal to m times ng.

778
00:54:29,910 --> 00:54:31,020
Wow!

779
00:54:31,020 --> 00:54:31,615
Look at this.

780
00:54:34,440 --> 00:54:36,400
What are we getting here?

781
00:54:36,400 --> 00:54:43,590
What we are getting here is that
the group velocity of the wave

782
00:54:43,590 --> 00:54:48,340
equation of the
waves is actually

783
00:54:48,340 --> 00:54:56,860
the classical velocity, p
equal to m times v. Now,

784
00:54:56,860 --> 00:55:01,330
everything actually is
becoming more and more clear.

785
00:55:01,330 --> 00:55:08,050
We know and we learned
already, from 8.03, what is

786
00:55:08,050 --> 00:55:10,670
the meaning of group velocity.

787
00:55:10,670 --> 00:55:14,590
The meaning of
the group velocity

788
00:55:14,590 --> 00:55:22,540
is the speed of the propagation
of a wave package, right?

789
00:55:22,540 --> 00:55:30,010
Remember our discussion
before about a AM radio?

790
00:55:30,010 --> 00:55:35,350
So what is actually the speed
of propagation of a wave packet

791
00:55:35,350 --> 00:55:38,830
is the group velocity.

792
00:55:38,830 --> 00:55:42,640
So now we have
solved the problem--

793
00:55:42,640 --> 00:55:48,120
why electron can be a
particle, at the same time,

794
00:55:48,120 --> 00:55:51,288
also like waves.

795
00:55:51,288 --> 00:55:58,190
It's essentially described
by wave functions.

796
00:55:58,190 --> 00:56:03,820
The classical behavior
we see on the electron

797
00:56:03,820 --> 00:56:06,730
is because it is,
as you described,

798
00:56:06,730 --> 00:56:09,740
by these wave packages.

799
00:56:09,740 --> 00:56:12,280
It's pretty localized.

800
00:56:12,280 --> 00:56:18,710
And the motion of this wave
package in a free space

801
00:56:18,710 --> 00:56:23,050
is actually the speed
of the propagation--

802
00:56:23,050 --> 00:56:25,550
is the group velocity.

803
00:56:25,550 --> 00:56:29,570
Therefore, there
is no contradiction

804
00:56:29,570 --> 00:56:32,270
between the
classical calculation

805
00:56:32,270 --> 00:56:36,030
and the wave interpretation
of the electron.

806
00:56:36,030 --> 00:56:40,830
So that really
surprised me very much.

807
00:56:40,830 --> 00:56:47,000
And you can see that, given
the dispersion relation, also,

808
00:56:47,000 --> 00:56:53,640
this is a rather
dynamical result.

809
00:56:53,640 --> 00:56:56,990
The real part of the wave
function is actually blue.

810
00:56:56,990 --> 00:57:00,200
And the imaginary
part is actually red.

811
00:57:00,200 --> 00:57:02,960
It's actually
oscillating up and down.

812
00:57:02,960 --> 00:57:06,440
And the oscillation
frequency, by now,

813
00:57:06,440 --> 00:57:11,410
you know is governed by
that dispersion relation.

814
00:57:11,410 --> 00:57:16,900
OK, now actually, everything
seems to make sense now--

815
00:57:16,900 --> 00:57:20,570
really, really, very cool.

816
00:57:20,570 --> 00:57:22,940
So on the other
hand, we also have

817
00:57:22,940 --> 00:57:25,850
to live with
probability density.

818
00:57:25,850 --> 00:57:31,070
So you cannot tell the exact
position of a particle any

819
00:57:31,070 --> 00:57:31,670
more.

820
00:57:31,670 --> 00:57:36,470
You cannot tell the exact
outcome of an experiment

821
00:57:36,470 --> 00:57:37,510
anymore.

822
00:57:37,510 --> 00:57:42,560
And that is actually to do
with this interpretation.

823
00:57:42,560 --> 00:57:47,690
And all of those phenomena,
at a very, very small scale,

824
00:57:47,690 --> 00:57:50,900
is actually described by
quantum mechanics, which we

825
00:57:50,900 --> 00:57:53,150
will learn some more in 8.04.

826
00:57:53,150 --> 00:57:55,430
And also, in the
future, you will

827
00:57:55,430 --> 00:58:00,980
be governed by the quantum
field theory, which

828
00:58:00,980 --> 00:58:04,360
is actually a father future.

