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PROFESSOR: Hi.

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00:00:21,720 --> 00:00:24,970
Welcome too Excitatory
Topics in Physics.

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00:00:24,970 --> 00:00:26,860
The last two weeks,
I've talked to you

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00:00:26,860 --> 00:00:30,280
all about one of the two
major revolutions in physics

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00:00:30,280 --> 00:00:31,150
in the 20th century.

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00:00:31,150 --> 00:00:33,760
I talked about Einstein's
theory of relativity

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and all of the strange,
bizarre, wonderful consequences

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00:00:38,050 --> 00:00:40,750
that it has in
store for all of us.

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00:00:40,750 --> 00:00:48,130
Space and time are much weirder
than you might at first guess.

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00:00:48,130 --> 00:00:52,080
Time travel is possible
in some circumstances.

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00:00:52,080 --> 00:00:54,080
It's certainly possible
to travel to the future.

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00:00:54,080 --> 00:00:55,315
There's no debate about that.

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00:00:55,315 --> 00:00:57,440
Whether or not it's possible
to travel to the past,

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00:00:57,440 --> 00:00:59,130
it's more controversial.

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00:00:59,130 --> 00:01:05,060
But the window of time travel is
certainly opened by relativity.

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00:01:05,060 --> 00:01:07,150
Relativity, as I mentioned
in the first class,

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was made necessary
because there was

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this great dispute
between Newton's mechanics

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00:01:14,560 --> 00:01:16,660
and Maxwell's electromagnetism.

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00:01:16,660 --> 00:01:19,930
And Einstein's theory of special
relativity fixed all of that.

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00:01:19,930 --> 00:01:22,300
Well, quantum
mechanics, which was

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00:01:22,300 --> 00:01:27,370
the other achievement of 20th
century physics fixes a lot

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of other problems.

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00:01:28,750 --> 00:01:34,760
I mentioned and the first class
that quantum mechanics fixes

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00:01:34,760 --> 00:01:42,550
the so-called
ultraviolet catastrophe--

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00:01:42,550 --> 00:01:44,770
that was a chalk catastrophe--

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00:01:44,770 --> 00:01:46,789
ultraviolet catastrophe.

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00:01:51,680 --> 00:01:55,840
And this was simply
the fact that

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00:01:55,840 --> 00:01:58,030
with the current physics
at the time, the physics

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00:01:58,030 --> 00:02:01,510
that everybody had in
the year 1900 or so,

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00:02:01,510 --> 00:02:05,734
predicted that if you had an
object like a microwave, just

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00:02:05,734 --> 00:02:07,150
a simple way of
putting it, if you

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00:02:07,150 --> 00:02:09,672
had an object like a microwave,
the only way it can exist

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00:02:09,672 --> 00:02:11,380
is if there's an
infinite amount infinite

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00:02:11,380 --> 00:02:14,120
amount of energy inside of it.

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00:02:14,120 --> 00:02:19,030
And that's a problem
that he talked about.

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00:02:19,030 --> 00:02:21,905
And it was Max Planck who
came up with a solution

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00:02:21,905 --> 00:02:22,530
to the problem.

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00:02:28,180 --> 00:02:32,860
And what he did was he proposed
that the energy of light

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00:02:32,860 --> 00:02:39,670
comes in individual
chunks, discrete units.

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00:02:39,670 --> 00:02:42,580
And he came up with
the mathematical trick

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00:02:42,580 --> 00:02:44,590
basically of fixing
this problem.

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00:02:44,590 --> 00:02:47,690
I won't go into detail of
precisely how he fixed it.

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00:02:47,690 --> 00:02:52,750
But he fixed this problem to
get at the result we expected

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00:02:52,750 --> 00:02:56,290
to be true about microwave,
in particular that microwaves

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00:02:56,290 --> 00:02:58,480
contain a finite
amount of energy, which

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00:02:58,480 --> 00:03:01,480
is what you'd exactly expect.

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00:03:01,480 --> 00:03:05,650
And it was Einstein
later, a few years later

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00:03:05,650 --> 00:03:15,940
I think, who made the bold guess
that this mathematical trick

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00:03:15,940 --> 00:03:22,360
of Planck's is actually a
real physical actuality,

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00:03:22,360 --> 00:03:24,270
a physical reality.

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00:03:24,270 --> 00:03:27,420
And Einstein was
the one who came up

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with the idea of photons.

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Photons are these chunks,
these bits of lights.

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Light comes in particles,
which are called photons.

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And this idea of
the photon allowed

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Einstein to explain
another problem which

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was unexplainable by
classical physics.

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And this was the
problem called--

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well, it was an effect called
the photoelectric effect.

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And it turns out that if you've
got some metal, like a cell

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phone, and you shine
some light at it,

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it turns out that some
electrons at the surface of it

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actually get kicked
off by the light.

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The light actually
kicks off the electrons.

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And these electrons
just go flying away.

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That's called the
photoelectric effect.

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And according to the
physics at the time, if you

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use the physics to make
some predictions about what

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00:04:46,790 --> 00:04:50,390
you'd observe, you
get the wrong answer.

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According to the physics
at it at the time,

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if I shined a bright enough
light of any color at a metal,

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00:05:01,520 --> 00:05:05,210
then electrons
would be kicked off.

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00:05:05,210 --> 00:05:07,460
But that turned
out not to be true.

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It turned out that there was
a special frequency of light,

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below which shining light--

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well, if you had
light of a frequency

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below this certain
frequency, then

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no electrons would
get kicked off.

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00:05:24,830 --> 00:05:26,840
Just to remind you all
who might be unfamiliar

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00:05:26,840 --> 00:05:31,370
with the frequency or
wavelengths of light,

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00:05:31,370 --> 00:05:35,100
light comes in many wavelengths.

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Some of those wavelengths
are the colors that we see--

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00:05:39,380 --> 00:05:42,530
red, yellow, blue.

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00:05:42,530 --> 00:05:46,370
And some of those
wavelengths are other things

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00:05:46,370 --> 00:05:48,980
that we can't see, like
microwaves and x-rays and gamma

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00:05:48,980 --> 00:05:50,645
rays.

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00:05:50,645 --> 00:05:51,230
And For.

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00:05:51,230 --> 00:05:55,280
Each wavelength there's
also a frequency

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00:05:55,280 --> 00:05:57,612
associated with the wavelength.

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00:06:01,030 --> 00:06:06,710
You can think of a wave
of light like this.

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00:06:06,710 --> 00:06:10,160
And the wavelength
is the distance

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00:06:10,160 --> 00:06:11,600
between two crests of the wave.

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00:06:14,044 --> 00:06:14,960
So it's some distance.

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00:06:14,960 --> 00:06:15,959
It could be centimeters.

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00:06:15,959 --> 00:06:17,410
It could be nanometers.

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00:06:17,410 --> 00:06:18,800
It could be miles.

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00:06:18,800 --> 00:06:19,910
That's the wavelength.

106
00:06:19,910 --> 00:06:27,740
And the frequency is how
many times in 1 second

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00:06:27,740 --> 00:06:29,140
you get a wavelength.

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00:06:29,140 --> 00:06:31,990
So how many times in 1
second you get a wavelength.

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00:06:31,990 --> 00:06:34,790
Well, I need to be more precise
about what I mean by that.

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00:06:34,790 --> 00:06:41,870
Well, so you can think of
some traveling wave moving

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00:06:41,870 --> 00:06:45,060
and you count how many times
a crest passes you in 1 second

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00:06:45,060 --> 00:06:48,140
and that's the frequency.

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00:06:48,140 --> 00:06:49,280
That's the frequency.

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00:06:49,280 --> 00:06:54,970
And so light comes in many
frequencies, which each have

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00:06:54,970 --> 00:06:56,440
their own wavelengths.

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00:06:56,440 --> 00:06:59,290
Just some background info.

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00:06:59,290 --> 00:07:03,850
Now this photoelectric
effect turned out

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00:07:03,850 --> 00:07:10,430
to be the case that's shining
light below a certain frequency

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00:07:10,430 --> 00:07:12,972
would result in no
electrons being kicked off.

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00:07:12,972 --> 00:07:14,680
But if you got above
that frequency, then

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00:07:14,680 --> 00:07:16,030
electrons would be kicked off.

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00:07:16,030 --> 00:07:19,420
And that was contrary to what
the current physics predicted.

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00:07:19,420 --> 00:07:22,300
It was contrary to
what's the idea of light

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00:07:22,300 --> 00:07:24,070
being a wave predicted.

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00:07:24,070 --> 00:07:25,834
So this was a big
blow to many people

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00:07:25,834 --> 00:07:27,250
who thought that
light was a wave.

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00:07:31,840 --> 00:07:43,040
So I'll just right down it was
contrary to wave predictions,

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00:07:43,040 --> 00:07:51,969
and it supported
particle predictions.

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00:07:51,969 --> 00:07:53,510
And I'll be more
precise what I mean.

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00:08:09,840 --> 00:08:15,430
Now for a long time,
up to the 20th century,

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00:08:15,430 --> 00:08:18,900
there was a lot of
debate among physicists

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00:08:18,900 --> 00:08:21,600
over whether a light
was a wave or particle.

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00:08:21,600 --> 00:08:23,590
You've probably heard
about this debate.

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00:08:23,590 --> 00:08:27,780
Newton always thought
that light was a particle.

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00:08:27,780 --> 00:08:31,050
And he had lots of
interesting reasoning

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00:08:31,050 --> 00:08:34,770
for why that should be the case.

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00:08:34,770 --> 00:08:37,450
This photoelectric
effect was also support

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00:08:37,450 --> 00:08:39,909
for light being a particle.

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00:08:39,909 --> 00:08:43,539
According to the particle
theory, particles of light

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00:08:43,539 --> 00:08:49,070
would simply come and
kick off electrons.

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00:08:49,070 --> 00:08:58,300
And that's not what you'd
get if light were a wave.

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00:09:01,460 --> 00:09:05,770
If light were a wave,
you'd be able to kick off

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00:09:05,770 --> 00:09:08,310
electrons with any frequency.

144
00:09:08,310 --> 00:09:14,920
But you get the wrong answer.

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00:09:14,920 --> 00:09:17,530
I don't want to go into
too much detail about this

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00:09:17,530 --> 00:09:21,190
because I really want to get
to the main features of quantum

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00:09:21,190 --> 00:09:21,690
mechanics.

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00:09:21,690 --> 00:09:23,610
This is just some
history, some history

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00:09:23,610 --> 00:09:26,050
that is necessary to
really appreciate it.

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00:09:28,670 --> 00:09:32,350
So the photoelectric effect was
more support for the particle

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00:09:32,350 --> 00:09:36,610
theory of light.

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00:09:36,610 --> 00:09:39,580
But as I mentioned, there
are many people that

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00:09:39,580 --> 00:09:41,270
believe that light was a wave.

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00:09:41,270 --> 00:09:43,940
And, well, why do they
believe the light was a wave?

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00:09:43,940 --> 00:09:46,120
Well, there were
some experiments

156
00:09:46,120 --> 00:09:48,654
that showed that light
was a wave, just like this

157
00:09:48,654 --> 00:09:49,945
shows that light is a particle.

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00:09:53,210 --> 00:09:58,670
And probably the most important
of all of these experiments

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00:09:58,670 --> 00:10:01,651
is the so-called
double slit experiment.

160
00:10:04,420 --> 00:10:11,830
So for instance, I can imagine
putting some screen in front

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00:10:11,830 --> 00:10:13,750
of me with a couple of slits.

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00:10:17,800 --> 00:10:18,895
That was three slits.

163
00:10:18,895 --> 00:10:20,020
I'm going to put two slits.

164
00:10:23,260 --> 00:10:26,959
No, that's-- how do
you draw two slits?

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00:10:26,959 --> 00:10:27,750
AUDIENCE: One line.

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00:10:27,750 --> 00:10:30,700
PROFESSOR: One line, yeah.

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00:10:30,700 --> 00:10:32,120
There you go.

