[CARILLON PLAYING "FAR ABOVE CAYUGA'S WATERS"]
[CARILLON ENDS]
[APPLAUSE]
RICHARD FEYNMAN: In the beginning of the history
of experimental observation or any other kind
of observation on scientific things, it's
intuition, which is really based on just experience
with everyday objects, that suggests reasonable
explanations for things.
But as we try to widen and make more consistent
our description of what we see, as it gets
wider and wider and we see a greater range
of phenomena, the explanations become what
we call "laws" instead of simple explanations.
But the one odd characteristic is that they
often seem to become more and more unreasonable
and more and more intuitively far from obvious.
To take an example is the relativity theory.
In which, for instance, the proposition is
that if you think that two things occur at
the same time, that's just a subjective opinion.
Someone else could conclude that those two
events-- those two events, one was before
the other, and that simultaneity is merely
a subjective impression.
Now there's no reason why they should be otherwise,
really.
The things of the direct, everyday experience
involve large numbers of particles or involve
things moving very slowly or involve other
conditions that are very special and represent,
in fact, a very limited experience with nature.
It's a small section, only, that one gets
of natural phenomena from a direct experience.
It's only through the refined measurements
and careful experimentation that we can get
a wider vision.
And then we see unexpected things.
We see things that are far from what we would
guess.
We see things that are very far from what
we could have imagined.
And so our imagination is stretched to the
utmost-- not, as in fiction, to imagine things
which aren't really there.
But our imagination is stretched to the utmost
just to comprehend those things which are
there.
And it's this kind of a situation that I want
to talk about, tonight.
Start, for instance, with the history of light.
At first, light was seen to behave-- it would
appear to behave very much like a rain of
particles-- of corpuscles.
Like rain.
Bullets from a gun.
Same idea.
Then, with further research, it was clear
that that was not right, but that light actually
behaved like waves-- like water waves, for
instance.
And then, in the 20th century, on further
research, it appeared that light actually
behaved in many ways, again, like particles.
In the photoelectric effect, you could count
these particles.
They're called "photons," now, and so forth.
Again, electrons, when they were first discovered,
behaved exactly like particles-- bullets--
very simple.
Further research showed, from electron diffraction
experiments and so on, that they behaved like
waves.
And as time went on, there was a growing confusion
in the question of how the things really behaved--
waves or particles, particles or waves?
But everything looked like both.
Now this growing confusion was resolved in
1925 or '26 with the advent of the correct
equations for quantum mechanics.
And now we know how the electrons and how
light behave.
But what can I call it?
I can't say they behave like a particle wave,
or they behave in typical quantum-mechanical
manners.
There isn't any word for it.
If I say they behave like particles, I give
the wrong impression-- if I say they behave
like waves.
They behave in their own inimitable way.
[LAUGHTER]
Which, technically, could be called a "quantum-mechanical"
way.
They behave in a way that is like nothing
that you have ever seen before.
[LAUGHTER]
Your experience with things that you have
seen before is inadequate-- is incomplete.
The behavior of things on a very tiny scale
is simply different.
They do not behave just like particles.
They do not behave just like waves.
Atoms do not behave like weights hanging on
a spring and oscillating.
Nor do they behave like miniature representations
of the solar system, with little planets going
around in orbit.
Nor does it appear to be somewhat like a cloud
or fog of some sort surrounding the nucleus.
It behaves like nothing that you've seen before.
Well, there's one simplification.
At least electrons behave exactly the same,
in this respect, as photons.
That is, they're both screwy--
[LAUGHTER]
--but in exactly the same way.
How they behave, therefore, 0 takes a great
deal of imagination to appreciate, because
we're going to describe something which is
different than anything you know about.
This-- in that respect, at least-- makes this
perhaps the most difficult lecture of the
series, in the sense that it's abstract--
in the sense that it's not close to experience.
And I cannot avoid that.
Were I to give a series of lectures on the
character of physical law and to leave out,
from this series, the description of the actual
behavior of particles on a small scale, I
would certainly not be doing the job.
Because this thing is completely characteristic
of all of the particles of nature and of a
universal character.
And it is, if you want to hear about the character
of physical law, essential to talk about this
particular aspect.
So it will be difficult.
But the difficulty, really, is psychological
and exists in the perpetual torment that results
from your saying to yourself "But how can
it be like that?"
Which really is a reflection of an uncontrolled,
but I say utterly vain, desire to see it in
terms of some analogy with something familiar.
I will not describe it in terms of an analogy
with something familiar.
I'll simply describe it.
There was a time when the newspapers said
that only 12 men understood the theory of
relativity.
I don't believe there ever was such a time.
There might have been a time when only one
man did, because he's the only guy who caught
on, before he wrote his paper.
But after people read the paper, a lot of
people kind of understood the theory of relativity
in some way or other.
But more than 12.
On the other hand, I think I can safely say
that nobody understands quantum mechanics.
[LAUGHTER]
Now if you appreciate this, and don't take
the lecture too seriously, that you really
have to understand, in terms of some model,
what I'm going to describe, and just relax
and enjoy it, I'm going to tell you what nature
behaves like.
And if you will simply admit that maybe she
does behave like this, you will find her a
delightful, entrancing thing.
So that's the way to look at the lecture--
is not to try to understand-- well, you have
to understand the English, of course.
But in any sense in terms of something else.