829
00:58:04,360 --> 00:58:10,270
And what is actually the life
living with quantum mechanics

830
00:58:10,270 --> 00:58:12,440
and quantum field theory?

831
00:58:12,440 --> 00:58:14,567
So this is a very simple--

832
00:58:14,567 --> 00:58:15,361
[LAUGHTER]

833
00:58:15,361 --> 00:58:19,810
--Lagrangian of
the standard model.

834
00:58:19,810 --> 00:58:26,080
And it describes everything
except the gravity.

835
00:58:26,080 --> 00:58:26,860
OK?

836
00:58:26,860 --> 00:58:28,160
And it's really simple.

837
00:58:28,160 --> 00:58:30,850
It's called Standard Model.

838
00:58:30,850 --> 00:58:34,630
And look at this part.

839
00:58:34,630 --> 00:58:42,010
This is governing the
Higgs decay to Z boson.

840
00:58:42,010 --> 00:58:47,060
And the experimental result--
we don't really know what

841
00:58:47,060 --> 00:58:49,120
is the mass of the Higgs.

842
00:58:49,120 --> 00:58:53,320
It's a missing
observable before.

843
00:58:53,320 --> 00:58:57,730
And on the other hand,
as a particle physicist

844
00:58:57,730 --> 00:59:02,020
or as a high energy
nuclear physicists,

845
00:59:02,020 --> 00:59:07,630
I have no idea about what will
happen in the next collision.

846
00:59:07,630 --> 00:59:08,210
Why is that?

847
00:59:08,210 --> 00:59:10,270
You know the reason now, right?

848
00:59:10,270 --> 00:59:14,290
Because we cannot
predict the exact outcome

849
00:59:14,290 --> 00:59:15,580
of our experiment.

850
00:59:15,580 --> 00:59:19,120
It's all governed
by wave functions.

851
00:59:19,120 --> 00:59:23,600
Therefore, what we are
doing is the following.

852
00:59:23,600 --> 00:59:27,020
We are doing the brute force.

853
00:59:27,020 --> 00:59:30,130
So we collide like crazy--

854
00:59:30,130 --> 00:59:33,340
collide, collide, collide,
collide like crazy,

855
00:59:33,340 --> 00:59:36,975
until something
interesting pops out.

856
00:59:36,975 --> 00:59:38,350
That's actually
what we're really

857
00:59:38,350 --> 00:59:42,160
doing as a particle physicist.

858
00:59:42,160 --> 00:59:47,500
And this is your beautiful event
from proton-proton collisions

859
00:59:47,500 --> 00:59:51,940
at the Large Hadron Collider--
is a Higgs to the boson event.

860
00:59:51,940 --> 00:59:58,680
And one of the Z bosons
becomes the two red lines.

861
00:59:58,680 --> 01:00:01,000
It's actually the two muons.

862
01:00:01,000 --> 01:00:03,980
And the other
decays to electrons,

863
01:00:03,980 --> 01:00:07,070
which are detected by
the kilometer as the two

864
01:00:07,070 --> 01:00:10,230
blue things there.

865
01:00:10,230 --> 01:00:14,590
As a high-energy
nuclear physicist,

866
01:00:14,590 --> 01:00:18,730
I am interested
in the production

867
01:00:18,730 --> 01:00:23,590
of quark-gluon plasma
from lead ion collisions.

868
01:00:23,590 --> 01:00:29,560
So I am now putting together
two ions, have them collide.

869
01:00:29,560 --> 01:00:32,680
And I hope that,
by chance, I can

870
01:00:32,680 --> 01:00:37,780
deposit a huge amount of
energy in a very small volume.

871
01:00:37,780 --> 01:00:41,930
And then I would like to
see this crazy matter,

872
01:00:41,930 --> 01:00:47,060
actually, gradually expand
and become a lot of particles.

873
01:00:47,060 --> 01:00:50,020
And I study those
particles to understand,

874
01:00:50,020 --> 01:00:53,470
what would be the nature
of this material, which

875
01:00:53,470 --> 01:00:56,410
starts to exist in
the very early part

876
01:00:56,410 --> 01:00:59,200
of the whole universe history?