168
00:10:32,120 --> 00:10:33,730
Those are two slits.

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00:10:33,730 --> 00:10:37,067
So let's say I've got this
screen in front of me.

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00:10:37,067 --> 00:10:37,900
There are two slits.

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00:10:37,900 --> 00:10:38,740
One's right here.

172
00:10:38,740 --> 00:10:40,510
The other one's right there.

173
00:10:40,510 --> 00:10:42,980
And I'm behind it.

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00:10:42,980 --> 00:10:46,000
And I shine some light
through those slits.

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00:10:46,000 --> 00:10:49,340
So they're going to
go through the slits.

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00:10:49,340 --> 00:10:52,769
Those beams of light that
I sent through the slits,

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00:10:52,769 --> 00:10:54,310
they're going to go
through the slits

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00:10:54,310 --> 00:10:57,550
and they're going to
reach the wall over there.

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00:10:57,550 --> 00:10:59,050
So I'll draw the wall over here.

180
00:11:02,590 --> 00:11:06,210
OK, that's the wall.

181
00:11:06,210 --> 00:11:13,210
And if you actually
do this experiment,

182
00:11:13,210 --> 00:11:17,380
and you make these
slits a suitable size,

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00:11:17,380 --> 00:11:20,140
you can observe what's called
an interference pattern

184
00:11:20,140 --> 00:11:23,650
on the wall, on this screen.

185
00:11:23,650 --> 00:11:27,430
And here's what I mean by
the interference pattern.

186
00:11:27,430 --> 00:11:30,220
So I've got one hole here.

187
00:11:30,220 --> 00:11:33,620
Let's see, I'll
make a little line.

188
00:11:33,620 --> 00:11:36,800
I'll call this A. I've
got another hole here,

189
00:11:36,800 --> 00:11:44,115
which corresponds to a
point B on the wall--

190
00:11:44,115 --> 00:11:46,860
that looks like a beta--

191
00:11:46,860 --> 00:11:48,180
point B on the wall.

192
00:11:48,180 --> 00:11:52,020
And I can look at what I see.

193
00:11:52,020 --> 00:11:55,080
I can look at the brightness
of the lights on the wall.

194
00:11:55,080 --> 00:11:57,940
And I can plot the
brightness on a graph.

195
00:12:01,170 --> 00:12:15,870
So if I put brightness here and,
well, this would be a position,

196
00:12:15,870 --> 00:12:23,120
let's say that this corresponds
to B. This corresponds to A.

197
00:12:23,120 --> 00:12:25,840
Then what I see is this.

198
00:12:31,581 --> 00:12:32,330
Also on this side.

199
00:12:39,669 --> 00:12:40,710
That's simply what I see.

200
00:12:45,440 --> 00:12:47,110
OK, that looks OK.

201
00:12:47,110 --> 00:12:48,180
That's simply what I see.

202
00:12:48,180 --> 00:12:49,290
And to understand this--

203
00:12:52,830 --> 00:12:56,320
you can understand this simply
by thinking of water waves.

204
00:12:59,347 --> 00:13:01,680
If I were to do this experiment
with water waves instead

205
00:13:01,680 --> 00:13:06,660
of light waves, then you can
think of the ripples making

206
00:13:06,660 --> 00:13:07,850
a pattern like this.

207
00:13:11,420 --> 00:13:17,820
So let's say I've got a
bunch of water waves coming

208
00:13:17,820 --> 00:13:20,240
from this way.

209
00:13:20,240 --> 00:13:22,850
What I see as they
emerge from the slit?

210
00:13:22,850 --> 00:13:25,190
Well, I would see
patterns like this.

211
00:13:28,790 --> 00:13:31,660
I would see these
circular patterns.

212
00:13:31,660 --> 00:13:34,210
Well, if I put two slits
next to each other--

213
00:13:40,700 --> 00:13:43,150
there you go-- I put two
slits next to each other,

214
00:13:43,150 --> 00:13:49,220
then you add up two
water waves, you add up

215
00:13:49,220 --> 00:13:59,390
these two sets of ripples, and
you get an interesting pattern.

216
00:13:59,390 --> 00:14:01,040
It's kind of hard
to draw, but I'm

217
00:14:01,040 --> 00:14:03,800
sure you've all seen this
in some way in a pond

218
00:14:03,800 --> 00:14:05,420
or something.

219
00:14:05,420 --> 00:14:09,830
You see certain points
which look like they're

220
00:14:09,830 --> 00:14:10,700
higher than others.

221
00:14:10,700 --> 00:14:13,209
You see some certain
points in the water which

222
00:14:13,209 --> 00:14:15,500
have maximum heights, certain
points in the water which

223
00:14:15,500 --> 00:14:16,820
have a minimum height.

224
00:14:20,330 --> 00:14:27,770
And if you were to ask, what
do the ripples look like over

225
00:14:27,770 --> 00:14:33,560
here, then the heights would
look something like this.

226
00:14:33,560 --> 00:14:41,990
I know I know it's kind
of confusing to visualize,

227
00:14:41,990 --> 00:14:44,120
but you can imagine adding
up ripples and getting

228
00:14:44,120 --> 00:14:47,560
some interesting
pattern at the end.

229
00:14:47,560 --> 00:14:51,080
I meant to bring a
cartoon showing this.

230
00:14:51,080 --> 00:14:54,050
But I'll send it to you
all so you can better

231
00:14:54,050 --> 00:14:55,550
see how this works.

232
00:14:58,690 --> 00:15:00,740
But this is a wave for now.

233
00:15:00,740 --> 00:15:02,900
You have water waves.

234
00:15:02,900 --> 00:15:05,010
You have these ripples
that move in waves.

235
00:15:05,010 --> 00:15:08,000
And if you allow them
to go through slits,

236
00:15:08,000 --> 00:15:11,850
you see something
that looks like that.

237
00:15:11,850 --> 00:15:19,130
And, well, if light
were a wave, you'd

238
00:15:19,130 --> 00:15:20,870
also expect to see
something like this.

239
00:15:20,870 --> 00:15:23,910
And this is precisely what you
get when you do the experiment.

240
00:15:23,910 --> 00:15:26,930
You can actually do
the experiment making

241
00:15:26,930 --> 00:15:28,070
this interference pattern.

242
00:15:28,070 --> 00:15:29,528
It's called an
interference pattern

243
00:15:29,528 --> 00:15:31,760
because these waves
interfere with each other.

244
00:15:31,760 --> 00:15:34,700
You get constructive
interference

245
00:15:34,700 --> 00:15:38,030
when the crests add up each
add up with each other.

246
00:15:38,030 --> 00:15:39,680
And you get destructive
interference

247
00:15:39,680 --> 00:15:44,330
when a crest adds with a
trough and the two cancel out.

248
00:15:44,330 --> 00:15:46,130
That's how you get an
interference pattern.

249
00:15:46,130 --> 00:15:47,463
That's how you get this pattern.

250
00:15:50,410 --> 00:15:52,530
This pattern is
not what you would

251
00:15:52,530 --> 00:15:56,860
expect to get if light
were made up of particles.

252
00:15:56,860 --> 00:15:59,220
If light were made
up of particles,

253
00:15:59,220 --> 00:16:01,352
you'd expect to get
something much different.

254
00:16:12,440 --> 00:16:16,750
So let's draw another couple
of slits with the screen.

255
00:16:19,760 --> 00:16:21,510
Why can't I draw this?

256
00:16:21,510 --> 00:16:22,499
What's that?

257
00:16:22,499 --> 00:16:23,824
AUDIENCE: It's right.

258
00:16:23,824 --> 00:16:25,990
PROFESSOR: No, I was about
to extend it all the way.

259
00:16:25,990 --> 00:16:29,120
That was going to be one slit.

260
00:16:29,120 --> 00:16:29,620
OK.

261
00:16:29,620 --> 00:16:32,110
And I have a screen here.

262
00:16:32,110 --> 00:16:35,320
Imagine that I'm sitting
on the other end of here,

263
00:16:35,320 --> 00:16:36,160
like I'm right here.

264
00:16:36,160 --> 00:16:37,540
Imagine I'm right here.

265
00:16:37,540 --> 00:16:45,220
And I'm simply throwing
things, like chalks.

266
00:16:45,220 --> 00:16:50,060
Or I'm shooting bullets
through these slits.

267
00:16:50,060 --> 00:16:53,260
I could be shooting bullets
through these slits.

268
00:16:53,260 --> 00:16:56,860
If I were to do
that, then what would

269
00:16:56,860 --> 00:17:00,694
you expect to see on the screen?

270
00:17:00,694 --> 00:17:01,360
AUDIENCE: Holes.

271
00:17:01,360 --> 00:17:02,370
PROFESSOR: Suppose--
what's that?

272
00:17:02,370 --> 00:17:03,590
You expect to see bullets.

273
00:17:03,590 --> 00:17:04,089
Holes?

274
00:17:04,089 --> 00:17:05,079
OK, holes.

275
00:17:05,079 --> 00:17:06,099
OK, good answer.

276
00:17:06,099 --> 00:17:07,859
Good answer.

277
00:17:07,859 --> 00:17:12,790
OK, suppose the screen
were magnetic and attracted

278
00:17:12,790 --> 00:17:16,000
the bullets once they
reach the screen,

279
00:17:16,000 --> 00:17:18,587
so that when the
bullets arrive at--

280
00:17:18,587 --> 00:17:20,170
sorry, when the
bullets hit the wall--

281
00:17:20,170 --> 00:17:23,440
when the bullets arrive at the
wall, then they would stick.

282
00:17:23,440 --> 00:17:26,694
And then they would
line up on each other.

283
00:17:26,694 --> 00:17:27,819
They line up on each other.

284
00:17:27,819 --> 00:17:29,760
They would pile up,
getting higher and higher.

285
00:17:29,760 --> 00:17:31,870
But really, they'd be
coming out this way.

286
00:17:31,870 --> 00:17:35,375
I mean, they're not
going to fall down.

287
00:17:35,375 --> 00:17:35,875
What's that?

288
00:17:35,875 --> 00:17:37,090
AUDIENCE: Have to
be a strong magnet.

289
00:17:37,090 --> 00:17:39,589
PROFESSOR: Yeah, it would have
to be a pretty strong magnet,

290
00:17:39,589 --> 00:17:40,332
yeah.

291
00:17:40,332 --> 00:17:42,540
But suppose you did that,
suppose you did it somehow.

292
00:17:45,980 --> 00:17:49,610
Then it's pretty clear
what you expect to see.

293
00:17:49,610 --> 00:17:50,485
So you shoot bullets.

294
00:17:53,580 --> 00:17:54,500
I'll just draw them.

295
00:17:54,500 --> 00:17:58,130
Suppose you have bullets.

296
00:17:58,130 --> 00:17:59,900
These are what
bullets look like.

297
00:18:05,865 --> 00:18:07,240
Those are what
bullets look like.

298
00:18:07,240 --> 00:18:11,310
They go through this.

299
00:18:11,310 --> 00:18:15,990
Eventually they reach the wall.

300
00:18:15,990 --> 00:18:21,120
So if I were to draw,
let's say, number

301
00:18:21,120 --> 00:18:28,660
of bullets as the height,
and position here--

302
00:18:32,630 --> 00:18:35,760
let's say this is
A and this is B--

303
00:18:41,310 --> 00:18:45,030
well, then I expect there to be
a big pile over both A and B.

304
00:18:45,030 --> 00:18:48,630
They just fall down on top
of each other like this.

305
00:18:53,670 --> 00:18:55,170
Yeah, something like that.

306
00:18:55,170 --> 00:18:58,830
I mean I wouldn't expect to
see all these extra humps.

307
00:18:58,830 --> 00:19:02,400
I mean, what's with that?

308
00:19:02,400 --> 00:19:05,730
Why should that happen?

309
00:19:05,730 --> 00:19:09,720
So this is what I
expect to see bullets.