And don't keep saying to yourself, if you
can possibly avoid it, "But how can it be
like that?"
Because you'll get down the drain.
You'll get down into a blind alley in which
nobody has yet escaped.
Nobody knows how it can be like that.
So then just let me describe to you the behavior
of electrons or of photons in their typical
quantum-mechanical way.
Now the way I'm going to do this is by a mixture
of analogy and contrast.
If I made a pure analogy, we would fail.
So it must be by analogy and contrast-- two
things that you're familiar with.
And so I make it by analogy and contrast,
first to the behavior of particles, for which
I will use bullets, and second to the behavior
of waves, for which I will use, say, water
waves or sound waves.
So we begin.
First to discuss, in a particular-- what I'm
going to do is I'm going to invent a particular
experiment and first tell how it would behave--
what the situation would be in that experiment
using particles, what you'd expect to happen
if waves were involved, and then what happens
when there are actually electrons or photons
in the system.
And I will just take this one experiment,
which has been designed to contain all of
the mystery of quantum mechanics, to put you
up against the paradoxes and mysteries and
peculiarities of nature, 100%.
Any other situation in quantum mechanics,
it turns out, can always be explained afterwards
by saying "You remember the case of the experiment
with the two holes?
It's the same thing."
And so I'm going to tell you about the experiment
with the two holes, which does contain the
general mystery.
I am avoiding nothing.
I am baring nature in her most elegant and
difficult form.
So I start with bullets.
And all the experiments are going to be in
the same general design, so I'll draw it this
way.
Suppose that we have some source of bullets,
which is-- just represent the source, which
we call the "source," and is, in fact, in
the case of bullets, a machine gun.
[STUDENTS CHUCKLING]
Then we have a plate in front, here, with
a hole in it for the bullets to come out of.
And this plate, in the case of bullets, is
armor plate.
Then a long distance from here, we have another
plate, which I'm drawing only a short distance,
because I haven't got room on the blackboard
for everything.
But this distance is supposed to be much longer
in proportion to the width.
You'll please expand that.
That's a small point, but--
And it has two holes in it.
That's the famous two-hole business.
I am going to talk a lot about these holes,
so I'll talk about this hole as number 1 hole
and the other hole as number 2.
And I'm only drawing it in two dimensions.
You can, if you wish to, imagine these as
round holes in three dimensions.
But just say this is a cross section.
And then, again, a long distance away-- but
we'll draw it relatively short distance, because
of the limitations of this blackboard-- we
have another screen, here, which is just a
backstop of some sort, on which we can put,
in various places, what I will call a "detector."
And I will mark that "detector."
[STUDENTS CHUCKLING]
Which, in the case of the bullets, is a box
of sand, into which the bullets will be caught,
and we can count them.
That's the detector for bullets.
I don't want to have to redraw the experiment
each time, so I'll label everything in this
way.
And then we will be able to catch on to situations
for different cases.
And also I'm going to do experiments in which
I count how many bullets come into this detector,
or box of sand, when the box is here or here
or here or here.
And to describe that, I'll measure the distance
of the box from somewhere down here and call
that x.
And I talk about what happens when we change
x.
It means only you move the doggone thing up
and down.
All right.
Now first I would like to make a few modifications
from real bullets, in two idealizations.
The first is that the machine gun is very
shaky and wobbly, and that the bullets go
in various directions-- not just exactly straight
on and bounce back.
And they can ricochet off the edges of the
slits-- the slits-- rather, the holes in these
armor plates.
And finally-- well, let's say, for instance,
that the bullets have all the same speed or
energy if you want, but that's not very important.
But the most important idealization in which
it differs from real bullets is I want these
bullets to be absolutely indestructible.
So that what we find in the box is not pieces
of lead of some bullet that broke in half,
but we get the whole bullet, please.
So imagine indestructible bullets, or hard
bullets and soft armor plate, or something.
[LAUGHTER]
And now the first thing that we will notice
about bullets is that the things that arrive
come in lumps.
When the energy comes, it's all in one bulletful--
a bang.
If you count the bullets, there's one, two,
three, four bullets.
The things come in lumps.
They're equal in size, we suppose, in this
case.
And when a thing comes into the box, it's
either all in the box or it's not in the box.
It comes in lumps.
Moreover, if I put up two boxes here, I never
get two bullets in the boxes at the same time.
Well, if the gun isn't going off too fast,
and I have enough time between them to see.
Slow down the gun so they go off very slowly--
bing! Bing, bing! Bing!
[STUDENTS CHUCKLING]
Then put the two things here and look very
quickly in the two boxes.
You'll never get two bullets at the same time
in the two boxes, because a bullet is a single,
identifiable lump.
I call that characteristic of the object that
it comes in lumps.
[LAUGHTER]
So the first thing about bullets is that they
come in lumps.
[LAUGHTER]
And now what I'm going to measure is how many
bullets arrive here, on the average, in a
long period of time.
So you wait an hour, and you count how many
bullets are in the can-- in the sand-- and
average that.
Now we call that, if you want-- let's say
we take a definite time, like per hour, and
say the number of bullets that arrive per
hour.
And sometimes you could call that what's called
the "probability of arrival," because it just
gives the chance that a bullet going through
this thing arrives in this particular box.
At least, it's proportional to the chance.
One way to measure is to measure the average
number of bullets that arrive over a period
of time.