877
01:00:59,200 --> 01:01:01,630
Just one microsecond
after the Big Bang,

878
01:01:01,630 --> 01:01:05,710
we have the whole universe
filled by this crazy material.

879
01:01:05,710 --> 01:01:08,850
And we are creating
this in the experiment.

880
01:01:08,850 --> 01:01:13,810
And we will only be able to
hope that, OK, by chance, I

881
01:01:13,810 --> 01:01:15,550
have the collision happen.

882
01:01:15,550 --> 01:01:19,840
By chance, I have a very
high-density environment.

883
01:01:19,840 --> 01:01:24,190
Somehow, multiple quanta decide
to scatter on each other.

884
01:01:24,190 --> 01:01:27,140
And they deposit the energy
in a very small volume.

885
01:01:27,140 --> 01:01:30,910
And then we collect all
those spectacular events

886
01:01:30,910 --> 01:01:34,780
to study the properties of
all those little Big Bangs.

887
01:01:34,780 --> 01:01:40,720
So that is actually the
consequence of this wave

888
01:01:40,720 --> 01:01:43,880
function interpretation.

889
01:01:43,880 --> 01:01:48,890
So now, coming back to the
Standard Model, this really

890
01:01:48,890 --> 01:01:54,290
simple one, you can't see,
that is a theory of almost

891
01:01:54,290 --> 01:01:58,630
everything, except the gravity.

892
01:01:58,630 --> 01:01:59,570
Really sad.

893
01:01:59,570 --> 01:02:02,820
So if you can actually
put them all together,

894
01:02:02,820 --> 01:02:04,540
then you will also
win the Nobel Prize.

895
01:02:04,540 --> 01:02:08,840
And giving you all
those ideas, so that I

896
01:02:08,840 --> 01:02:12,260
can have a very good student
winning the Nobel Prize.

897
01:02:12,260 --> 01:02:14,090
Of course you will.

898
01:02:14,090 --> 01:02:19,250
And now, I would like to discuss
and use the remaining, maybe,

899
01:02:19,250 --> 01:02:24,800
10 minutes to discuss
with you the gravity.

900
01:02:24,800 --> 01:02:31,560
So here is actually
something related to gravity.

901
01:02:31,560 --> 01:02:38,180
So Einstein actually
predicted that the distortion

902
01:02:38,180 --> 01:02:42,650
of the space-time
generated by objects

903
01:02:42,650 --> 01:02:45,860
can travel through the space.

904
01:02:45,860 --> 01:02:48,020
I don't have the
derivation here,

905
01:02:48,020 --> 01:02:52,350
because it would take another,
maybe, two hours to do this.

906
01:02:52,350 --> 01:02:55,910
But I would like to
ask you to trust me.

907
01:02:55,910 --> 01:03:01,850
This is actually a result
coming from general relativity.

908
01:03:01,850 --> 01:03:07,040
And you can see
that we can actually

909
01:03:07,040 --> 01:03:09,850
generate gravitational waves.

910
01:03:09,850 --> 01:03:13,550
And I can actually do
the generation here,

911
01:03:13,550 --> 01:03:16,760
like this and rotating.

912
01:03:16,760 --> 01:03:19,320
I'm generating
gravitational waves.

913
01:03:19,320 --> 01:03:21,320
And that student in the
back is also generating.

914
01:03:21,320 --> 01:03:21,970
Yes, you are.

915
01:03:21,970 --> 01:03:23,330
Yeah, you are generating.

916
01:03:23,330 --> 01:03:24,290
Everybody's generating.

917
01:03:24,290 --> 01:03:25,880
Ah, you are also generating.

918
01:03:25,880 --> 01:03:27,460
Yeah, very good.

919
01:03:27,460 --> 01:03:31,820
But the problem is that
the space-time distortion

920
01:03:31,820 --> 01:03:38,120
is really small for people who
are not very massive, like me.

921
01:03:38,120 --> 01:03:40,020
So that's a problem.

922
01:03:40,020 --> 01:03:41,710
So I can generate.

923
01:03:41,710 --> 01:03:43,290
I'm doing the demo here.

924
01:03:43,290 --> 01:03:45,740
But it doesn't help.

925
01:03:45,740 --> 01:03:48,800
You cannot really detect them.