310
00:19:09,720 --> 00:19:12,090
And so this is what I
expect to see for particles.

311
00:19:12,090 --> 00:19:15,040
I'd expect to see them all just
falling on top of each other,

312
00:19:15,040 --> 00:19:18,820
creating piles like this.

313
00:19:18,820 --> 00:19:22,680
Well, if light were a particle,
then, yeah, we should see that.

314
00:19:22,680 --> 00:19:26,030
But that's not what we see.

315
00:19:26,030 --> 00:19:27,960
We see this.

316
00:19:27,960 --> 00:19:29,870
So light's a wave.

317
00:19:33,590 --> 00:19:43,270
Well, how could light be a
wave if it also acts in ways

318
00:19:43,270 --> 00:19:45,750
that particles act?

319
00:19:45,750 --> 00:19:48,820
If acts in ways
that are consistent

320
00:19:48,820 --> 00:19:52,074
with the photoelectric effect
and some other effects?

321
00:19:52,074 --> 00:19:53,740
I mean, there are
some other experiments

322
00:19:53,740 --> 00:19:57,520
that you can do where
you take an electron

323
00:19:57,520 --> 00:19:59,500
and you shine light at it.

324
00:19:59,500 --> 00:20:05,020
And the electron
moves in such a way

325
00:20:05,020 --> 00:20:07,110
as if it were hit
by a billiard ball.

326
00:20:07,110 --> 00:20:11,751
It moves in such a way that
indicative of a particle

327
00:20:11,751 --> 00:20:12,250
hitting it.

328
00:20:12,250 --> 00:20:15,250
It moves in such a way
that's indicative of light

329
00:20:15,250 --> 00:20:17,990
being made up of particles.

330
00:20:17,990 --> 00:20:23,499
So how could light be
both wave and a particle?

331
00:20:23,499 --> 00:20:24,040
Is that true?

332
00:20:24,040 --> 00:20:26,467
Is light both a
wave and a particle?

333
00:20:26,467 --> 00:20:27,550
Or is it one or the other?

334
00:20:27,550 --> 00:20:29,120
Is it a wave or
is it a particle?

335
00:20:31,524 --> 00:20:32,940
This is something
that people have

336
00:20:32,940 --> 00:20:36,930
thought about for a long
time, for hundreds of years,

337
00:20:36,930 --> 00:20:41,090
until finally quantum mechanics
answered the question.

338
00:20:41,090 --> 00:20:43,680
Finally, quantum mechanics
answered the question.

339
00:20:43,680 --> 00:20:47,230
According to quantum
mechanics light is neither

340
00:20:47,230 --> 00:20:49,200
a wave nor a particle.

341
00:20:49,200 --> 00:20:52,340
It's just this thing.

342
00:20:52,340 --> 00:20:57,900
It's just this thing that
behaves in some ways that

343
00:20:57,900 --> 00:21:00,240
one associates
with wave behavior,

344
00:21:00,240 --> 00:21:04,830
and it behaves in other
ways that one associates

345
00:21:04,830 --> 00:21:07,060
with particle behavior.

346
00:21:07,060 --> 00:21:08,640
So light's just
this weird thing.

347
00:21:15,142 --> 00:21:20,570
But electrons, electrons are
certainly particles, right?

348
00:21:20,570 --> 00:21:21,640
Right?

349
00:21:21,640 --> 00:21:22,500
AUDIENCE: Right.

350
00:21:22,500 --> 00:21:23,910
PROFESSOR: No, they're not.

351
00:21:23,910 --> 00:21:25,830
According to quantum
mechanics electrons

352
00:21:25,830 --> 00:21:30,090
are just these things in
some ways act particles

353
00:21:30,090 --> 00:21:32,160
and in other ways act as waves.

354
00:21:32,160 --> 00:21:40,900
I can do this
experiment with bullets.

355
00:21:40,900 --> 00:21:43,630
And if I make the slits
of a certain width,

356
00:21:43,630 --> 00:21:45,640
I'd see exactly that.

357
00:21:45,640 --> 00:21:48,400
I can do this experiment
with-- one second--

358
00:21:48,400 --> 00:21:50,770
I can do this experiment
with electrons.

359
00:21:50,770 --> 00:21:53,260
And if I make these
widths a certain length,

360
00:21:53,260 --> 00:21:55,840
if I make the widths of
these slits a certain length,

361
00:21:55,840 --> 00:21:57,710
then I'd see exactly that.

362
00:21:57,710 --> 00:22:00,440
I'd see the electrons
piling up on each other.

363
00:22:00,440 --> 00:22:04,510
But if I make these
widths narrower,

364
00:22:04,510 --> 00:22:08,350
if I make these with smaller,
then I no longer see this.

365
00:22:08,350 --> 00:22:10,630
I no longer see what you'd
expect with the particle

366
00:22:10,630 --> 00:22:11,470
theory.

367
00:22:11,470 --> 00:22:16,420
Now, when I actually do the
experiments, I see this.

368
00:22:16,420 --> 00:22:18,190
So now electrons
have become waves.

369
00:22:21,250 --> 00:22:23,400
I'm not making this up.

370
00:22:23,400 --> 00:22:25,005
You can actually
do this experiment.

371
00:22:25,005 --> 00:22:27,130
You know, shoot electrons
through a couple of slits

372
00:22:27,130 --> 00:22:28,130
and see what happens.

373
00:22:28,130 --> 00:22:31,120
Look at them in front of you.

374
00:22:31,120 --> 00:22:39,934
Look at the intensity of
these electrons, the intensity

375
00:22:39,934 --> 00:22:41,350
pattern that these
electrons make.

376
00:22:41,350 --> 00:22:45,190
Look at them on the
wall and you see that.

377
00:22:45,190 --> 00:22:48,940
You can also do this
experiment with protons.

378
00:22:48,940 --> 00:22:53,770
And if you make the
slits a certain width,

379
00:22:53,770 --> 00:22:54,880
then you see that.

380
00:22:54,880 --> 00:22:59,620
But if you make them
smaller, then you see that.

381
00:22:59,620 --> 00:23:03,170
You can also do this experiment
with larger molecules.

382
00:23:03,170 --> 00:23:06,220
And if you make the widths a
certain length, you see that.

383
00:23:06,220 --> 00:23:10,420
And you make them
smaller, and you see that.

384
00:23:10,420 --> 00:23:14,157
In fact, people have done this
experiments with molecules--

385
00:23:14,157 --> 00:23:16,490
I don't know if you should
even call them molecules now.

386
00:23:16,490 --> 00:23:18,430
But they've actually
done it with viruses.

387
00:23:18,430 --> 00:23:23,770
They've done it with viruses
and they don't see that.

388
00:23:23,770 --> 00:23:27,274
Well, you would see that if you
made the slits narrow enough.

389
00:23:27,274 --> 00:23:28,690
But they've made
them small enough

390
00:23:28,690 --> 00:23:30,130
so that you actually see this.

391
00:23:30,130 --> 00:23:36,050
You actually see the
wave nature of viruses.

392
00:23:36,050 --> 00:23:45,250
So if viruses can also
have a wave nature then,

393
00:23:45,250 --> 00:23:50,320
what about larger things
like chairs or people?

394
00:23:55,190 --> 00:23:56,170
What's that?

395
00:23:56,170 --> 00:23:56,670
Question?

396
00:23:56,670 --> 00:23:58,450
AUDIENCE: Slits?

397
00:23:58,450 --> 00:24:04,540
PROFESSOR: Well, in principle,
you can arrange an experiment

398
00:24:04,540 --> 00:24:07,960
where you see an interference
pattern like this with people,

399
00:24:07,960 --> 00:24:09,790
but no one's ever done that yet.

400
00:24:09,790 --> 00:24:11,640
But if you were to
do that, then what

401
00:24:11,640 --> 00:24:13,420
would actually go
through your mind?

402
00:24:13,420 --> 00:24:22,750
Because you can send through
individual particles,

403
00:24:22,750 --> 00:24:27,260
and the individual particles
will interfere with themselves.

404
00:24:27,260 --> 00:24:30,340
And so if you sent
yourself, then what would

405
00:24:30,340 --> 00:24:33,790
it feel like to
interfere with yourself?

406
00:24:33,790 --> 00:24:37,520
And this is maybe more a topic
of philosophy than physics,

407
00:24:37,520 --> 00:24:40,120
so I'll just let
you ponder that.

408
00:24:40,120 --> 00:24:40,740
Question?

409
00:24:40,740 --> 00:24:42,490
AUDIENCE: So that's
the brilliant solution

410
00:24:42,490 --> 00:24:44,600
of quantum mechanics,
they just call everything

411
00:24:44,600 --> 00:24:46,320
that can't understood things?

412
00:24:46,320 --> 00:24:49,114
PROFESSOR: OK, the question was
that's the brilliant solution

413
00:24:49,114 --> 00:24:50,530
of quantum mechanics,
we just call

414
00:24:50,530 --> 00:24:52,321
everything that can't
be understood things?

415
00:24:52,321 --> 00:24:53,766
No, we can understand them.

416
00:24:53,766 --> 00:24:55,890
We just have to come up
with better names for them.

417
00:24:55,890 --> 00:24:58,530
Particle is a bad
name for things--

418
00:24:58,530 --> 00:25:02,352
a particle is a
bad name for light.

419
00:25:02,352 --> 00:25:03,560
Wave is a bad name for light.

420
00:25:03,560 --> 00:25:06,356
AUDIENCE: But you use particle
as a bad name for everything

421
00:25:06,356 --> 00:25:08,686
because it doesn't
behave like a particle

422
00:25:08,686 --> 00:25:10,893
when it passes
through small slits.

423
00:25:10,893 --> 00:25:13,126
So they just call
everything-- they basically

424
00:25:13,126 --> 00:25:14,515
took particles away.

425
00:25:14,515 --> 00:25:16,999
And just called
everything weird things.

426
00:25:16,999 --> 00:25:18,040
PROFESSOR: In a way, yes.

427
00:25:18,040 --> 00:25:19,620
In a way, yes.

428
00:25:19,620 --> 00:25:21,646
They took away the title
of particle and wave,

429
00:25:21,646 --> 00:25:23,395
and they just started
to call them things.

430
00:25:27,480 --> 00:25:30,639
In practice, physicists actually
do call electrons still--

431
00:25:30,639 --> 00:25:31,930
they still call them particles.

432
00:25:31,930 --> 00:25:36,550
But we realize they don't
behave as ideal particles

433
00:25:36,550 --> 00:25:37,900
in every way.

434
00:25:37,900 --> 00:25:40,120
Under some
circumstances, electrons

435
00:25:40,120 --> 00:25:41,270
behave like particles.

436
00:25:41,270 --> 00:25:43,555
Under other circumstances,
they behave like waves.

437
00:25:43,555 --> 00:25:45,430
And that's the same for
every other type of--

438
00:25:45,430 --> 00:25:48,390
AUDIENCE: So there are no
particles because nothing

439
00:25:48,390 --> 00:25:49,600
behaves as a particle.

440
00:25:49,600 --> 00:25:52,510
PROFESSOR: There are no ideal
particles, yeah, that's true.

441
00:25:52,510 --> 00:25:55,330
And that's something
that quantum mechanics

442
00:25:55,330 --> 00:25:58,510
has forced us to accept,
as strange as it may seem.

443
00:25:58,510 --> 00:26:02,650
This is the so-called
wave particle duality

444
00:26:02,650 --> 00:26:05,320
of not only light
but also of electrons

445
00:26:05,320 --> 00:26:08,030
and neutrons and people.

446
00:26:13,954 --> 00:26:14,620
So this is the--

447
00:26:18,050 --> 00:26:19,570
well, I'll just write it--

448
00:26:29,262 --> 00:26:31,735
this is the very confusing
wave particle duality.

449
00:26:45,600 --> 00:26:48,180
The dual nature of
light, particle and wave,

450
00:26:48,180 --> 00:26:52,430
the dual nature of electrons,
the dual nature of people.