Now the number of bullets that arrive in this
box, here, will vary as I vary x.
And I'm going to make a graph here in which
I plot horizontally the number of bullets
that I get if I hold this thing here for an
hour.
And I'll get a curve that will probably look
more or less like this.
Because when the box is behind one of these
holes, it gets a lot of bullets-- the ones
that went through this hole.
And otherwise it gets the ones that went through
this hole.
And if it's a little bit out of line, it doesn't
get as many.
They have to bounce a little off the edges
of the hole.
And so it disappears, like this.
And this is the number that we get in an hour
when both holes are open.
And I call that by an abbreviation "N12,"
which merely means the number which arrive
when hole number 1 and hole number 2 are both
open.
Looks like that [INAUDIBLE].
And I must insist that the number that we're
plotting here doesn't come in lumps.
It can have any size it wants.
For example, there can be two and half bullets
in an hour.
In spite of the fact that the bullets come
in lumps, what I mean by "two and a half bullets
in an hour" is that if you're on a long time,
like 10 hours, you get 25 bullets.
So it's on the average two and a half bullets.
The end can have any size.
It doesn't have to be in lumps, because it's
an average.
I'm sure you're all familiar with the joke
about fact that the average family in the
United States seems to have two and a half
children.
It doesn't mean that there's a half a child
in any family whatever.
The children come in lumps.
[LAUGHTER]
But nevertheless, when you take the average
number for a family, it can be any number
whatsoever.
And so this number N, which is the number
that arrive in this container per hour, on
the average, need not be an integer.
It can be a tenth, which would mean, under
those circumstances, that you have to wait,
on the average, 10 hours, more or less, per
bullet.
So what we measure, then, is the probability
of arrival, which is a technical measure.
The probability of arrival, which is technical
term, really, for the average number that
arrive in a given length of time.
And now, finally, if we go to analyze this
curve, N12, we can interpret it very nicely.
We can interpret it as the sum of two curves,
which I will draw here.
You see, that's why I need the blackboard
wider, because I've got several cases.
So I draw two curves here, one which would
represent what I call "N1"-- the number which
would come if hole number 2 is closed by another
piece of armor plate in front, and so they
all come through number 1.
And N2 would be the number that come through
hole number 2 alone.
So N1 is the number that come through hole
number 1 alone, and N2 is the number that
come through hole number 2 alone, those numbers
being determined by closing the respective
holes.
And then we discover a very important law,
which is that the number that arrive with
both holes open is the number that arrive
by coming through number 1 hole plus the number
that come through number 2 hole.
And this proposition-- the fact that all you
have to do is add these two together-- I call
"nice," or "no interference."
That is, what you get from the two holes open
is the same as you get by simply adding each
hole separately.
That's for bullets.
Done.
We've done with bullets.
All right.
Now I begin again, this time with water waves.
Here is standing some kind of a big mass of
stuff which is being shaken up and down.
This is a long line of barges, or jetties,
with a gap in the water in between.
Perhaps it's better to do it with ripples
than it is to do it with big ocean waves.
It'd sound more sensible.
Wiggle my finger up and down, here, and I
have a little piece of wood, here.
And ripples start out here.
And then I've arranged, in a tank, to put
boards in the way, here, so that I have these
two holes.
And then I have this so-called detector.
And then what I do with the detector-- what
the detector defects is how much the water
is jiggling.
For instance, I put a cork in the water and
measure how it moves up and down.
And what I'm going to measure, in fact, is
the energy of the agitation of the cork, which
is exactly proportional to the energy carried
by the waves.
Also, I forgot to say that this jiggling is
made very regular and perfect so that the
waves are all of the same spacing from one
another.
And then I'll describe what we get under those
circumstances.
For that, I first remark-- well, let's see.
First, we can measure the energy of the cork.
But then another thing is important for water
waves-- for waves-- water waves-- is that
the thing that we're measuring can have any
size at all.
We're measuring the intensity of the waves,
or the energy in the cork.
And if the waves are very quiet-- if the fellow
over here is only jiggling a little bit--
then there'll be very little motion of the
cork, and so on.
No matter how much it is, it's proportional.
So it can have any size.
It doesn't come in lumps.
It's not all there or nothing.
And what we're going to measure is the intensity
of the waves which, to be precise, if you
want, is the energy generated by the waves
at a point.
And now what happens if we measure the intensity--
which I'll draw on a third curve, here-- which
I'll call "I" to remind you it's an intensity
and not a number of particles of any kind,
and "I12" when both holes are open-- is a
curve that looks something like this.
Rather an interesting, complicated-looking
curve, which ought to be symmetrical.
I didn't do too badly, actually.
[STUDENTS CHUCKLING]
Very complicated-looking curve.
That is, if we put the thing in different
places, we get a very, very different intensity
which varies very rapidly in a peculiar manner.
And you're probably all familiar with the
reason for that.
The reason is that the ripples, as they come
out of here, have crests and troughs, spreading
from here.
And they have crests and troughs spreading
from here.
Now if we're at a place which, say, is exactly
in between these two things, so that the two
waves arrive at the same time, the crests
will come on top of each other.
And they'll be plenty of jiggling, which is
the exact opposite of this curve.
[LAUGHTER]
So I'll have to put-- there should be another
bump.