926
01:03:48,800 --> 01:03:53,420
And even Einstein himself thinks
it's impossible to detect them,

927
01:03:53,420 --> 01:03:56,720
maybe, in our lifetime.

928
01:03:56,720 --> 01:04:00,260
And what would be the
outcome of the calculation?

929
01:04:00,260 --> 01:04:02,330
The outcome of the calculation--

930
01:04:02,330 --> 01:04:10,130
if you have gravitational
wave passing toward you--

931
01:04:10,130 --> 01:04:12,540
so what it does
is the following.

932
01:04:12,540 --> 01:04:17,480
So basically, the space
is distorted in a way such

933
01:04:17,480 --> 01:04:20,390
that it first expands
in this direction

934
01:04:20,390 --> 01:04:23,510
and then expanding the other
direction, perpendicular

935
01:04:23,510 --> 01:04:25,470
to the original distortion.

936
01:04:25,470 --> 01:04:29,000
And if you put a
ray of particles,

937
01:04:29,000 --> 01:04:34,160
the circular array of particles,
and look at what is going on,

938
01:04:34,160 --> 01:04:37,030
when the gravitational
wave pass through it,

939
01:04:37,030 --> 01:04:40,580
it pass through the array
in this direction, what

940
01:04:40,580 --> 01:04:45,040
you are going to get
is effect like that.

941
01:04:45,040 --> 01:04:47,620
Of course, this
is actually highly

942
01:04:47,620 --> 01:04:50,920
exaggerated in this set-up.

943
01:04:50,920 --> 01:04:55,990
You don't really see this
kind of sizable distortion

944
01:04:55,990 --> 01:04:58,600
when Yen-Jie is dancing around.

945
01:05:01,170 --> 01:05:06,780
OK, so how about we actually
visualize this thing.

946
01:05:06,780 --> 01:05:10,200
The problem is that we
cannot really see the space

947
01:05:10,200 --> 01:05:11,690
distortion.

948
01:05:11,690 --> 01:05:15,740
But what we can, as
you see, is the light

949
01:05:15,740 --> 01:05:19,500
which actually pass through
those little distortions.

950
01:05:19,500 --> 01:05:23,810
So this is a stimulation
from LIGO Collaboration.

951
01:05:23,810 --> 01:05:30,740
They are simulating the merging
of the two massive black holes.

952
01:05:30,740 --> 01:05:32,480
And you can see that
they are rotating

953
01:05:32,480 --> 01:05:34,490
with respect to each other.

954
01:05:34,490 --> 01:05:41,010
They are radiating energy
out of this two-body system.

955
01:05:41,010 --> 01:05:42,710
Let's take a look at this again.

956
01:05:42,710 --> 01:05:49,400
So this is actually a simulation
of the event observed by LIGO.

957
01:05:49,400 --> 01:05:58,640
So both black holes have a mass
roughly 30 times of our sun.

958
01:05:58,640 --> 01:05:59,840
It's very massive.

959
01:05:59,840 --> 01:06:02,750
And they are rotating with
respect to each other.

960
01:06:02,750 --> 01:06:05,430
And that generates
space-time distortion.

961
01:06:05,430 --> 01:06:10,050
And you can see that the
space-time distortion stops

962
01:06:10,050 --> 01:06:12,400
after they merge each other.

963
01:06:12,400 --> 01:06:16,430
And we were hoping that
we can detect those.

964
01:06:16,430 --> 01:06:17,750
How crazy is that?

965
01:06:21,050 --> 01:06:23,140
So how do we detect them?

966
01:06:23,140 --> 01:06:26,870
Actually, you already
have the knowledge

967
01:06:26,870 --> 01:06:30,750
to design the experiment to
detect this kind of effect.

968
01:06:30,750 --> 01:06:35,960
So remember, the effect
of the gravitational wave

969
01:06:35,960 --> 01:06:36,710
is like this.

970
01:06:36,710 --> 01:06:40,640
So you have
distortion like this.

971
01:06:40,640 --> 01:06:43,180
What we actually--

972
01:06:43,180 --> 01:06:47,300
MIT and Cal Tech and the
many other collaborators

973
01:06:47,300 --> 01:06:50,634
designed the LIGO experiment.

974
01:06:50,634 --> 01:06:51,800
Are what is, actually, LIGO?

