[BELLS RINGING]
[AUDIENCE CHATTERING]
[APPLAUSE]
RICHARD FEYNMAN: What I want to talk to you
about tonight is strictly speaking not on
the character of physical laws.
Because one might imagine at least that one's
talking about nature, when one's talking about
the character of physical laws.
But I don't want to talk about nature, but
rather how we stand relative to nature now.
I want to tell you what we think we know and
what there is to guess and how one goes about
guessing it.
Someone suggested that it would be ideal if,
as I went along, I would slowly explain how
to guess the laws and then create a new law
for you right as I went along.
[LAUGHTER]
I don't know whether I'll be able to do that.
But first, I want to tell about what the present
situation is, what it is that we know about
the physics.
You think that I've told you everything already,
because in all the lectures, I told you all
the great principles that are known.
But the principles must be principles about
something.
The principles that I just spoke of, the conservation
of energy-- the energy of something-- and
quantum mechanical laws are quantum mechanical
principles about something.
And all these principles added together still
doesn't tell us what the content is of the
nature, that is, what we're talking about.
So I will tell you a little bit about the
stuff, on which all these principles are supposed
to have been working.
First of all is matter, and remarkably enough,
all matter is the same.
The matter of which the stars are made is
known to be the same as the matter on the
earth, by the character of the light that's
emitted by those stars-- they give a kind
of fingerprint, by which you can tell that
it's the same kind of atoms in the stars.
As on the earth, the same kind of atoms appear
to be in living creatures as in non-living
creatures.
Frogs are made out of the same goop-- in different
arrangement-- than rocks.
So that makes our problem simpler.
We have nothing but atoms, all the same, everywhere.
And the atoms all seem to be made from the
same general constitution.
They have a nucleus, and around the nucleus
there are electrons.
So I begin to list the parts of the world
that we think we know about.
One of them is electrons, which are the particles
on the outside the atoms.
Then there are the nuclei.
But those are understood today as being themselves
made up of two other things, which are called
neutrons and protons.
They're two particles.
Incidentally, we have to see the stars and
see the atoms and they emit light.
And the light is described by particles, themselves,
which are called photons.
And at the beginning, we spoke about gravitation.
And if the quantum theory is right, then the
gravitation should have some kind of waves,
which behave like particles too.
And they call those gravitons.
If you don't believe in that, just read gravity
here, it's the same.
Now finally, I did mention that in what's
called beta decay, in which a neutron can
disintegrate into a proton and an electron
and a neutrino-- or alien anti-neutrino--
there's another particle, here, a neutrino.
In addition to all the particles that I'm
listing, there are of course all the anti-particles.
But that's just a quick statement and takes
care of doubling the number of particles immediately.
But there's no complications.
Now with the particles that I've listed here,
all of the low energy phenomena, all of in
fact ordinary phenomena that happen everywhere
in the universe as far as we know, with the
exception of here and there some very high
energy particle does something, or in a laboratory
we've been able to do some peculiar things.
But if we leave out those special cases, all
ordinary phenomena are presumably explained
by the action and emotions of these kinds
of things.
For example, life itself is supposedly made,
if understood-- I mean understandable in principle--
from the action of movements of atoms.
And those atoms are made out of neutrons,
protons, and electrons.
I must immediately say that when we say, we
understand it in principle, I only mean that
we think we would, if we could figure everything
out, find that there's nothing new in physics
to be discovered, in order to understand the
phenomena of light.
Or, for instance, for the fact that the stars
emit energy-- solar energy or stellar energy--
is presumably also understood in terms of
nuclear reactions among these particles and
so on.
And all kinds of details of the way atoms
behave are accurately described with this
kind of model, at least as far as we know
at present.
In fact, I can say that in this range of phenomena
today, as far as I know there are no phenomena
that we are sure cannot be explained this
way, or even that there's deep mystery about.
This wasn't always possible.
There was, for instance, for a while a phenomenon
called super conductivity-- there still is
the phenomenon-- which is that metals conduct
electricity without resistance at low temperatures.
And it was not at first obvious that this
was a consequence of the known laws with these
particles.
But it turns out that it has been thought
through carefully enough.
And it's seen, in fact, to be a consequence
of known laws.
There are other phenomena, such as extrasensory
perception, which cannot be explained by this
known knowledge of physics here.