[LAUGHTER]
We have a lot of jiggling right in dead center.
On the other hand, if I were to move to some
point here, since I'm further from hole 2
than hole 1, it takes a little longer for
the waves to come from 2 than from 1.
And when 1 has a crest arriving, the crest
hasn't quite reached there yet from 2.
In fact, it's a trough from 2.
So the water tries to move up, and it tries
to move down from the influences of the waves
coming from the 2 hole.
And the net result is it doesn't move at all,
or practically not at all.
And so we have these low bumps at that place.
And then, if you move still further over,
you get enough delay that when a crest is
here, this other crest is, in fact, one whole
wave behind.
So, in fact, it's a crest that-- two crests
are coming on top of each other, but not the
same crests, so to speak.
The fourth crest from here, and the fifth
crest from there.
So you get a big one again, then a small one,
a big one, a small one, depending upon the
way the crests and troughs "interfere," as
we say.
The word "interference," again, is used in
science in a funny way, because we'll have
what we call a "constructive interference."
When they both interfere here, it makes it
stronger.
Well, they call it "interference," anyway.
But the very important thing is that I12 is
not the same as I1 plus I2.
And we say it shows interference.
Yes, interference.
That's a funny term we use-- "constructive"
and "destructive" interference.
I didn't mention what I1 and I2 look like,
but we can find out by closing this, for instance,
to find I1.
The intention that you get here, if the hole
is closed, is simply the waves from one hole
from which there's no interference.
And that's this curve.
N1 is the same as I1, and the same way, otherwise
I2.
And this curve is quite different than the
sum of these two.
As an matter of fact, the mathematics of this
curve is rather an interesting one.
What is true is this.
That the height of the water, when both holes
are open, is equal to the height that you
would get from number 1 open plus the height
you get from number 2 open.
Thus, if it's a trough, the height from 2
is negative and cancels out the height from
1.
So you can represent it by talking about the
height of the water.
But it turns out that the intensity, in any
case-- for instance, when both holes are open--
is not the same as the height, but it's proportional
to the square of the height.
And it's because of this-- the fact that we're
dealing with the squares-- that we get these
very interesting curves.
All right.
Now we erase the machinery and start over.
This time, we start with electrons.
We have a filament, here.
Tungsten plate, holes in the tungsten plate.
And for a detector, any electrical system
which is sufficiently sensitive to pick up
the charge of an electron arriving with whatever
energy the source had.
Or, if you would prefer, we could use photons.
And this is a black paper with a hole in it,
two holes in another sheet of black paper.
Paper isn't very good, because the fibers
don't make a sharp hole, so use something
better.
And here, for a detector, a photomultiplier
that can detect the individual photons arriving.
Now what happens with either case?
And I'll discuss only the electron case.
The other case is exactly the same-- the case
with the photon-- is this, first.
That what we receive in this electrical detector,
with a sufficiently powerful amplifier behind
it, are clicks.
Click!
Click, click, click!
And so on, with the source here.
Lumps.
Absolutely lumps.
When the click comes, it's a certain size.
And the size is the same if you turn the source
weaker.
The clicks come farther apart, but it's the
same size click.
You turn it up, they go click-click-click-click--
and it jams the amplifier.
So you have to turn it down enough that there
aren't too many clicks for the machinery that
you're using to detect.
Next, if you were to put up another detector
here and listen to both of them, you never
get two clicks at the same time, at least
if the source is weak enough, because of the
precision with which you measure the same
time.
If you cut down the intensity of the source
so they come few and far between, they never
come a click in both detectors.
So that means that the thing which is coming
comes in lumps.
It has a definite size, and it only comes
to one place at a time.
All right.
So for electrons, or for photons-- we'll just
use that-- it comes in lumps.
And therefore what we can do is the same thing
as we did with the bullets.
We measure how many come.
We measure the probability of arrival.
What we do is we hold the detector in a certain
place.
Actually, if you wanted to, although it's
expensive, we could put detectors all over
at the same time and make the whole curve
simultaneously.
But let's suppose we put it in a certain place,
and we measure, at the end of an hour, how
many electrons came.
And we average it.
By the way, if I put detectors all along the
back, here, when one comes, it comes into
1 but not to others.
It just-- one goes off, then the other goes
off, then this goes off, and that one goes
off, and so on.
Just like with bullets.
And we measure, then, the probability of arrival
of the electrons.
And what do we get?
The number of electrons that arrive.
The same kind of an N12 as before.
This is what we get for N12.
[LAUGHTER]
N12.
This is what we get with both holes open.
And that's the phenomenon of nature-- that
she produces the curve which is the same as
you would get from an interference of waves.
But she produces a curve for what?
Not for the energy in a wave, but for the
probability of arrival of one of these lumps.
The mathematics is simple.
You change I to N. And you have to change
H to something else, which is nu.
And you call it something, because it's not
the height of anything.
But in order-- this curve has a simple mathematical
form.
There is an a, which can be represented as
an a1 plus an a2, which we call a "probability
amplitude"-- (MUTTERING) because we don't
know what it means-- to arrive from hole 1,
plus the probability amplitude to arrive from
hole 2.
And you add the two together to get the total
probability amplitude to arrive, and square
it.
Just direct imitation of what happens with
the waves, because we've got to get the same
curve out, so we use the same mathematics.
Let's find out.
I'd better check on one point, though, about
the interference.