975
01:06:51,800 --> 01:06:57,350
It's a Laser Interferometer
Gravitational wave Observatory.

976
01:06:57,350 --> 01:07:00,320
It is actually always good
to have a very good name

977
01:07:00,320 --> 01:07:02,880
of your experiment.

978
01:07:02,880 --> 01:07:04,880
So this is actually LIGO.

979
01:07:04,880 --> 01:07:07,410
So what, actually, it
does is the following.

980
01:07:07,410 --> 01:07:10,370
So basically, it emits a laser.

981
01:07:10,370 --> 01:07:13,260
And you split the
laser into two pieces.

982
01:07:13,260 --> 01:07:18,170
And there were mirrors in
the very far end, reflect

983
01:07:18,170 --> 01:07:19,490
those lasers.

984
01:07:19,490 --> 01:07:21,080
And they come together.

985
01:07:21,080 --> 01:07:24,560
And there is a
photo-detector, which

986
01:07:24,560 --> 01:07:29,100
detects the interference pattern
of these two optical path

987
01:07:29,100 --> 01:07:29,600
lengths.

988
01:07:29,600 --> 01:07:30,100
Wow!

989
01:07:30,100 --> 01:07:31,780
Sounds familiar to you, right?

990
01:07:31,780 --> 01:07:34,610
Hey, you already know how to
explain this to your friends

991
01:07:34,610 --> 01:07:35,480
already.

992
01:07:35,480 --> 01:07:36,470
Really cool.

993
01:07:36,470 --> 01:07:42,320
And in order to have
redundant management--

994
01:07:42,320 --> 01:07:46,310
for example, if you only
have a single experiment,

995
01:07:46,310 --> 01:07:48,350
maybe one graduate
student is like, oh,

996
01:07:48,350 --> 01:07:50,810
doing dancing next
to a detector.

997
01:07:50,810 --> 01:07:53,030
Then you see some fake signal.

998
01:07:53,030 --> 01:07:55,610
And that's not
going to be helpful.

999
01:07:55,610 --> 01:07:58,400
So what it does is
that-- basically, we

1000
01:07:58,400 --> 01:07:59,760
have two experiments.

1001
01:07:59,760 --> 01:08:02,180
One is actually in Hanford.

1002
01:08:02,180 --> 01:08:04,520
The other one is
actually in Livingston.

1003
01:08:04,520 --> 01:08:08,990
And they are actually
3,000 kilometers away

1004
01:08:08,990 --> 01:08:10,190
from each other.

1005
01:08:10,190 --> 01:08:15,950
So that there should not be any
correlation between the signal

1006
01:08:15,950 --> 01:08:19,430
coming from a
earthquake or dancing

1007
01:08:19,430 --> 01:08:22,939
of the graduate
students or whatever.

1008
01:08:22,939 --> 01:08:29,330
So they can you use that to
suppress any coincidence which

1009
01:08:29,330 --> 01:08:34,080
is actually not related
to gravitational waves.

1010
01:08:34,080 --> 01:08:37,020
So what does this do?

1011
01:08:37,020 --> 01:08:39,500
So now, we have,
oh, the knowledge

1012
01:08:39,500 --> 01:08:41,270
to actually explain
this phenomena.

1013
01:08:41,270 --> 01:08:43,210
So what this does
is the following.

1014
01:08:43,210 --> 01:08:45,050
So you meet the laser.

1015
01:08:45,050 --> 01:08:49,460
And when the gravitational
waves come in,

1016
01:08:49,460 --> 01:08:53,060
then it does this
space-time distortion.

1017
01:08:53,060 --> 01:08:57,680
And then the
interference pattern

1018
01:08:57,680 --> 01:09:03,859
of the waves going through
different optical path lengths

1019
01:09:03,859 --> 01:09:07,470
is going to change.

1020
01:09:07,470 --> 01:09:09,760
So you can see that,
originally, the experiment

1021
01:09:09,760 --> 01:09:13,130
is designed so that you
have complete cancellation.

1022
01:09:13,130 --> 01:09:19,220
But when the gravitational
waves is hitting the side,

1023
01:09:19,220 --> 01:09:21,319
you will be able to see that.

1024
01:09:21,319 --> 01:09:27,130
Really, you have constructive
interference at some point,

1025
01:09:27,130 --> 01:09:31,220
because of the movement
of the mirrors.