451
00:26:52,430 --> 00:26:52,930
Question?

452
00:26:52,930 --> 00:26:55,000
AUDIENCE: But people jump
through holes in walls

453
00:26:55,000 --> 00:27:00,110
all the time, but they
don't move like a wave.

454
00:27:00,110 --> 00:27:03,160
What speed do you have to-- do
you have to be traveling fast?

455
00:27:03,160 --> 00:27:11,980
PROFESSOR: OK, the
question is how can we

456
00:27:11,980 --> 00:27:13,930
arrange circumstances
such that we

457
00:27:13,930 --> 00:27:18,850
can observe the wave properties
of people or electrons

458
00:27:18,850 --> 00:27:20,090
or things like that?

459
00:27:20,090 --> 00:27:27,650
Well, there's this number
called de Broglie wavelength.

460
00:27:27,650 --> 00:27:29,250
Well, I'll just tell you.

461
00:27:29,250 --> 00:27:32,170
There's this length called
the de Broglie wavelength.

462
00:27:32,170 --> 00:27:35,130
And any object in motion
has a de Broglie wavelength.

463
00:27:37,660 --> 00:27:41,470
It's some constant divided by
your mass divided your speed.

464
00:27:41,470 --> 00:27:45,117
That's your wavelength.

465
00:27:45,117 --> 00:27:46,450
You could calculate this number.

466
00:27:46,450 --> 00:27:48,699
And it turns out to be an
extraordinarily small number

467
00:27:48,699 --> 00:27:50,690
for people, people just
moving very slightly.

468
00:27:50,690 --> 00:27:53,290
It turns out to be an
extraordinary small number.

469
00:27:53,290 --> 00:27:56,380
Well, it turns out that if you
make those slits approximately

470
00:27:56,380 --> 00:27:58,780
the size of the de
Broglie wavelength,

471
00:27:58,780 --> 00:28:03,475
then you would observe
your wave nature.

472
00:28:03,475 --> 00:28:05,089
AUDIENCE: So if you
made small enough,

473
00:28:05,089 --> 00:28:07,360
you wouldn't be able
to pass through.

474
00:28:07,360 --> 00:28:10,030
PROFESSOR: Well, if you
make it small enough,

475
00:28:10,030 --> 00:28:15,070
then there's really a
subtle interpretation

476
00:28:15,070 --> 00:28:19,000
of how we understand
the word "you."

477
00:28:19,000 --> 00:28:21,310
It becomes confusing
to think about you.

478
00:28:30,060 --> 00:28:32,210
I understand this
is confusing stuff.

479
00:28:32,210 --> 00:28:37,210
And it's probably
different from things

480
00:28:37,210 --> 00:28:39,310
you've thought about before.

481
00:28:39,310 --> 00:28:41,980
Time travel is
confusing as you saw.

482
00:28:41,980 --> 00:28:43,360
Well, this is quantum mechanics.

483
00:28:43,360 --> 00:28:46,210
And it's confusing
in its own ways,

484
00:28:46,210 --> 00:28:51,610
because it really asks
us to rethink about--

485
00:28:51,610 --> 00:28:53,440
well, we think about
the nature of reality

486
00:28:53,440 --> 00:28:56,200
in ways that
relativity forced us to

487
00:28:56,200 --> 00:28:59,020
but in different ways,
perhaps more difficult ways.

488
00:29:02,620 --> 00:29:07,480
So I said that's
quantum mechanics

489
00:29:07,480 --> 00:29:11,037
resolves this question, is
light a particle or a wave?

490
00:29:11,037 --> 00:29:12,370
Are electrons particles or wave?

491
00:29:12,370 --> 00:29:13,536
Well, the answer is neither.

492
00:29:13,536 --> 00:29:14,530
They're things.

493
00:29:14,530 --> 00:29:18,250
But what specifically does
quantum mechanics say?

494
00:29:18,250 --> 00:29:21,100
What explicitly does it say?

495
00:29:21,100 --> 00:29:37,210
Well, in classical physics, the
way that we think about objects

496
00:29:37,210 --> 00:29:41,947
is you have an object
in front of you.

497
00:29:41,947 --> 00:29:44,530
You have an object in front of
you, and I can say where it is.

498
00:29:44,530 --> 00:29:47,690
I can say how fast it's moving.

499
00:29:47,690 --> 00:29:48,680
And that's it.

500
00:29:48,680 --> 00:29:52,190
That's a complete and
sufficient description

501
00:29:52,190 --> 00:29:55,455
of the states of the object.

502
00:29:55,455 --> 00:29:56,830
Of course, you
can ask what is it

503
00:29:56,830 --> 00:30:02,180
made of, what are the objects
made of, and how hard is it.

504
00:30:02,180 --> 00:30:04,200
You can also ask
questions like that.

505
00:30:04,200 --> 00:30:07,220
But in classical physics,
it's easy to talk

506
00:30:07,220 --> 00:30:11,900
about the state of an object.

507
00:30:11,900 --> 00:30:15,340
It's easy to talk about
its position and its speed.

508
00:30:15,340 --> 00:30:24,754
So classical states
of an object is simply

509
00:30:24,754 --> 00:30:25,670
the object's position.

510
00:30:36,370 --> 00:30:37,376
and it's speed.

511
00:30:37,376 --> 00:30:39,520
That's all there is to it.

512
00:30:39,520 --> 00:30:44,860
Well, in quantum
mechanics, the whole notion

513
00:30:44,860 --> 00:30:51,290
of position and speed are
undefined for a particle--

514
00:30:51,290 --> 00:30:54,390
well, are undefined-- I'll
simply use the word particle

515
00:30:54,390 --> 00:30:56,470
when I mean electron
or when I mean

516
00:30:56,470 --> 00:30:59,530
photon or something like that.

517
00:30:59,530 --> 00:31:03,550
The whole notion of a position
and a speed for a particle

518
00:31:03,550 --> 00:31:09,400
are undefined until you try to
measure the object's position,

519
00:31:09,400 --> 00:31:12,630
until you try to measure
the object's speed.

520
00:31:12,630 --> 00:31:19,060
It doesn't make any sense to
talk about where something is

521
00:31:19,060 --> 00:31:21,040
until you make a measurement.

522
00:31:21,040 --> 00:31:25,880
And until you make
a measurement,

523
00:31:25,880 --> 00:31:30,100
the object is in a mixture
of many possible places.

524
00:31:30,100 --> 00:31:33,480
It's in a mixture of
many possible speeds.

525
00:31:33,480 --> 00:31:36,640
It's in, in the language
of quantum mechanics,

526
00:31:36,640 --> 00:31:40,930
a superposition of
many possible states.

527
00:31:40,930 --> 00:31:42,670
And that sounds crazy.

528
00:31:42,670 --> 00:31:46,026
So I'll just write down
what I mean before I talk

529
00:31:46,026 --> 00:31:47,150
a little bit more about it.

530
00:31:47,150 --> 00:31:58,350
Now, quantum mechanics--
well, quantum states,

531
00:31:58,350 --> 00:32:21,310
position and speed, are
meaningless until position

532
00:32:21,310 --> 00:32:22,870
or speed are measured.

533
00:32:40,429 --> 00:32:41,720
You all have interesting looks.

534
00:32:44,810 --> 00:32:55,130
Now, suppose I were
to ask where is

535
00:32:55,130 --> 00:32:57,140
some electron in the universe?

536
00:32:57,140 --> 00:32:59,750
Where is it?

537
00:32:59,750 --> 00:33:05,900
Well, when I make a
measurement of the position

538
00:33:05,900 --> 00:33:09,200
of the electron, I'll
certainly get some position.

539
00:33:09,200 --> 00:33:11,380
I'll certainly get
something somehow.

540
00:33:11,380 --> 00:33:13,490
I'll certainly get something.

541
00:33:13,490 --> 00:33:16,820
Now, there are many possible
places the electron can be.

542
00:33:16,820 --> 00:33:19,640
The electron can
be in this room.

543
00:33:19,640 --> 00:33:21,920
The electron can be outside.

544
00:33:21,920 --> 00:33:24,850
The electron can be on the moon.

545
00:33:24,850 --> 00:33:30,200
The electron can be billions
of light years away.

546
00:33:30,200 --> 00:33:37,624
Now, until I've actually
measured the electron,

547
00:33:37,624 --> 00:33:39,665
it's not that I don't know
where the electron is.

548
00:33:43,160 --> 00:33:46,710
The electron is
simply everywhere.

549
00:33:46,710 --> 00:33:50,540
It's in a mixture of
every possible place.

550
00:33:50,540 --> 00:33:54,620
It's in a superposition
of possible places.

551
00:33:57,420 --> 00:33:58,275
It's in a mixture.

552
00:33:58,275 --> 00:33:59,900
That's another way
you can think of it.

553
00:33:59,900 --> 00:34:04,680
It's in a mixture of
many possible places.

554
00:34:04,680 --> 00:34:09,220
And similarly, I can ask what's
the speed of the electron.

555
00:34:09,220 --> 00:34:10,469
Well, the speed could be this.

556
00:34:10,469 --> 00:34:12,260
The speed could be that.

557
00:34:12,260 --> 00:34:13,750
It could be 10
meters per second.

558
00:34:13,750 --> 00:34:15,820
It could be 50
meters per second.

559
00:34:15,820 --> 00:34:19,449
It could be a million
meters per second.

560
00:34:19,449 --> 00:34:21,199
Well, until I measure
the speed, it's

561
00:34:21,199 --> 00:34:22,679
in a mixture of all of those.

562
00:34:25,639 --> 00:34:34,810
And this idea of objects
being in a mixture of states,

563
00:34:34,810 --> 00:34:37,060
of being in a
superposition of states--

564
00:34:37,060 --> 00:34:38,560
that's the technical
term-- of being

565
00:34:38,560 --> 00:34:41,889
in a superposition of
states, this notion

566
00:34:41,889 --> 00:34:46,250
is completely unheard
of in classical physics.

567
00:34:46,250 --> 00:34:53,469
We don't talk about
a person being

568
00:34:53,469 --> 00:34:58,210
both here where I'm standing
and the person also being there.

569
00:34:58,210 --> 00:35:08,607
We don't talk about people
being both alive and dead.

570
00:35:08,607 --> 00:35:10,690
We don't talk about cats
being both alive and dead

571
00:35:10,690 --> 00:35:12,420
in particular.

572
00:35:12,420 --> 00:35:16,390
And some of you might be
curious about my shirts, which

573
00:35:16,390 --> 00:35:20,080
on the front says
Schrodinger's cat is dead

574
00:35:20,080 --> 00:35:25,330
and which on the back says
Schrodinger's cat is not dead.

575
00:35:25,330 --> 00:35:28,510
And dome people asked
me to explain it.

576
00:35:28,510 --> 00:35:31,810
Well, it has everything to
do with the superposition

577
00:35:31,810 --> 00:35:33,010
principle.

578
00:35:33,010 --> 00:35:37,960
And I'll be more explicit what
I mean by the superposition

579
00:35:37,960 --> 00:35:38,853
principle.

580
00:35:46,159 --> 00:35:49,570
The superposition principle is a
principle of quantum mechanics.

581
00:35:49,570 --> 00:35:51,180
It's a law of quantum mechanics.

582
00:36:07,440 --> 00:36:12,380
And the principle says that
it's possible for an object

583
00:36:12,380 --> 00:36:19,680
to be in many possible
states at the same time.

584
00:36:19,680 --> 00:36:22,050
It's in a mixture of states,

585
00:36:22,050 --> 00:36:25,320
Now, exactly which
states are these?

586
00:36:25,320 --> 00:36:29,240
Well, there's a technical
name for these states.

587
00:36:37,652 --> 00:36:39,360
They're only certain
numbers which you'll

588
00:36:39,360 --> 00:36:41,050
get when you measure something.