I forgot to say what happens if we close one
of the holes.
Let's try to analyze this interesting curve,
which now, for electrons, I erase all the
stuff with the light.
Well, everything with light is erased.
And now we're talking about electrons.
This curve isn't important in our case.
This is the number which arrive.
Now we would like to analyze this curve.
And we try this.
We say maybe it comes-- we can analyze this
by thinking that the electrons come through
this hole or through the other.
So we can close one hole and measure how many
come through hole number 1, and we get that
curve.
Or we can close this hole and measure how
many come through hole number 2, and we get
that curve.
And these two added together is not this.
And so this is not the same as N1 plus N2.
And it does show interference.
It shows interference.
And, in fact, the mathematics is given by
this funny formula that the probability of
arrival is the square of an amplitude, which
itself is the sum of two pieces.
The question is, how can that come about?
That when they go through hole 1, they would
be distributed this way.
When they go through hole 2, they would be
distributed that way.
How can it be that when both holes are open,
you don't get the sum of the two?
For instance, if I hold a detector at this
point, here, I get practically nothing.
If I close one of the holes, I get plenty.
If I close the other hole, I get something.
If I leave both holes open, I get nothing.
If I let them go through both holes, they
won't come anymore.
Or take the point in the center.
You can show that that's higher than the sum--
than it was in the other case-- than the sum
of these two.
I get more here, when both holes are open,
than I would get with either one of the two
closed.
Now you might think that, if you were clever
enough, you could argue that they have some
way of going around through the holes, back
and forth, and they do something complicated,
or it splits in half and goes through the
two holes, and so forth, in order to explain
this phenomenon.
Nobody, however, has succeeded to get an explanation
of this that's satisfactory.
Because the mathematics in the end are so
very simple.
The curve is so very simple.
I will summarize, then, by saying that electrons
arrive in lumps, like particles.
But the probability of arrival of these lumps
is determined like the intensity of waves
would be.
And it is in this sense that the electron
behaves, as you might say, sometimes like
a particle and sometimes like a wave.
It behaves in these two different ways at
the same time.
And that's all there is to say.
I give a mathematical description to figure
out the probability of arrival of electrons
under any circumstances, and so on.
And that would, in principle, be the end of
the lecture.
Except that there are a number of subtleties
involved in the fact that nature works this
way.
There's a number of peculiar things.
And I would like to discuss those peculiarities,
because they may not be self-evident at this
point.
So, to discuss the subtleties, we begin by
discussing a proposition which we would have
thought to use since these things are lumps.
Since what comes is always one complete nah,
which I'll call an "electron"-- one complete
lump, one complete electron-- it's obvious
that it's reasonable--
[LAUGHTER]
--that either an electron arrives-- or "goes,"
let's say.
That either an electron goes through hole
number 1, or it goes through hole number 2.
That seems like-- it goes through hole number
2.
That seems very obvious, that it can't do
anything else, if it's a lump.
And I'm going to discuss this proposition,
so I have to give it a name.
I'll call it "proposition A."
Now we've already discussed, a little bit,
what happens with proposition A. If it were
true that an electron either goes through
hole number 1 or it goes through hole number
2, then the total number which arrive here
would have to be analyzable as a sum of two
contributions.
The total number which arrive here will be
the number that come here via hole 1 plus
the number that come via hole 2.
And since this curve cannot easily be analyzed
as the sum of two pieces in such a nice manner,
and since the experiments which determine
how many would have arriven-- "would have
arrived"--
[STUDENTS CHUCKLING]
If only hole number 1 were open, don't give
the result that this number is the sum of
these two.
It is obvious that we should conclude that
this proposition is false.
It is not true that the electron either comes
through hole number 1 or hole number 2.
Maybe it divides itself in half, temporarily,
or something.
So proposition A is false.
That's logic.
Unfortunately, or otherwise, we can test logic
by experiment.
So we just have to do, to find out whether
it's true or not that the electrons come through
hole 1 and hole 2.
Or maybe they go around through both holes,
or they split up, or something.
All we have to do is watch them.
To watch them, we need light.
So we put, back here, behind the holes, a
source of light.
A very intense light.
Light is scattered by electrons.
It is bounced off electrons.
In other words, you can see electrons as they
go by, if the light's strong enough.
So we stand back here, and we look to see
whether we see, when the electron is counted,
here, a flash-- or have seen, the moment before
the electrons got here-- a flash behind hole
1 or a flash behind hole 2.
Or maybe a sort of a half flash in each place
at the same time.
Because we're going to find out, now, how
it goes-- by looking.
Well, you turn on the light and look.
And lo, you discover that you see flashes
behind either one hole or the other hole every
time you get a count here.
Every time there's a count here, you see a
flash behind number 1 or behind number 2.
What you see is that the electron come 100%
complete through hole 1 or through hole 2,
when you look.
Kind of a paradox.
Well, let's squeeze nature into some kind
of a difficulty, here.
I'll show you what we're gonna do, see?
[STUDENTS CHUCKLING]
We're going to keep the light on.
We're gonna watch.
And we're going to count how many electrons
come through.
And we're going to make two columns.
I'll watch the holes very carefully while
you please count how many are arriving in
the detector.
[STUDENTS CHUCKLING]
All right, you say, one arrived!
I said, I saw that when it went through hole
number 1.