1026
01:09:31,220 --> 01:09:35,090
And those mirrors are
really, really far away

1027
01:09:35,090 --> 01:09:36,270
from the sources.

1028
01:09:36,270 --> 01:09:40,010
Each of them is, like,
four kilometers away

1029
01:09:40,010 --> 01:09:42,050
from the mirror.

1030
01:09:42,050 --> 01:09:46,220
And due to the
incredible precision

1031
01:09:46,220 --> 01:09:48,979
which were achieved
by this experiment,

1032
01:09:48,979 --> 01:09:55,680
we will be able to detect this
signal of gravitational waves.

1033
01:09:55,680 --> 01:09:57,650
So you can see,
again, from here--

1034
01:09:57,650 --> 01:10:03,530
so basically, when the
gravitational wave comes in,

1035
01:10:03,530 --> 01:10:07,810
first you split the light
source into two pieces,

1036
01:10:07,810 --> 01:10:12,200
have them hit the mirror, which
is actually four kilometers far

1037
01:10:12,200 --> 01:10:13,280
away from each other.

1038
01:10:13,280 --> 01:10:15,000
And they come back.

1039
01:10:15,000 --> 01:10:20,540
And initially, the experiment
is designed so that, very

1040
01:10:20,540 --> 01:10:24,490
precisely, there
will be no amplitude

1041
01:10:24,490 --> 01:10:27,350
detected by the photo-detector.

1042
01:10:27,350 --> 01:10:30,810
And when the gravitational
waves come in,

1043
01:10:30,810 --> 01:10:35,390
you actually really
change the length

1044
01:10:35,390 --> 01:10:39,020
between a splitter
and the mirror.

1045
01:10:39,020 --> 01:10:46,290
Therefore, you see light,
constructive interference even,

1046
01:10:46,290 --> 01:10:49,440
from the photo-detector.

1047
01:10:49,440 --> 01:10:51,170
So that is really cool.

1048
01:10:51,170 --> 01:10:55,820
And this is actually
the experimental result.

1049
01:10:55,820 --> 01:10:58,600
Look at this.

1050
01:10:58,600 --> 01:11:02,360
You actually can see
that light actually

1051
01:11:02,360 --> 01:11:06,020
achieve the sensitivity.

1052
01:11:06,020 --> 01:11:14,690
The gravitational wave was first
observed on September 14, 2015.

1053
01:11:14,690 --> 01:11:20,530
And the LIGO is actually
announcing that February 11--

1054
01:11:20,530 --> 01:11:23,590
earlier this year.

1055
01:11:23,590 --> 01:11:27,070
And what we actually see from
here is that this is actually--

1056
01:11:27,070 --> 01:11:28,720
as I mentioned to you--

1057
01:11:28,720 --> 01:11:31,900
there are two
measurements, two sides.

1058
01:11:31,900 --> 01:11:36,760
The left hand side is actually
the measurement from Hanford.

1059
01:11:36,760 --> 01:11:40,240
And the other one is
actually the measurement

1060
01:11:40,240 --> 01:11:42,370
from Livingston.

1061
01:11:42,370 --> 01:11:44,620
So they are two
different curves.

1062
01:11:44,620 --> 01:11:51,820
And they all have almost
exactly the same pattern.

1063
01:11:51,820 --> 01:11:53,710
Of course, there's time
has actually shifted,

1064
01:11:53,710 --> 01:11:57,460
because they are in different
places on the earth.

1065
01:11:57,460 --> 01:11:59,920
They are 3,000 kilometers apart.

1066
01:11:59,920 --> 01:12:02,920
So therefore, there
will be a shift in time.

1067
01:12:02,920 --> 01:12:05,960
And this is actually
a time-shifted result.

1068
01:12:05,960 --> 01:12:09,280
And you can see, also,
the calculation below,

1069
01:12:09,280 --> 01:12:11,390
which is actually
what you should

1070
01:12:11,390 --> 01:12:20,000
expect if you have the merger
of the two massive black holes.

1071
01:12:20,000 --> 01:12:23,680
So you can see that they are
actually rotating with respect

1072
01:12:23,680 --> 01:12:26,230
to each other.

1073
01:12:26,230 --> 01:12:31,300
One of them is actually
29 times larger

1074
01:12:31,300 --> 01:12:33,450
than the mass of the sun.