589
00:36:44,790 --> 00:36:49,650
And when you make
that measurement,

590
00:36:49,650 --> 00:36:52,350
that object will have
the property of being,

591
00:36:52,350 --> 00:36:56,040
for example, over
here or it will

592
00:36:56,040 --> 00:37:01,020
have the property of being in
motion at 10 meters per second.

593
00:37:01,020 --> 00:37:04,650
Now, those states,
which are the states

594
00:37:04,650 --> 00:37:08,760
that you get once you make
a measurement on an object,

595
00:37:08,760 --> 00:37:12,340
are called eigenstates,
which is a lovely word.

596
00:37:21,310 --> 00:37:35,750
And these are states
you get once you make

597
00:37:35,750 --> 00:37:45,152
a measurement of an object.

598
00:37:50,000 --> 00:37:55,790
So for example, there
are position eigenstates.

599
00:37:55,790 --> 00:37:58,400
These are the
states corresponding

600
00:37:58,400 --> 00:38:01,760
to various positions
that you can measure.

601
00:38:01,760 --> 00:38:05,114
There are momentum eigenstates,
or speed eigenstates,

602
00:38:05,114 --> 00:38:06,530
which is just the
momentum divided

603
00:38:06,530 --> 00:38:09,320
by the mass of the object.

604
00:38:09,320 --> 00:38:12,860
There are also
energy eigenstates.

605
00:38:12,860 --> 00:38:16,010
And these are the states
that the particle is in

606
00:38:16,010 --> 00:38:16,940
or the object--

607
00:38:16,940 --> 00:38:18,565
these are the states
that the object is

608
00:38:18,565 --> 00:38:22,460
in once you measure its energy.

609
00:38:22,460 --> 00:38:26,830
And these states
are very special.

610
00:38:26,830 --> 00:38:33,466
These states are very
special because these

611
00:38:33,466 --> 00:38:34,840
are the only states
in which it's

612
00:38:34,840 --> 00:38:37,732
meaningful to talk about the
position of the particle.

613
00:38:37,732 --> 00:38:39,190
These are the only
states when it's

614
00:38:39,190 --> 00:38:41,560
meaningful to talk about
the speed of the particle.

615
00:38:41,560 --> 00:38:43,060
These are the only
states where it's

616
00:38:43,060 --> 00:38:48,080
meaningful to talk about
the energy of the particle.

617
00:38:48,080 --> 00:38:58,940
Now, measurement is actually
a very weird process,

618
00:38:58,940 --> 00:39:02,090
because before you
make a measurement,

619
00:39:02,090 --> 00:39:07,590
an object is in a superposition
of many eigenstates.

620
00:39:07,590 --> 00:39:10,610
But once you make a
measurement, the object

621
00:39:10,610 --> 00:39:14,490
is no longer in a superposition
of many eigenstates.

622
00:39:14,490 --> 00:39:17,120
But it's now in
only one eigenstate.

623
00:39:22,400 --> 00:39:24,585
I'll let you think about.

624
00:39:24,585 --> 00:39:28,690
OK, the superposition
principle--

625
00:39:28,690 --> 00:39:30,160
OK, let me write this down.

626
00:39:30,160 --> 00:39:31,170
Eigenstates are
the states you get

627
00:39:31,170 --> 00:39:32,336
once you make a measurement.

628
00:39:32,336 --> 00:39:36,140
And the superposition
principle is--

629
00:39:36,140 --> 00:39:49,642
well, superposition is
mixture of eigenstates.

630
00:40:03,330 --> 00:40:05,430
Measurement is very
fishing because it

631
00:40:05,430 --> 00:40:09,310
takes the superposition
and destroys it.

632
00:40:09,310 --> 00:40:10,564
It destroys it.

633
00:40:10,564 --> 00:40:11,980
An object is in
the superposition,

634
00:40:11,980 --> 00:40:15,780
and then it's only
in one eigenstate.

635
00:40:15,780 --> 00:40:21,380
And this is called collapse,
collapse of the quantum states.

636
00:40:27,212 --> 00:40:28,635
Shall I write that down?

637
00:40:28,635 --> 00:40:29,510
I'll write that down.

638
00:40:49,750 --> 00:40:53,380
OK, now, I know this sounds
extremely, extremely confusing,

639
00:40:53,380 --> 00:40:56,590
because first of all, I've been
introduced a bunch of jargon.

640
00:40:56,590 --> 00:40:59,620
And second of all,
I haven't given you

641
00:40:59,620 --> 00:41:04,450
very many examples of how to
visualize these eigenstates

642
00:41:04,450 --> 00:41:06,610
and how to visualize
the superpositions

643
00:41:06,610 --> 00:41:09,650
and how to visualize
this collapse.

644
00:41:09,650 --> 00:41:15,100
And last of all,
these are ideas that

645
00:41:15,100 --> 00:41:19,060
are completely unfamiliar
to our intuitive minds.

646
00:41:19,060 --> 00:41:24,100
They're ideas that you don't
expect to be true at all.

647
00:41:24,100 --> 00:41:26,810
You would have never
guessed them to be true.

648
00:41:26,810 --> 00:41:31,480
But it turns out that when
you make predictions using

649
00:41:31,480 --> 00:41:34,610
these rules or you make
predictions using this theory,

650
00:41:34,610 --> 00:41:35,920
they're completely right.

651
00:41:35,920 --> 00:41:40,257
They completely agree with
experiments, completely.

652
00:41:43,370 --> 00:41:47,850
Now, I mentioned that--

653
00:41:47,850 --> 00:41:48,770
yes, question?

654
00:41:48,770 --> 00:41:51,183
AUDIENCE: If an experiment
in space of measurements,

655
00:41:51,183 --> 00:41:56,824
how do you ever measure or take
into account a superposition?

656
00:41:56,824 --> 00:41:58,740
PROFESSOR: How do you
measure a superposition?

657
00:41:58,740 --> 00:42:01,198
AUDIENCE: How do you ever take
into account a superposition

658
00:42:01,198 --> 00:42:03,825
because any experiment you
do is going to be based

659
00:42:03,825 --> 00:42:07,610
on some kind of measurement?

660
00:42:07,610 --> 00:42:09,320
PROFESSOR: You mean,
how do you prepare

661
00:42:09,320 --> 00:42:10,760
a certain superposition?

662
00:42:10,760 --> 00:42:12,920
I'm not exactly
sure I understand.

663
00:42:12,920 --> 00:42:16,736
AUDIENCE: If I want to try to
say that you're this position,

664
00:42:16,736 --> 00:42:19,050
and you're half away
around the and I haven't

665
00:42:19,050 --> 00:42:24,790
made a measurement, then I don't
have any scientific evidence--

666
00:42:24,790 --> 00:42:30,950
PROFESSOR: Oh, OK, so the
question is, suppose an object

667
00:42:30,950 --> 00:42:33,560
is in a superposition
of states right now.

668
00:42:33,560 --> 00:42:34,470
How do I know that?

669
00:42:34,470 --> 00:42:37,834
Because once I make a
measurement on the object,

670
00:42:37,834 --> 00:42:39,500
then it's only going
to be in one state.

671
00:42:39,500 --> 00:42:41,090
It's no longer going to
be in a superposition.

672
00:42:41,090 --> 00:42:42,464
That's what you're
asking, right?

673
00:42:42,464 --> 00:42:45,410
OK, the way that you
measure positions

674
00:42:45,410 --> 00:42:48,890
is by doing interference
experiments.

675
00:42:54,320 --> 00:43:00,050
So what I can do is I can
prepare some electrons to be

676
00:43:00,050 --> 00:43:03,350
in one type of
superposition and I

677
00:43:03,350 --> 00:43:04,880
can prepare other
electrons to be

678
00:43:04,880 --> 00:43:07,010
in another type
of superposition.

679
00:43:07,010 --> 00:43:11,170
And then what I can do is
I can send those electrons

680
00:43:11,170 --> 00:43:16,490
into specific superpositions,
send those electrons

681
00:43:16,490 --> 00:43:18,350
through a couple of slits.

682
00:43:18,350 --> 00:43:27,080
And I could make them interact
with each other in some way,

683
00:43:27,080 --> 00:43:32,720
in a way that I'll
be able to make

684
00:43:32,720 --> 00:43:35,750
a measurement of the intensity
of the electron, some type

685
00:43:35,750 --> 00:43:41,150
of intensity of the
electrons, that's

686
00:43:41,150 --> 00:43:43,760
indicative of the type of
superposition in which they

687
00:43:43,760 --> 00:43:45,860
were initially in.

688
00:43:45,860 --> 00:43:50,420
So the only way you can really
measure superpositions--

689
00:43:50,420 --> 00:43:56,090
well, actually, I
thought of another one.

690
00:43:56,090 --> 00:43:57,950
Sorry.

691
00:43:57,950 --> 00:43:58,874
OK, that's one way.

692
00:43:58,874 --> 00:44:00,790
That's one way you can
measure superpositions.

693
00:44:00,790 --> 00:44:05,720
There are ways in which you
can prepare superpositions,

694
00:44:05,720 --> 00:44:09,380
involving spins of atoms
and things like that.

695
00:44:09,380 --> 00:44:13,360
But I won't get
into that right now.

696
00:44:13,360 --> 00:44:14,690
OK, where are we?

697
00:44:22,850 --> 00:44:26,130
As I said, I know this is
confusing to a lot of you.

698
00:44:26,130 --> 00:44:30,860
I hear a lot of people
whispering probably.

699
00:44:30,860 --> 00:44:35,180
Maybe discussing Harry
Potter, probably not.

700
00:44:35,180 --> 00:44:39,100
Perhaps discussing
this confusing stuff.

701
00:44:39,100 --> 00:44:42,230
And I know it's confusing.

702
00:44:42,230 --> 00:44:44,030
It's weird.

703
00:44:44,030 --> 00:44:46,610
And it's hard to really
get a grasp of it

704
00:44:46,610 --> 00:44:49,000
without getting mathematical.

705
00:44:49,000 --> 00:44:54,880
But there are certain
things that you

706
00:44:54,880 --> 00:44:56,260
can at least appreciate.

707
00:44:56,260 --> 00:44:58,480
You can at least
appreciate this idea

708
00:44:58,480 --> 00:45:04,820
of the states, this idea
of a mixture of states,

709
00:45:04,820 --> 00:45:08,320
this idea of
collapsing into states,

710
00:45:08,320 --> 00:45:13,180
this idea of meaninglessness
of the notions of position

711
00:45:13,180 --> 00:45:15,290
and speed.

712
00:45:15,290 --> 00:45:17,650
And we'll take a
break right here.

713
00:45:21,110 --> 00:45:24,980
So some of you have asked
about what does my shirt mean.

714
00:45:24,980 --> 00:45:28,650
What is Schrodinger's cats?

715
00:45:28,650 --> 00:45:30,890
What does it mean for it
to be dead and not dead?

716
00:45:30,890 --> 00:45:35,540
Well, this is an extreme example
of the superposition principle

717
00:45:35,540 --> 00:45:37,520
at work.

718
00:45:37,520 --> 00:45:41,334
Schrodinger was one of the
founders of quantum mechanics.

719
00:45:41,334 --> 00:45:42,500
So Schrodinger was a person.

720
00:45:42,500 --> 00:45:43,970
I mean, I know
it's a weird word.

721
00:45:43,970 --> 00:45:45,920
But Schrodinger was a person.

722
00:45:45,920 --> 00:45:48,989
Schrodinger was one of the
founders of quantum mechanics.

723
00:45:48,989 --> 00:45:51,530
There's a very famous equation
named after Schrodinger called

724
00:45:51,530 --> 00:45:53,510
the Schrodinger equation.

725
00:45:53,510 --> 00:45:57,920
And it describes how the
quantum state of an object

726
00:45:57,920 --> 00:45:59,536
changes in time.

727
00:45:59,536 --> 00:46:01,160
And it's a pretty
complicated equation.

728
00:46:01,160 --> 00:46:03,070
So I won't write it down.

729
00:46:03,070 --> 00:46:04,651
I wrote it down
for somebody, then

730
00:46:04,651 --> 00:46:06,650
I erased it because it
scared some other people.