[LAUGHTER]
But we put here two columns, which is column
1 for number 1 hole and number 2 hole.
And every time you get one, you tell me you
got one, I have seen it, of course.
And I say either number 1 or 2.
The first one was 1.What's the next one?
Number 2.
All right.
Number 2.
Number 2.
Number 1.
And so on.
Hmm?
So as we watch the electrons-- as I watch
the electrons-- for every one that you count,
I can separate them experimentally into two
columns-- them what have arrived via hole
1, and those-- (ASIDE) I know the English
isn't right-- I'm just trying-- (FULL VOICE)
that arrive--
[STUDENTS CHUCKLING]
--via hole 2.
So the number-- the total number that arrives--
Well, first, what does this column look like,
when you add it all together for different
position here, which is just the number that
are supposed to have come through 1?
I watch behind 1, and what do I see?
I see this curve.
That column is distributed this way.
Just like we thought when we closed hole 2.
It works the same way whether we're looking
or not.
If we close hole 2, we get the same distribution
in those that arrived as if we are watching.
And likewise, the number in this column that
are supposed to have arrived via hole number
2 is also this simple curve.
Now look.
The total number which arrives has to be the
total number.
I'm just counting little marks.
It has to be the sum of this number plus that
number.
The total number which arrive absolutely has
to be the sum of these two.
It has to be distributed this way.
When I said it was distributed this way, it's
distributed this way.
[LAUGHTER]
It really is, of course.
It has to be.
And it is.
It's distributed this way.
[STUDENTS CHUCKLING]
If, then, we mark with a prime the results
when a light is lit-- prime means with the
light lit-- then we find N1 prime is practically
the same as N1 without the light.
And N2 prime is almost the same as N2.
But the number that we see when the light
is on is equal to the number that we see through
1 plus the number that we see through 2.
This is the result that we get when the light
is on.
In other words, we get a different answer,
whether I turned on the light or not.
If I had the light turned on, this is the
distribution which you measure over here.
If I turn off the light, this is the distribution
that you measure over here.
Turn on the light, this is the answer.
Turn off the light, that's the answer.
See, nature's squeezed out!
[STUDENTS CHUCKLING]
Now we could say, then, that the light affects
the result.
If the light is on, you get a different answer
than if the light is off.
If you want to, you can say they are light
effects.
It does affect-- in fact, we found, by this
experiment, we get a difference with the light
on and off.
Light affects the behavior of electrons.
If you want to talk about the motion of the
electrons through here-- which is a little
inaccurate-- you can.
You can say that the light affects the motion
so that those which might have arrived at
the maximum have somehow been deviated or
kicked by the light and arrived at the minimum,
instead smoothing the curve to produce this
thing.
You see, electrons are very delicate.
Although, when you're looking at a baseball
and you shine light on it, it doesn't make
any difference.
The baseball goes the same way.
Electrons are very flimsy-- very delicate.
And when you shine a light on them, it's a
little tough on the electrons.
It knocks them about a bit.
And instead of doing that, they do this, because
you turn the light on so strong.
You hit 'em with a hammer.
It's not just a delicate thing, like when
you're looking at a baseball with light.
There you are, hitting them with a hammer.
What you do is you turn up the light too strong.
Turn it weaker and weaker and weaker, until
it's very dim.
And then use very careful detectors that can
see very dim light.
And look with the dim light.
Now, as the light gets dimmer and dimmer,
you can't expect with very, very, very weak
light to affect the electron so completely
as to change the pattern 100% from this pattern
to this pattern.
As the light gets weaker and weaker and weaker,
somehow it should get more and more like no
light at all.
And how, then, does this turn into that?
Well, it turns out that light is not like
a wave of water.
But light also comes in particle-like characters
called "photons."
And as you turn down the intensity of the
light, you're not turning down this effect.
You're turning down the number of photon particle-like
things that are coming out of the source.
So as I turn down the light, I'm getting fewer
and fewer photons.
The least I can scatter from an electron is
one photon.
And if I have too few photons, well, sometimes
the electron would get through.
And it just happens there wasn't enough light.
There was no photon coming by.
I didn't see it.
So a very weak light doesn't mean a small
disturbance.
It just means a few photons.
And what happens is that I have to invent
a third column.
You see, you get a click over here.
I say, I saw that one.
That was in number 1 hole.
This was behind hole number 2.
Then another comes, I'm sorry.
I didn't see that.
There wasn't enough light to give a photon,
at that time.
So there must be a third column under "didn't
see."
[LAUGHTER]
And when the light is very strong, there are
very few in there.
And when the light is very weak, most of them
end in there.
So that there are three columns-- this one,
this one, and sometimes in here.
Now you can guess what happens.
The ones I do see are distributed this way.
The ones I didn't see are distributed that
way.
[STUDENTS CHUCKLING]
And as I turn the light weaker and weaker,
well, I see less and less of them.
A greater and greater fraction are not seen,
and the actual curve, in any case, is a sort
of a mixture of this and this.
And as the light gets weaker so that fewer
and fewer are seen, it gets more and more
like that, in a continuous fashion.
So, in this case, if the electrons are not
seen and nothing bounced off the light, under
those circumstances you get this complicated
pattern for those electrons which were not
seen.
The ones in the column "didn't see" are exactly
distributed in this complicated way.
And the other two columns are in these two
ways, here.