1075
01:12:33,450 --> 01:12:37,210
And the other one
is 36 times larger

1076
01:12:37,210 --> 01:12:38,350
than the mass of our sun.

1077
01:12:38,350 --> 01:12:41,110
It's not precision.

1078
01:12:41,110 --> 01:12:44,740
And they generate,
theoretically,

1079
01:12:44,740 --> 01:12:47,270
this kind of pattern.

1080
01:12:47,270 --> 01:12:50,440
And this is actually
really detected

1081
01:12:50,440 --> 01:12:56,680
by both LIGO experiments, which
lay at 3,000 kilometers apart

1082
01:12:56,680 --> 01:12:58,790
from each other.

1083
01:12:58,790 --> 01:13:02,850
So I think this is really
a historical moment--

1084
01:13:02,850 --> 01:13:06,960
that we actually were very
lucky to live in this moment.

1085
01:13:06,960 --> 01:13:08,800
What does that mean?

1086
01:13:08,800 --> 01:13:16,300
That means we have a
new way to really hear

1087
01:13:16,300 --> 01:13:20,660
about what the universe is
actually trying to tell us.

1088
01:13:20,660 --> 01:13:24,470
We have a new way
to detect phenomena,

1089
01:13:24,470 --> 01:13:28,310
which is actually really
happening very, very far away

1090
01:13:28,310 --> 01:13:29,360
from the Earth.

1091
01:13:29,360 --> 01:13:31,700
How far is,
actually, this event?

1092
01:13:31,700 --> 01:13:34,655
This event, according
to calculation,

1093
01:13:34,655 --> 01:13:42,860
is actually something like
1.3 billion light years

1094
01:13:42,860 --> 01:13:44,890
away from the Earth.

1095
01:13:44,890 --> 01:13:46,670
And we can detect that.

1096
01:13:46,670 --> 01:13:51,061
And we even know the mass
of the two black holes.

1097
01:13:51,061 --> 01:13:51,560
Wow!

1098
01:13:51,560 --> 01:13:52,730
What does that mean?

1099
01:13:52,730 --> 01:13:56,870
This is really crazy to
me and really exciting,

1100
01:13:56,870 --> 01:13:58,760
because we are opening up--

1101
01:13:58,760 --> 01:13:59,930
OK, I have two ears.

1102
01:13:59,930 --> 01:14:04,470
And it's opening up
another ear in my brain.

1103
01:14:04,470 --> 01:14:09,980
And that is actually the way
to hear the gravitational wave

1104
01:14:09,980 --> 01:14:14,930
with the experiment
we've performed on Earth.

1105
01:14:14,930 --> 01:14:19,900
So I hope, until now,
I have convinced you

1106
01:14:19,900 --> 01:14:25,970
that this is really not the end
of vibration of waves, which

1107
01:14:25,970 --> 01:14:29,000
is actually the end of 8.03.

1108
01:14:29,000 --> 01:14:32,550
Instead, this is actually
just the beginning.

1109
01:14:32,550 --> 01:14:36,170
You have a lot more
to explore when

1110
01:14:36,170 --> 01:14:39,920
you take general or
special relativity course.

1111
01:14:39,920 --> 01:14:43,910
You have a lot, really,
more to explore when

1112
01:14:43,910 --> 01:14:46,700
you take quantum mechanics.

1113
01:14:46,700 --> 01:14:51,800
And I hope you really enjoy
the content of this course.

1114
01:14:51,800 --> 01:14:55,010
Personally, I really
enjoy that very much.

1115
01:14:55,010 --> 01:14:56,360
I love this course.

1116
01:14:56,360 --> 01:14:59,090
And I hope you also love
it and understand something

1117
01:14:59,090 --> 01:15:00,460
from my lecture.

1118
01:15:00,460 --> 01:15:02,750
And thank you very much.

1119
01:15:02,750 --> 01:15:04,760
And the next time,
we are going to have

1120
01:15:04,760 --> 01:15:09,190
a review of all concepts we have
learned from 8.03 next Tuesday.

1121
01:15:09,190 --> 01:15:09,790
Thank you.

1122
01:15:09,790 --> 01:15:11,290
[APPLAUSE]

1123
01:15:13,090 --> 01:15:15,240
Thank you very much.