731
00:46:09,269 --> 00:46:11,810
But Schrodinger was one of the
founders of quantum mechanics.

732
00:46:11,810 --> 00:46:15,530
And he proposed a very
interesting thought experiment

733
00:46:15,530 --> 00:46:19,340
to visualize the
superposition principle.

734
00:46:19,340 --> 00:46:24,560
And it involved cats
and it involved death.

735
00:46:24,560 --> 00:46:33,090
So what he proposed was
you get a cat, get a box,

736
00:46:33,090 --> 00:46:35,810
put a cat inside
the box, but also

737
00:46:35,810 --> 00:46:38,000
get some radioactive poison
and put that in the box

738
00:46:38,000 --> 00:46:44,720
too and close the box.

739
00:46:44,720 --> 00:46:49,750
So that when the
box is closed we

740
00:46:49,750 --> 00:46:52,570
don't know whether the
cat is alive or dead.

741
00:46:52,570 --> 00:46:54,520
Well, OK, let's suppose
there's enough air.

742
00:46:54,520 --> 00:46:57,130
Suppose there's a lot
of air in the box.

743
00:46:57,130 --> 00:47:00,580
The only thing dangerous
in the box is the poison.

744
00:47:00,580 --> 00:47:03,530
Within a given hour, suppose
that there's a 50% probability

745
00:47:03,530 --> 00:47:11,050
that the poison will
decay and reach the cat

746
00:47:11,050 --> 00:47:14,020
and therefore kill the cat.

747
00:47:14,020 --> 00:47:17,680
So unless the poison
decays and kills the cats,

748
00:47:17,680 --> 00:47:20,230
the cat's going to be alive.

749
00:47:20,230 --> 00:47:22,630
But until we actually
open up the box

750
00:47:22,630 --> 00:47:24,630
and make a measurement
on the cat,

751
00:47:24,630 --> 00:47:26,620
whether we measure it
to be alive or dead,

752
00:47:26,620 --> 00:47:28,990
the cat is both
in a superposition

753
00:47:28,990 --> 00:47:30,790
of alive and dead.

754
00:47:30,790 --> 00:47:36,100
So in that sense,
Schrodinger's cat is dead,

755
00:47:36,100 --> 00:47:39,850
and Schrodinger's
cat is not dead.

756
00:47:39,850 --> 00:47:45,160
And it's a lovely way
to think about things,

757
00:47:45,160 --> 00:47:48,730
because if we can think about
super positions of things

758
00:47:48,730 --> 00:47:50,530
being alive and
dead, we can think

759
00:47:50,530 --> 00:47:52,980
about a lot of different
superpositions.

760
00:47:52,980 --> 00:47:55,091
You can think of
superpositions of--

761
00:47:55,091 --> 00:47:57,340
well, I mentioned you can
think of superposition of me

762
00:47:57,340 --> 00:47:59,590
here or superstition
of me there.

763
00:47:59,590 --> 00:48:04,450
You can think of a
superposition of the chalk

764
00:48:04,450 --> 00:48:08,320
being both here and the
chalk being on the moon.

765
00:48:08,320 --> 00:48:11,644
But for some reason we don't
observe those superpositions.

766
00:48:11,644 --> 00:48:13,810
Well, the reason we don't
observe the superpositions

767
00:48:13,810 --> 00:48:18,310
has to do with the fact
that many of our everyday

768
00:48:18,310 --> 00:48:22,960
experiences with
states that are robust.

769
00:48:22,960 --> 00:48:26,890
And the way that they stay
robust is kind of complicated

770
00:48:26,890 --> 00:48:31,960
and involves an idea known
as quantum decoherence.

771
00:48:31,960 --> 00:48:34,510
And if any of you are
interested about that,

772
00:48:34,510 --> 00:48:37,100
you can talk to me
about it after class.

773
00:48:37,100 --> 00:48:38,630
Question?

774
00:48:38,630 --> 00:48:39,130
What's that?

775
00:48:39,130 --> 00:48:40,170
AUDIENCE: The infinity.

776
00:48:40,170 --> 00:48:41,610
PROFESSOR: Oh, about robustness?

777
00:48:41,610 --> 00:48:42,220
Yeah.

778
00:48:42,220 --> 00:48:43,760
Yeah, that's an
important question.

779
00:48:43,760 --> 00:48:45,200
That's an important question.

780
00:48:45,200 --> 00:48:48,970
Why does the world look
normal when I've just

781
00:48:48,970 --> 00:48:51,130
told you it's so crazy?

782
00:48:51,130 --> 00:48:52,660
Why does it look normal?

783
00:48:52,660 --> 00:48:57,320
Why does it look like
what we would expect?

784
00:48:57,320 --> 00:49:03,110
Well, it has to be true that
quantum mechanics describes

785
00:49:03,110 --> 00:49:05,070
adequately the everyday objects.

786
00:49:05,070 --> 00:49:08,290
It has to be true that
quantum mechanics makes

787
00:49:08,290 --> 00:49:14,920
correct predictions about how
high a chalk if I threw it

788
00:49:14,920 --> 00:49:18,495
up and caught it--
if I did catch it.

789
00:49:18,495 --> 00:49:21,670
And it has to make predictions
about everyday objects that

790
00:49:21,670 --> 00:49:23,200
are true.

791
00:49:23,200 --> 00:49:25,810
Unfortunately, a lot
of everyday objects

792
00:49:25,810 --> 00:49:29,369
are very complicated because
they involve lots of atoms.

793
00:49:29,369 --> 00:49:30,910
There are lots of
atoms in the chalk.

794
00:49:30,910 --> 00:49:32,680
There are lots of
atoms in a person.

795
00:49:32,680 --> 00:49:36,100
And so actually describing
everyday objects

796
00:49:36,100 --> 00:49:39,260
is extraordinarily difficult.

797
00:49:39,260 --> 00:49:42,646
However, we have
reason to believe

798
00:49:42,646 --> 00:49:44,770
that quantum mechanics
should describe the objects,

799
00:49:44,770 --> 00:49:48,450
because quantum mechanics
describes the very small.

800
00:49:48,450 --> 00:49:50,890
It describes electrons.

801
00:49:50,890 --> 00:49:53,140
It describes atoms.

802
00:49:53,140 --> 00:49:56,940
It describes molecules.

803
00:49:56,940 --> 00:50:00,550
It even describes viruses.

804
00:50:00,550 --> 00:50:03,070
We simply don't have
the experiments know

805
00:50:03,070 --> 00:50:07,300
how to test quantum mechanics
on extremely large objects,

806
00:50:07,300 --> 00:50:09,460
but we suspect that
it's still true,

807
00:50:09,460 --> 00:50:16,810
although we don't
know for a fact

808
00:50:16,810 --> 00:50:20,530
if you were to go through
a slit then interfered

809
00:50:20,530 --> 00:50:21,550
with another person.

810
00:50:21,550 --> 00:50:24,790
We don't know exactly what would
happen or that to be the case.

811
00:50:24,790 --> 00:50:28,020
But quantum mechanics says
that interference should occur.

812
00:50:28,020 --> 00:50:30,400
It says that many weird
things should happen.

813
00:50:35,056 --> 00:50:36,680
Now, I'd like to talk
a little bit more

814
00:50:36,680 --> 00:50:41,980
about this collapse of
eigenstate, this collapse of--

815
00:50:41,980 --> 00:50:44,600
well, another word for quantum
state is wave function.

816
00:50:58,230 --> 00:51:00,810
And you more often hear about
collapsing of wave functions

817
00:51:00,810 --> 00:51:04,077
than you hear about
collapsing of quantum states.

818
00:51:04,077 --> 00:51:05,910
So just to give you a
little bit more words.

819
00:51:05,910 --> 00:51:09,540
They're cool words
too, because once you

820
00:51:09,540 --> 00:51:13,350
know what these words mean,
you can make jokes about them.

821
00:51:13,350 --> 00:51:15,840
And you can wear T-shirts
about them, like I am.

822
00:51:15,840 --> 00:51:21,087
And it's one of the pleasures
of learning new terminology

823
00:51:21,087 --> 00:51:22,920
and learning new subjects,
the fact that you

824
00:51:22,920 --> 00:51:23,878
get to make more jokes.

825
00:51:26,700 --> 00:51:29,040
I'm not saying that that's
the reason I've taken classes

826
00:51:29,040 --> 00:51:33,920
on relativity or taking
classes on quantum mechanics,

827
00:51:33,920 --> 00:51:34,610
but it's a perk.

828
00:51:34,610 --> 00:51:35,880
It's a really cool perk.

829
00:51:35,880 --> 00:51:39,870
You can say lots of things
interestingly with new language

830
00:51:39,870 --> 00:51:42,620
and new ideas.

831
00:51:42,620 --> 00:51:47,700
The space of jokes is
enhanced by physics knowledge.

832
00:51:47,700 --> 00:51:50,520
OK, but now, I'd
like to talk more

833
00:51:50,520 --> 00:51:54,840
about this collapse
of eigenstates.

834
00:51:54,840 --> 00:51:59,970
Now, there are certain states
which correspond to positions

835
00:51:59,970 --> 00:52:01,060
that you can measure.

836
00:52:01,060 --> 00:52:03,150
We can measure a position
to be here or there

837
00:52:03,150 --> 00:52:04,220
or there or there.

838
00:52:04,220 --> 00:52:06,690
But until you make
a measurements,

839
00:52:06,690 --> 00:52:11,200
the object is in a superposition
of those various states.

840
00:52:11,200 --> 00:52:13,950
Let's talk about atoms.

841
00:52:13,950 --> 00:52:16,410
We know that atoms
have a nucleus, which

842
00:52:16,410 --> 00:52:19,290
has some stuff in it, like
protons and neutrons, maybe

843
00:52:19,290 --> 00:52:20,790
some other stuff.

844
00:52:20,790 --> 00:52:26,910
And we know that's surrounding
these nuclei are electrons.

845
00:52:26,910 --> 00:52:30,020
Precisely how they surround
them is a little complicated.

846
00:52:30,020 --> 00:52:35,970
But I can still discuss them.

847
00:52:35,970 --> 00:52:38,980
I can still discuss
it in a certain way.

848
00:52:38,980 --> 00:52:43,560
I can still discuss
an essential point

849
00:52:43,560 --> 00:52:45,125
that I've been
trying to illustrate.

850
00:52:49,010 --> 00:52:52,370
There are certain
super positions

851
00:52:52,370 --> 00:52:55,460
that electrons and
atoms can be in.

852
00:52:55,460 --> 00:52:58,370
And probably a lot of you
have heard about these type

853
00:52:58,370 --> 00:52:59,910
of superpositions.

854
00:52:59,910 --> 00:53:01,850
In chemistry, they're
called orbitals.

855
00:53:01,850 --> 00:53:04,850
You might have heard about
S orbitals, P orbitals, D

856
00:53:04,850 --> 00:53:08,610
orbitals, F orbitals,
G orbitals, H orbitals,

857
00:53:08,610 --> 00:53:09,750
and so forth.

858
00:53:09,750 --> 00:53:15,110
And these orbitals are really
just types of superpositions

859
00:53:15,110 --> 00:53:18,650
that electrons can be in.

860
00:53:18,650 --> 00:53:24,740
For example, an electron can be
in what's called a 1s orbital.

861
00:53:24,740 --> 00:53:26,660
It can be in 1s orbital.

862
00:53:26,660 --> 00:53:28,268
That's a type of superposition.

863
00:53:31,860 --> 00:53:34,710
It's in a mixture of
various possible--

864
00:53:34,710 --> 00:53:38,100
the electron is not
at one point in space.

865
00:53:38,100 --> 00:53:40,060
It's in a mixture of
various points in space.

866
00:53:40,060 --> 00:53:42,570
It's in a superposition of
various points in space.

867
00:53:42,570 --> 00:53:45,600
But it's not an equal mixture.