Now you say, I got another way to measure
which hole it goes through.
And I'm sorry I haven't got enough time to
discuss a large number of different inventions
that you might have to find out which hole
the electron went through and what happens
in each case.
It always turns out, however, that it's impossible
to arrange the light in any way so that you
can tell through which hole the thing is going
without disturbing the pattern of arrival
of electrons from this form to this form without
destroying the interference.
And not only light, but anything else.
You use neutrinos, you use anything.
In principle, it's impossible to do it.
You can, if you want, invent a way to tell
which hole the electron's going through.
Then it turns out it's going through one or
the other.
But if you try to make that instrument so
that, at the same time, it doesn't disturb
the motion of the electrons, well, then what
happens is you get back-- you can't tell anymore
which one it goes through, and you get this.
If you can tell, you get this.
Heisenberg noticed, when he discovered the
laws of quantum mechanics, that the new laws
of nature that he'd discovered could only
be consistent if there was some basic limitation
to our experimental abilities that had not
been previously recognized.
In other words, you can't experimentally be
as delicate as you wish.
And he proposed his uncertainty principle,
which, stated in terms of our experiment,
is the following.
He stated it another way, but they're exactly
equivalent.
You can get from one to the other.
But unfortunately I haven't time to explain
that.
In our experiment, his uncertainty principle
would be stated in this manner.
It is impossible to design any apparatus whatsoever
to determine which hole the electron passes
and one succeeds in determining which hole
the electron passes-- passes-- which-- through
which hole the elect-- which can determine
who which hole the electron passes that will
not, at the same time, disturb the electron
enough to destroy the interference pattern.
And no one has found a way around this.
And I'm sure you're itching with inventions
as to methods of detecting which hole the
electron went through.
But if each one of them is analyzed carefully,
you'll find out there's something the matter
with it, and that if, without disturbing the
electron, you think you could do it.
But it turns out there's always something
the matter.
And you can account for the difference in
the patterns due to the disturbance of the
instruments used to determine through which
hole the electron comes.
Now this, therefore, is a basic characteristic
of nature and tells us something about everything.
If a new particle is found tomorrow, the kaon--
actually, it's already been found.
Something.
Give it a name.
Let's say a kaon.
And I use kaons to interact with electrons
to determine which hole the electron is going
through.
I already know, ahead of time-- I hope-- enough
about the behavior of the kaon to say that
it cannot be of such a type that I could tell
through which hole the electron would go without,
at the same time, producing a disturbance
on the electron to change the pattern from
here to here.
The uncertainty principle is used as a general
principle to guess ahead at many of the characteristics
of unknown objects.
They are kind of limited in their character.
Well, then, let's go back.
What about this proposition A?
Does it go either through one hole or the
other, or not?
Well, physicists have the convention-- a way
of avoiding the pitfalls which exist.
And they make their game-- their rules of
thinking-- as follows.
That if you have an apparatus which is capable
of telling which hole the electron goes through--
and you can have such apparati-- then one
can say that it either goes through one hole
or the other.
And it does, when you look.
It always is going through one hole or the
other, when you look.
But when you do not try to determine, or you
have no disturbance-- no apparatus-- there
to determine through which hole the thing
goes, under those circumstances you cannot
say that it either goes through one hole or
the other.
You can always say it, provided you stop thinking
immediately and don't make any deduction from
it.
We prefer not to say it, rather than to stop
thinking at the moment.
In other words, when we don't look, we can't
say through which hole it's going.
But if you try to look to see, you find it
always goes through one hole or the other.
Still, to conclude that goes either through
one hole or the other when you're not looking
is to produce an error in prediction.
And that is the logical tightrope on which
we have to walk, if we wish to interpret nature.
This proposition that I'm talking about is
more general.
It's not just for two holes.
It's a general proposition-- reads something
like this.
That the probability of any event in an ideal
experiment-- that just means that everything
is specified as well as it can be-- the probability
of an event is the square of something-- which
I call "A" here-- is called the "probability
amplitude."
And when an event can occur in several alternative
ways, the probability amplitude, this A number,
is the sum of the As for each of the various
alternatives.
And finally, if an experiment is performed
which is capable of determining which alternative
is taken, the probability of the event is
the sum of the probabilities for each alternative.
That is, you lose the interference.
Now the question is, how does it really work?
What machinery is actually producing this
thing?
Well, nobody knows any machinery.
Nobody can give you a deeper explanation of
this phenomenon than I have given.
That as a description of it.
They can give you a wider explanation, in
the sense that they can do more examples to
show how it's impossible to tell which hole
it goes and at the same time not destroy the
interference pattern.
They can give a wider class of experiments
than just the two-slit interference experiment,
and so on.
But they're all just repeating the same thing
to drive it in.
It's not any deeper; it's only wider.
The mathematics can be made more precise.
You can mention that they're complex numbers
instead of real numbers, and a couple of other
minor points which have nothing to do with
the main idea.
And the deep mystery is what I describe.
And no one can go any deeper today, but only
wider.
Now I mentioned probabilities in this calculation.
What we're calculating here-- this curve--
is the probability of arrival of an electron.
The question is, is there any way to determine
where it really arrives?
We are not adverse to using the theory of
probability-- that is, calculating odds--
when a situation is very complicated.