And it is interesting, however, that that
phenomena had not been well-established, and--
[LAUGHTER]
--That we cannot guarantee that it's there.
So if it could be demonstrated, of course
that would prove that the physics is incomplete.
And therefore, it's extremely interesting
to physicists, whether it's right or wrong.
And many, many experiments exist which show
it doesn't work.
The same goes for astrological influences.
If it were true that the stars could affect
the day that it was good to go to the dentist,
then-- because in America we have that kind
of astrology-- then it would be wrong.
The physics theory would be wrong, because
there's no mechanism understandable in principle
from these things that would make it go.
And that's the reason that there's some skepticism
among scientists, with regard to those ideas.
[LAUGHTER]
On the other hand, in the case of hypnotism,
at first it looked like that also would be
impossible, when it was described incompletely.
But now that it's known better, it is realized
that it is not absolutely impossible that
hypnosis could occur through normal physiological
but unknown processes.
It doesn't require some special, new kind
of course.
Now, today although the knowledge or the theory
of what goes on outside the nucleus of the
atom seems precise and complete enough, in
the sense that given enough time, we can calculate
anything as accurately as it can be measured,
it turns out that the forces between neutrons
and protons, which constitute the nucleus,
are not so completely known and are not understood
at all well.
And that's what I mean by-- that is, that
we cannot today, we do not today understand
the forces between neutrons and protons to
the extent that if you wanted me to, and give
me enough time and computers, I could calculate
exactly the energy levels of carbon or something
like that.
Because we don't know enough about that.
Although we can do the corresponding thing
for the energy levels of the outside electrons
of the atom, we cannot for the nuclei.
So the nuclear forces are still not understood
very well.
Now in order to find out more about that,
experimenters have gone on.
And they have to study phenomena at very high
energy, where they hit neutrons and protons
together at very high energy and produced
peculiar things.
And by studying those peculiar things, we
hope to understand better the forces between
neutrons and protons.
Well, a Pandora's box has been opened by these
experiments, although all we really wanted
was to get a better idea of the forces between
neutrons and protons.
When we hit these things together hard, we
discover that there are more particles in
the world.
And as a matter of fact, in this column there
was plus over four dozen other particles have
been dredged up in an attempt--
[LAUGHTER]
--to understand these.
And these four dozen other are put in this
column, because they've very relevant to the
neutron proton problem.
They interact very much with neutrons and
protons.
And they've got something to do with the force
between neutrons and protons.
So we've got a little bit too much.
In addition to that, while the dredge was
digging up all this mud over here, it picked
up a couple of pieces that are not wanted
and are irrelevant to the problem of nuclear
forces.
And one of them is called a mu meson, or a
muon.
And the other was a neutrino, which goes with
it.
There are two kinds of neutrinos, one which
goes with the electron, and one which goes
with the mu meson.
Incidentally, most amazingly, all the laws
of the muon and its neutrino are now known.
As far as we can tell experimentally, the
law is they behave precisely the same as the
electron and its neutrino, except that the
mass of the mu meson is 207 times heavier
than the electron.
And that's the only difference known between
those objects.
But it's rather curious.
But I can't say anymore, because nobody knows
anymore.
Now four dozen other particles is a frightening
array-- plus the anti-particles-- is a frightening
array of things.
But it turns out, they have various names,
mesons, pions, kaons, lambda, sigma-- four
dozen particles, there are going to be a lot
of names.
[LAUGHTER]
But it turns out that these particles come
in families, so it helps us a little bit.
Actually, some of these so-called particles
last such a short time that there are debates
whether it's in fact possible to define their
very existence and whether it's a particle
or not.
But I won't enter into that debate.
In order to illustrate the family idea, I
take the two-part cases of a neutron and a
proton.
The neutron and proton have the same mass,
within 0.10% or so.
One is 1836, the other is 1839 times as heavy
as an electron roughly, if I remember the
numbers.
But the thing that's very remarkable is this.
That for the nuclear forces, which are the
strong forces inside the nucleus, the force
between a pair of protons-- two protons--
is the same as between a proton and a neutron
and is the same again between a neutron and
a neutron.
In other words, for the strong nuclear forces,
you can't tell a proton from a neutron.
Or a symmetry law-- neutrons may be substituted
for protons, without changing anything, provided
you're only talking about the strong forces.
If you're talking about electrical forces,
oh no.