868
00:53:45,600 --> 00:53:52,530
There are some points in space
where there is more weight.

869
00:53:52,530 --> 00:53:57,640
In particular, as you go closer
to the nucleus of an atom,

870
00:53:57,640 --> 00:54:00,010
this weight becomes larger.

871
00:54:00,010 --> 00:54:02,730
And this weight actually has an
interesting physical meaning,

872
00:54:02,730 --> 00:54:04,470
which I'll tell you in a moment.

873
00:54:08,940 --> 00:54:13,120
So let's say I plotted position.

874
00:54:13,120 --> 00:54:14,910
I'll write down distance
from the nucleus.

875
00:54:25,210 --> 00:54:28,300
And over here, I'll
right down weight.

876
00:54:32,360 --> 00:54:35,190
It turns out that
it has the greatest

877
00:54:35,190 --> 00:54:39,790
weights near the nucleus.

878
00:54:39,790 --> 00:54:41,790
Now, when I say it has
the greatest weight,

879
00:54:41,790 --> 00:54:43,680
that doesn't really mean
anything to you yet.

880
00:54:46,240 --> 00:54:50,400
And what gives
meaning to this weight

881
00:54:50,400 --> 00:54:56,670
is a probability interpretation
of quantum mechanics

882
00:54:56,670 --> 00:55:01,020
where this weight is
larger, an electron

883
00:55:01,020 --> 00:55:04,245
is more likely to be found
once you make a measurement.

884
00:55:07,310 --> 00:55:11,387
If an electron is
initially in a 1s state--

885
00:55:11,387 --> 00:55:12,720
that's just a name of the state.

886
00:55:12,720 --> 00:55:15,450
It's just a weird name
we've given to it.

887
00:55:15,450 --> 00:55:16,187
Well, not us.

888
00:55:16,187 --> 00:55:18,020
I mean, they did a long
before we were born.

889
00:55:18,020 --> 00:55:19,853
But it's a weird name
that people have given

890
00:55:19,853 --> 00:55:24,390
to this kind of superposition.

891
00:55:24,390 --> 00:55:27,060
According to this
probability interpretation

892
00:55:27,060 --> 00:55:32,490
of quantum mechanics, wherever
this weight is larger,

893
00:55:32,490 --> 00:55:35,810
an object is more likely
to be found in measurement.

894
00:55:35,810 --> 00:55:40,220
An electron is more likely
to be found near the nucleus

895
00:55:40,220 --> 00:55:44,640
than it is to be found, say,
a nanometer from the nucleus,

896
00:55:44,640 --> 00:55:48,690
anywhere at some distance
from the nucleus.

897
00:55:48,690 --> 00:55:54,327
But it's interesting, though,
that this probability--

898
00:55:54,327 --> 00:55:56,160
so I can right now
probability, because this

899
00:55:56,160 --> 00:56:00,330
is the interpretation
that we give to it--

900
00:56:00,330 --> 00:56:01,170
probability.

901
00:56:04,050 --> 00:56:09,690
What's interesting is that
this probability actually

902
00:56:09,690 --> 00:56:11,040
never reaches zero.

903
00:56:11,040 --> 00:56:12,950
I know I've drawn
it to be zero here,

904
00:56:12,950 --> 00:56:15,210
and effectively it's zero--

905
00:56:15,210 --> 00:56:16,200
I just made it bigger.

906
00:56:16,200 --> 00:56:18,740
I didn't mean to do that--

907
00:56:18,740 --> 00:56:22,230
effectively at zero, but it
never actually reaches zero.

908
00:56:22,230 --> 00:56:24,480
So if I have an atom over here--

909
00:56:24,480 --> 00:56:27,030
well, the chalk is
made up of atoms.

910
00:56:27,030 --> 00:56:28,650
There are atoms in there.

911
00:56:28,650 --> 00:56:33,270
And if I try to measure
the position of an electron

912
00:56:33,270 --> 00:56:37,380
in the atom, then
there's a chance

913
00:56:37,380 --> 00:56:40,320
that I can measure
the electron to be

914
00:56:40,320 --> 00:56:45,370
over here or over here or a
mile away or 100 miles away.

915
00:56:45,370 --> 00:56:47,280
There's a chance I
could measure to be

916
00:56:47,280 --> 00:56:49,900
a billion light years away.

917
00:56:49,900 --> 00:56:52,380
And this is something
really weird

918
00:56:52,380 --> 00:56:54,450
that quantum mechanics
simply predicts.

919
00:57:01,210 --> 00:57:06,100
I can't really give you a whole
lot of justification for it

920
00:57:06,100 --> 00:57:07,210
right now.

921
00:57:07,210 --> 00:57:08,710
But it's something
that it predicts.

922
00:57:13,092 --> 00:57:14,800
Quantum mechanics also
has lots of things

923
00:57:14,800 --> 00:57:20,320
to predict about probabilities
of events occurring.

924
00:57:20,320 --> 00:57:22,870
Not only is there--

925
00:57:22,870 --> 00:57:25,030
can talk about probabilities
of finding an electron

926
00:57:25,030 --> 00:57:30,550
at some place, but we can also
talk about the probability

927
00:57:30,550 --> 00:57:33,920
that an electron will
pass through my hand,

928
00:57:33,920 --> 00:57:36,670
or the probability
that a chalk will

929
00:57:36,670 --> 00:57:40,210
pass through my hand
or the fact that I

930
00:57:40,210 --> 00:57:42,550
will pass through the wall
or something like that.

931
00:57:45,310 --> 00:57:50,860
And I did a very precise,
sophisticated experiment

932
00:57:50,860 --> 00:57:51,997
in the first class.

933
00:57:51,997 --> 00:57:53,330
I don't know if you remember it.

934
00:57:53,330 --> 00:57:56,620
But it took me it took
like an hour to set up.

935
00:57:56,620 --> 00:58:01,650
And then I finally engaged
in the experiments.

936
00:58:01,650 --> 00:58:03,490
I started preparing
before class so I

937
00:58:03,490 --> 00:58:05,890
could do the experiment again.

938
00:58:05,890 --> 00:58:08,600
But I'll now test
the experiment.

939
00:58:08,600 --> 00:58:10,510
The experiment is
to test whether I

940
00:58:10,510 --> 00:58:12,340
can walk through a wall.

941
00:58:12,340 --> 00:58:14,422
And I'll just test--

942
00:58:14,422 --> 00:58:15,880
well, there's a
certain probability

943
00:58:15,880 --> 00:58:17,950
that I can walk to the wall.

944
00:58:17,950 --> 00:58:20,110
And I'll test to see
if that's the case.

945
00:58:25,080 --> 00:58:28,332
OK, it didn't work then.

946
00:58:28,332 --> 00:58:30,665
But it doesn't mean that
there's a non-zero probability.

947
00:58:30,665 --> 00:58:33,560
It doesn't mean that there's
a non-zero probability.

948
00:58:33,560 --> 00:58:35,830
That took me an hour to set up.

949
00:58:35,830 --> 00:58:37,850
Took me an hour to
set up, by the way.

950
00:58:37,850 --> 00:58:39,630
What's that?

951
00:58:39,630 --> 00:58:41,470
Why?

952
00:58:41,470 --> 00:58:45,234
Oh, well-- what's that?

953
00:58:45,234 --> 00:58:46,761
AUDIENCE: We wanted to know why?

954
00:58:46,761 --> 00:58:48,760
PROFESSOR: Why did it
take me an hour to set up?

955
00:58:48,760 --> 00:58:50,384
Well, you can't
actually see everything

956
00:58:50,384 --> 00:58:52,210
behind this experiment.

957
00:58:52,210 --> 00:58:56,260
There are lots of apparatuses
stationed everywhere

958
00:58:56,260 --> 00:59:00,490
around the classroom to
do it very precisely,

959
00:59:00,490 --> 00:59:02,800
to make sure things
don't go wrong.

960
00:59:02,800 --> 00:59:06,590
To ensure the safety of you
all, I had to take precautions.

961
00:59:06,590 --> 00:59:13,930
I have some charms that
have cast upon you all.

962
00:59:13,930 --> 00:59:16,930
So it took a while to do that.

963
00:59:16,930 --> 00:59:24,790
And this type of existence
of non-zero probability

964
00:59:24,790 --> 00:59:29,470
arises from an effect known
as quantum tunneling, which

965
00:59:29,470 --> 00:59:35,800
I think is one of the most
fascinating predictions

966
00:59:35,800 --> 00:59:36,820
of quantum mechanics.

967
00:59:53,590 --> 00:59:55,410
How much time do I have?

968
00:59:55,410 --> 01:00:02,020
OK, suppose I'm on my bicycle.

969
01:00:02,020 --> 01:00:04,740
And there's a hill
in front of me,

970
01:00:04,740 --> 01:00:06,590
and I'm traveling at
some constant speed.

971
01:00:06,590 --> 01:00:11,970
Let's say I'm traveling at
10 miles an hour on my bike.

972
01:00:16,215 --> 01:00:17,940
So here's the landscape.

973
01:00:17,940 --> 01:00:21,630
It's flat, and then
there's a hill,

974
01:00:21,630 --> 01:00:23,400
and then it gets flat again.

975
01:00:23,400 --> 01:00:25,460
And I start out here.

976
01:00:25,460 --> 01:00:26,530
I started here.

977
01:00:26,530 --> 01:00:28,290
I'm on my bicycle.

978
01:00:28,290 --> 01:00:30,420
I'm traveling at
a constant speed.

979
01:00:30,420 --> 01:00:33,310
I start going up the hill.

980
01:00:33,310 --> 01:00:35,760
And whether or not I
can get over the hill

981
01:00:35,760 --> 01:00:40,860
depends on if I was traveling
at a high speed, right?

982
01:00:40,860 --> 01:00:43,800
If I was traveling at 100
MPH, then probably certainly

983
01:00:43,800 --> 01:00:45,530
I would get over the hill.

984
01:00:45,530 --> 01:00:47,790
But if I'm only traveling
at 1 miles an hour,

985
01:00:47,790 --> 01:00:53,090
then there's not a very good
chance I'll get over the hill.

986
01:00:53,090 --> 01:00:57,729
But according to
classical physics,

987
01:00:57,729 --> 01:00:59,270
there is a certain
energy that I have

988
01:00:59,270 --> 01:01:01,010
to have, a sort
of kinetic energy

989
01:01:01,010 --> 01:01:07,960
that I have to get over this
barrier, to get over this hill.

990
01:01:07,960 --> 01:01:11,670
And according to
classical physics,

991
01:01:11,670 --> 01:01:14,840
there's a zero chance for
me to get over the hill

992
01:01:14,840 --> 01:01:17,820
unless I have this
certain kinetic energy.

993
01:01:17,820 --> 01:01:19,370
There's just no chance at all.

994
01:01:19,370 --> 01:01:23,060
There's no hope for me
to get over the hill.

995
01:01:23,060 --> 01:01:25,760
Well things are different
in quantum mechanics.

996
01:01:25,760 --> 01:01:27,870
Things are very strange
in quantum mechanics.

997
01:01:27,870 --> 01:01:30,260
And in quantum
mechanics, there actually

998
01:01:30,260 --> 01:01:32,650
is a non-zero probability.

999
01:01:32,650 --> 01:01:41,030
And the idea is that in a way--

1000
01:01:44,390 --> 01:01:58,280
well, because there's-- suppose
I have some objects traveling

1001
01:01:58,280 --> 01:02:03,410
at some speed moving
across the landscape.

1002
01:02:03,410 --> 01:02:07,520
That object is described
by a certain probability

1003
01:02:07,520 --> 01:02:10,640
distribution in position.

1004
01:02:10,640 --> 01:02:18,970
And as the object moves, this
probability distribution moves.

1005
01:02:18,970 --> 01:02:24,134
So for example, the
probability distribution

1006
01:02:24,134 --> 01:02:25,550
could start out
looking like this.

1007
01:02:28,390 --> 01:02:29,860
I don't know if
you can see that.