You throw up a die, and it spins so many times
in the air, with the various resistance and
atoms and all this complicated business that
we're perfectly willing to allow that we don't
know enough details.
And so we calculate the odds that the thing
will come this way or that way.
But here what we're proposing, is it not,
is that there be probability all the way back
at the fundamental laws.
That in the fundamental laws of physics, there
are odds.
For example, suppose that I have an experiment
so set up that with the light out I get this
interference situation and know that.
Then I'd say that, with the light on, I can't
predict through which hole it will go.
I only know that each time I look it will
be one hole or the other.
But there is no way to predict ahead of time
through which hole it goes.
The future, in other words, is unpredictable.
It is impossible to predict in any way, from
any information ahead of time, through which
the thing will go or which hole it will be
seen behind.
That means that physics has kind of given
up, if the original purpose was-- (ASIDE)
and everybody thought it was-- to know enough
that in a given situation you could predict
what's going to happen next.
Given the circumstances, you can predict what
happens.
Here are the circumstances.
Source, strong light source.
Tell me which hole-- behind which hole will
I see the electron.
You say, well, the reason you can't tell through
which hole you're going to see the electron
is it's determined by some very complicated
things, back here.
If I knew enough about that electron-- it
has internal wheels, internal gears, and so
forth-- and that this is what determines through
which hole it goes.
So it's 50-50 probability, because, like a
die, it's set sort of at random.
And that if I were to have studied it carefully
enough, your physics is incomplete.
If you get a complete-enough physics, then
you'll be able to predict through which hole
it goes.
That's the "hidden-variable theory"-- so called.
Well, that's not possible.
It is not due to a lack of detailed knowledge
that we cannot make the prediction.
Because I said that if I didn't turn on the
light I should get this interference pattern.
If I have a circumstance in which I get that
interference pattern, then it is impossible
to analyze it, in terms of saying it goes
through here or here.
Because that curve is so simple-- mathematically
a different thing than the contribution of
this and this as probabilities.
So if it were possible for you to have determined
through which hole it was going to go if I
had the light on, the fact that I had the
light on hasn't got anything to do with it.
Whatever gears there are back here that you
observed which permitted you to tell me whether
it was going to go through 1 or 2, you could
have observed if I had the light off.
And therefore you could have told me, with
the light off, which hole-- each time an electron
goes-- which hole it's going to go through.
But if you can do this, then that curve would
have to be represented as the sum of those
that goes through there and those that goes
through there.
And it ain't.
And therefore it's impossible to have any
information ahead of time as to which hole
it's going to go through when the light is
out-- or when the light is on or out, in a
circumstance when the experiment is set up
that it can produce this interference pattern.
So it is not a lack of unknown gears-- a lack
of internal complications-- that make nature
have probability in it.
It seems to be, in some sense, intrinsic.
Someone has said it this way.
Nature herself doesn't know which way the
electron is going to go.
A philosopher once said-- pompously-- (POMPOUSLY)
"It is necessary for the very existence of
science that the same conditions always produce
the same result."
(NORMAL VOICE) Well, they don't.
[LAUGHTER]
You can set up the electrons in any way--
I mean, you set up the circumstance, here,
in the same conditions, every time, and you
cannot predict behind which hole you'll see
the electron.
And yet the science goes on, in spite of it,
although the same conditions don't produce
the same results.
That makes us unhappy that we can't predict
exactly what'll happen.
Incidentally, you can make a circumstance
which is very dangerous and serious and man
must know, and still can't predict.
For instance, we could cook up-- although
we would rather not-- but we could cook up
a scheme by which we arrange photo cells so
that if it-- one electron's going to go through.
If we see it behind hole number 1, we set
off the atomic bomb and start World War III.
If we see it behind hole 2, we just make peace
feelers-- and delay the war a little longer.
[STUDENTS CHUCKLING]
Then the thing is that the future of man would
then be dependent upon something which no
amount of science can predict.
[INAUDIBLE] the future is unpredictable.
What is necessary for the very existence of
science and so forth, and what the characteristics
of nature are, are not to be determined by
pompous preconditions.
They are determined, always, by the material
with which we work-- by nature herself.
We look and we see what we find.
And we cannot say ahead of time-- successfully--
what it's going to look like.
The most reasonable possibilities turn out
often not be the situation.
What is necessary for the very existence of
science is just the ability to experiment,
the honesty in reporting results-- the results
must be reported without somebody saying what
they'd like the results to have had been,
rather than [INAUDIBLE].
And finally, an important thing is the intelligence
to interpret the results but-- important point
about this intelligence is-- that it should
not be sure ahead of time about what must
be.
Now it can be prejudiced and say "that's very
unlikely.
I don't like that."
Prejudice is different than absolute certainty.
I don't mean absolute prejudice; just bias.
But not strict bias.
Not complete prejudice.
As long as you're biased, it doesn't make
any difference.
Because if the fact is true, there will be
a perpetual accumulation of experiments that
perpetually will annoy you until they cannot
be disregarded anymore.
Only can be disregarded if you're absolutely
sure, ahead of time, of some precondition
that science has to have.
In fact, it is necessary for the very existence
of science that minds exist which do not allow
that nature must satisfy some preconceived
conditions like those of our philosopher.
Thank you.
[APPLAUSE]
[CARILLON PLAYING "FAR ABOVE CAYUGA'S WATERS"]
[CARILLON ENDS]