If you change a neutron for a proton, you
have a terrible difference.
Because the proton carries electrical charge,
and a neutron doesn't.
So by electric measurement, immediately you
can see the difference between a proton and
a neutron.
So this symmetry, that you can replace neutrons
by protons, is what we call an approximate
symmetry.
It's right for the strong interactions in
nuclear forces.
But it's not right in some deep sense of nature,
because it doesn't work for the electricity.
It's just called a partial symmetry.
And we have to struggle with these partial
symmetries.
Now the families have been extended.
It turns out that the substitution neutron
proton can be extended to substitution over
a wider range of particles.
But the accuracy is still lower.
You see, that neutrons can always be substituted
for protons is only approximate.
It's not true for electricity.
And that the wider substitutions that have
been discovered are legitimate is still more
poor, a very poor symmetry, not very accurate.
But they have helped to gather the particles
into families, and thus to locate places where
particles are missing and to help to discover
the new ones.
This kind of game, of roughly guessing at
family relations and so on, is illustrative
of a kind of preliminary sparring which one
does with nature, before really discovering
some deep and fundamental law.
Before you get the deeper discoveries, examples
are very important in the previous history
of science.
For instance, Mendeleev's discovery of the
periodic table for the elements is analogous
to this game.
It is the first step, but the complete description
of the reason for the periodic table came
much later, with atomic theory.
In the same way, organization of the knowledge
of nuclear levels and characteristics was
made by Maria Mayer and Jensen, in what they
call the shell model of nuclei some years
ago.
And it's an analogous game, in which a reduction
of a complexity is made by some approximate
guesses.
And that's the way it stands today.
In addition to these things, then we have
all these principles that we were talking
about before.
Principle of relativity, that the things must
behave quantum mechanically.
And combining that with the relativity that
all conservation laws must be local.
And so when we put all these principles together,
we discover there are too many.
They are inconsistent with each other.
It seems as if, if we add quantum mechanics
plus relativity plus the proposition that
everything has to be local plus a number of
tacit assumptions-- which we can't really
find out, because we are prejudiced, we don't
see what they are, and it's hard to say what
they are.
Adding it all together we get inconsistency,
because we really get infinity for various
things when we calculate them.
Well, if we get infinity, how will we ever
agree that this agrees with nature?
It turns out that it's possible to sweep the
infinities under the rug by a certain crude
skill.
And temporarily, we're able to keep on calculating.
But the fact of the matter is that all the
principles that I told you up till now, if
put together, plus some tacit assumptions
that we don't know, it gives trouble.
They cannot mutually consistent, nice problem.
An example of the tacit assumptions that we
don't know what the significance is, such
propositions are the following.
If you calculate the chance for every possibility--
there is 50% probably this will happen, 25%
that'll happen-- it should add up to one.
If you add all the alternatives, you should
get 100% probability.
That seems reasonable, but reasonable things
are where the trouble always is.
Another proposition is that the energy of
something must always be positive, it can't
be negative.
Another proposition that is probably added
in, in order before we get inconsistency,
is what's called causality, which is something
like the idea that effects cannot proceed
their causes.
Actually, no one has made a model, in which
you disregard the proposition about the probability,
or you disregard the causality, which is also
consistent with quantum mechanics, relativity,
locality, and so on.
So we really do not know exactly what it is
we're assuming that gives us the difficulty
producing infinities.
OK, now that's the present situation.
Now I'm going to discuss how we would look
for a new law.
In general, we look for a new law by the following
process.
First, we guess it.
[LAUGHTER]
Then, we compute-- well, don't laugh, that's
really true.
Then we compute the consequences of the guess,
to see what, if this is right, if this law
that we guessed is right, we see what it would
imply.
And then we compare those computation results
to nature.
Or we say, compare to experiment or experience.
Compare it directly with observation, to see
if it works.
If it disagrees with experiment, it's wrong.
And that simple statement is the key to science.
It doesn't make any difference how beautiful
your guess is, it doesn't make any difference
how smart you are, who made the guess, or
what his name is.
If it disagrees with experiment, it's wrong.
That's all there is to it.
[LAUGHTER]
It's true, however, that one has to check
a little bit, to make sure that it's wrong.
Because someone who did the experiment may
have reported incorrectly.
Or there may have been some feature in the
experiment that wasn't noticed, like some
kind of dirt and so on.
You have to obviously check.