1008
01:02:29,860 --> 01:02:31,121
Can you all see it?

1009
01:02:31,121 --> 01:02:31,620
No?

1010
01:02:31,620 --> 01:02:33,550
AUDIENCE: Yes.

1011
01:02:33,550 --> 01:02:36,930
PROFESSOR: Of course,
you can see it.

1012
01:02:36,930 --> 01:02:39,310
Well, I don't have
an extra col--

1013
01:02:39,310 --> 01:02:40,470
I'll draw it larger.

1014
01:02:40,470 --> 01:02:46,120
OK, let's say that
this is the probability

1015
01:02:46,120 --> 01:02:52,280
distribution of the
position of this particle.

1016
01:02:52,280 --> 01:02:55,030
So the particle's moving.

1017
01:02:55,030 --> 01:02:58,180
And at a given instant in
time-- suppose you stop time--

1018
01:02:58,180 --> 01:03:00,910
at a given instant in time,
there's a certain probability

1019
01:03:00,910 --> 01:03:03,640
that you'll measure the
particle to be over here.

1020
01:03:03,640 --> 01:03:05,681
There's a certain probability
that you'll measure

1021
01:03:05,681 --> 01:03:07,000
the particle to be over here.

1022
01:03:07,000 --> 01:03:08,666
There's the high
probability that you'll

1023
01:03:08,666 --> 01:03:11,200
measure the particle to
be here, and so forth.

1024
01:03:11,200 --> 01:03:14,680
Now, as the particle moves, this
probability distribution moves.

1025
01:03:21,630 --> 01:03:25,140
And it keeps moving
as the particle moves.

1026
01:03:25,140 --> 01:03:33,420
Now, when the particle gets
to near the top of the hill,

1027
01:03:33,420 --> 01:03:36,720
when he gets, for
example, to over here,

1028
01:03:36,720 --> 01:03:39,160
the probability distribution
might look this.

1029
01:03:44,560 --> 01:03:48,150
If the particle didn't have
enough energy, enough kinetic

1030
01:03:48,150 --> 01:03:53,040
energy, to get over
the hill according

1031
01:03:53,040 --> 01:03:54,640
to the laws of
classical physics.

1032
01:03:54,640 --> 01:04:01,140
If they have enough kinetic
energy to break this barrier,

1033
01:04:01,140 --> 01:04:03,990
then according to
quantum mechanics

1034
01:04:03,990 --> 01:04:11,940
it might now have a chance
of getting over the hill,

1035
01:04:11,940 --> 01:04:15,300
because if you look at this
probability distribution,

1036
01:04:15,300 --> 01:04:17,370
there's now a
non-zero probability

1037
01:04:17,370 --> 01:04:20,020
that you'll measure the
particle to be over the hill.

1038
01:04:20,020 --> 01:04:24,540
There's a small probability,
but it's still non-zero.

1039
01:04:24,540 --> 01:04:28,260
And this is a simple
way of understanding

1040
01:04:28,260 --> 01:04:30,540
how this tunneling
phenomenon works.

1041
01:04:30,540 --> 01:04:33,210
And we call it
tunneling, because it's

1042
01:04:33,210 --> 01:04:39,000
as if the particle
tunnels through this hill.

1043
01:04:39,000 --> 01:04:41,220
It doesn't actually
get over the hill,

1044
01:04:41,220 --> 01:04:44,230
but it goes through the
hill in a certain way.

1045
01:04:44,230 --> 01:04:48,350
It tunnels through the hill.

1046
01:04:48,350 --> 01:04:56,490
And this makes a lot
of things possible,

1047
01:04:56,490 --> 01:05:00,010
a lot of very interesting
things possible.

1048
01:05:00,010 --> 01:05:09,040
For example,
ordinarily when I pull

1049
01:05:09,040 --> 01:05:11,770
at this desk trying
to lift it up,

1050
01:05:11,770 --> 01:05:13,960
when I use the amount of
force I'm using right now,

1051
01:05:13,960 --> 01:05:16,390
the desk isn't going to lift up.

1052
01:05:16,390 --> 01:05:24,320
But there's a chance
that I can get it

1053
01:05:24,320 --> 01:05:30,650
up even using that
same amount of force.

1054
01:05:30,650 --> 01:05:38,210
There's a chance that
air molecules around me

1055
01:05:38,210 --> 01:05:41,420
can knock me over.

1056
01:05:41,420 --> 01:05:43,420
There's a chance that
they'll have enough energy

1057
01:05:43,420 --> 01:05:46,420
to knock me over, enough energy
as provided by this quantum

1058
01:05:46,420 --> 01:05:48,370
tunneling phenomenon.

1059
01:05:48,370 --> 01:05:50,590
So there's a chance that
while talking to you all,

1060
01:05:50,590 --> 01:05:54,100
I'll simply be knocked over.

1061
01:05:54,100 --> 01:05:56,500
It can happen.

1062
01:05:56,500 --> 01:05:59,140
The chance is very small.

1063
01:05:59,140 --> 01:06:01,904
So you don't usually
see it happening.

1064
01:06:01,904 --> 01:06:03,820
And you probably never
will see it happen ever

1065
01:06:03,820 --> 01:06:08,200
in your whole entire life unless
you live forever, in which case

1066
01:06:08,200 --> 01:06:10,212
you'd see it happen
infinitely many times,

1067
01:06:10,212 --> 01:06:11,920
because if there's a
non-zero probability

1068
01:06:11,920 --> 01:06:14,730
that it will happen, then
if you wait long enough,

1069
01:06:14,730 --> 01:06:15,744
it will happen.

1070
01:06:18,880 --> 01:06:25,450
With this idea you can envision
lots of possible worlds.

1071
01:06:25,450 --> 01:06:28,900
You can envision
magical worlds being

1072
01:06:28,900 --> 01:06:33,580
possible being possible as a
result of quantum tunneling.

1073
01:06:33,580 --> 01:06:38,260
You can imagine people flying
as a result of air molecules,

1074
01:06:38,260 --> 01:06:40,660
pushing on them, giving
them enough energy

1075
01:06:40,660 --> 01:06:43,540
to surpass these
barriers, to allow the air

1076
01:06:43,540 --> 01:06:47,842
molecules to tunnel
through these barriers.

1077
01:06:47,842 --> 01:06:48,800
And you can go further.

1078
01:06:51,640 --> 01:06:54,850
You can say, well,
let's say I want

1079
01:06:54,850 --> 01:06:59,170
to punch one of the
guys in the back row.

1080
01:06:59,170 --> 01:07:04,390
Well, if I just do this, then
I give a little bit of energy

1081
01:07:04,390 --> 01:07:06,555
to these air molecules
right in front of me.

1082
01:07:06,555 --> 01:07:08,680
And those air molecules
give a little bit of energy

1083
01:07:08,680 --> 01:07:11,110
to those air molecules
in front of them.

1084
01:07:11,110 --> 01:07:15,070
And eventually, they can
reach you and punch you

1085
01:07:15,070 --> 01:07:17,500
with a very strong force.

1086
01:07:22,686 --> 01:07:24,310
So quantum tunneling
can make possible,

1087
01:07:24,310 --> 01:07:31,090
for instance, the
force of Star Wars.

1088
01:07:31,090 --> 01:07:33,100
I could choke one
of you in the back.

1089
01:07:33,100 --> 01:07:34,810
You can think of
some very complex way

1090
01:07:34,810 --> 01:07:38,080
that quantum tunneling can
allow for air molecules

1091
01:07:38,080 --> 01:07:40,780
to move and to
have enough energy

1092
01:07:40,780 --> 01:07:43,690
to surpass lots of barriers.

1093
01:07:43,690 --> 01:07:46,930
You can let your imaginations
run wild with this.

1094
01:07:46,930 --> 01:07:48,760
Pretty much any
idea, pretty much

1095
01:07:48,760 --> 01:07:53,560
anything that you can imagine,
you can think of a way for it

1096
01:07:53,560 --> 01:07:55,300
to happen.

1097
01:07:55,300 --> 01:07:59,930
You can think of a very complex
mechanism for it to happen.

1098
01:07:59,930 --> 01:08:02,840
And if you can think of a
mechanism for it to happen,

1099
01:08:02,840 --> 01:08:06,110
then you can associate a
probability for it to happen.

1100
01:08:06,110 --> 01:08:09,040
And therefore, if you
wait a long enough time,

1101
01:08:09,040 --> 01:08:10,406
it will happen.

1102
01:08:10,406 --> 01:08:13,930
But I don't know if you all have
enough patient to use the force

1103
01:08:13,930 --> 01:08:15,250
on people.

1104
01:08:15,250 --> 01:08:15,920
Question?

1105
01:08:15,920 --> 01:08:18,726
AUDIENCE: Is there any record
of quantum tunneling happening?

1106
01:08:18,726 --> 01:08:20,100
PROFESSOR: Oh,
quantum tunneling.

1107
01:08:20,100 --> 01:08:25,870
OK, so quantum tunneling
has a very small probability

1108
01:08:25,870 --> 01:08:29,830
of occurring for everyday
objects like people.

1109
01:08:29,830 --> 01:08:31,930
But, in fact, it's used
in modern electronics

1110
01:08:31,930 --> 01:08:34,450
all the time.

1111
01:08:34,450 --> 01:08:38,290
For electrons and for other
small particles, quantum

1112
01:08:38,290 --> 01:08:42,250
mechanics, you can very
easily see it work.

1113
01:08:42,250 --> 01:08:46,750
As I said, our only real
experimental evidence

1114
01:08:46,750 --> 01:08:48,310
for quantum mechanics
is what we see

1115
01:08:48,310 --> 01:08:53,890
in these experiments for very
small objects in this very

1116
01:08:53,890 --> 01:08:56,710
microscopic realm.

1117
01:08:56,710 --> 01:09:00,269
We think it's true
for macroscopic realm.

1118
01:09:00,269 --> 01:09:01,810
But we don't exactly
have a whole lot

1119
01:09:01,810 --> 01:09:03,260
of experimental evidence for it.

1120
01:09:03,260 --> 01:09:06,080
But why shouldn't it be true?

1121
01:09:06,080 --> 01:09:06,580
Yes.

1122
01:09:06,580 --> 01:09:09,889
AUDIENCE: Does the same basic
principle apply for things

1123
01:09:09,889 --> 01:09:12,224
like spontaneous combustion.

1124
01:09:12,224 --> 01:09:13,140
PROFESSOR: Ah, no, no.

1125
01:09:13,140 --> 01:09:14,781
It's kind of different.

1126
01:09:19,849 --> 01:09:21,640
I don't have a whole
lot to say about that,

1127
01:09:21,640 --> 01:09:22,810
about spontaneous combustion.

1128
01:09:22,810 --> 01:09:23,309
Sorry.

1129
01:09:26,640 --> 01:09:29,109
But this is one of
the things that I

1130
01:09:29,109 --> 01:09:31,029
love about quantum
mechanics, the fact

1131
01:09:31,029 --> 01:09:32,830
that it makes so
many things possible,

1132
01:09:32,830 --> 01:09:36,399
the fact that it gives you hope.

1133
01:09:36,399 --> 01:09:40,689
I mean, if things
are looking bleak,

1134
01:09:40,689 --> 01:09:43,420
if you fall over a hill,
for instance-- no, if you've

1135
01:09:43,420 --> 01:09:45,188
fallen off a cliff.

1136
01:09:45,188 --> 01:09:46,229
Things are looking bleak.

1137
01:09:46,229 --> 01:09:48,103
It doesn't look like
you're going to make it.

1138
01:09:48,103 --> 01:09:50,050
Well, quantum mechanics
gives you hope.

1139
01:09:50,050 --> 01:09:52,750
Quantum mechanics says that
there is a chance that the air

1140
01:09:52,750 --> 01:09:56,440
molecules can lift you up and
lift you up to the heavens

1141
01:09:56,440 --> 01:10:00,180
and save you, save your life.