Furthermore, the man who computed the consequences
may have been the same one that made the guesses,
may have made some mistake in the analysis.
Those are obvious remarks.
So when I say, if it disagrees with experiment,
it's wrong, I mean after the experiment has
been checked, the calculations have been checked,
and the thing has been rubbed back and forth
a few times to make sure that the consequences
are logical consequences from the guess, and
that, in fact, it disagrees with our very
carefully checked experiment.
This will give you somewhat the wrong impression
of science.
It means that we keep on guessing possibilities
and comparing to experiments.
And this is-- to put an experiment on a little
bit weak position.
It turns out that the experimenters have a
certain individual character.
They like to do experiments, even if nobody's
guessed yet.
[LAUGHTER]
So it's very often true that experiments in
a region in which people know the theorist
doesn't know anything, nobody has guessed
yet-- for instance, we may have guessed all
these laws, but we don't know whether they
really work at very high energy because it's
just a good guess that they work at high energy.
So experimenters say, let's try higher energy.
And therefore experiment produces trouble
every once in a while.
That is it produces a discovery that one of
things that we thought of is wrong, so an
experiment can produce unexpected results.
And that starts us guessing again.
For instance, an unexpected result is the
mu meson and its neutrino, which was not guessed
at by anybody, whatever, before it was discovered.
And still nobody has any method of guessing,
by which this is a natural thing.
Now you see, of course, that with this method,
we can disprove any definite theory.
If you have a definite theory and a real guess,
from which you can really compute consequences,
which could be compared to experiment, then
in principle, we can get rid of any theory.
We can always prove any definite theory wrong.
Notice, however, we never prove it right.
Suppose that you invent a good guess, calculate
the consequences, and discover that every
consequence that you calculate agrees with
experiment.
Your theory is then right?
No, it is simply not proved wrong.
Because in the future, there could be a wider
range of experiments, you can compute a wider
range of consequences.
And you may discover, then, that the thing
is wrong.
That's why laws like Newton's Laws for the
Motion of Planets lasts such a long time.
He guessed the law of gravitation, tackling
all the kinds of consequences for the solar
system and so on, compared them to experiment,
and it took several years before the slight
error of the motion of Mercury was developed.
During all that time, the theory had been
failed to be proved wrong and could be taken
to be temporarily right.
But it can never be proved right, because
tomorrow's experiment may succeed in proving
what you thought was right, wrong.
So we never are right.
We can only be sure we're wrong.
[LAUGHTER]
However, it's rather remarkable that we can
last so long, I mean to have some idea which
will last so long.
Incidentally, some people, one of the ways
of stopping the science would be to only do
experiments in the region where you know the
laws.
But the experimenters search most diligently
and with the greatest effort in exactly those
places where it seems most likely that we
can prove their theories wrong.
In other words, we're trying to prove ourselves
wrong as quickly as possible.
Because only in that way do we find workers
progress.
For example, today among ordinary low energy
phenomena, we don't know where to look for
trouble.
We think everything's all right.
And so there isn't any particular big program
looking for trouble in nuclear reactions or
in superconductivity.
I must say, I'm concentrating on discovering
fundamental laws.
There's a whole range of physics, which is
interesting and understanding at another level
these phenomena like super conductivity in
nuclear reactions.
But I'm talking about discovering trouble,
something wrong with the fundamental law.
So nobody knows where to look there, therefore
all the experiments today-- in this field,
of finding out a new law-- are in high energy.
I must also point out to you that you cannot
prove a vague theory wrong.
If the guess that you make is poorly expressed
and rather vague, and the method that you
used for figuring out the consequences is
rather vague, you're not sure, and you just
say I think everything is because it's all
due to moogles, and moogles do this and that,
more or less.
So I can sort of explain how this works.
Then you say that that theory is good, because
it can't be proved wrong.
[LAUGHTER]
If the process of computing the consequences
is indefinite, then with a little skill, any
experimental result can be made to look like
an expected consequence.
You're probably familiar with that in other
fields.
For example, a hates his mother.
The reason is, of course, because she didn't
caress him or love him enough when he was
a child.
Actually, if you investigate, you find out
that as a matter of fact, she did love him
very much.
And everything was all right.
Well, then, it's because she was overindulgent
when he was young.
[LAUGHTER]
So by having a vague theory, it's possible
to get either result.
[APPLAUSE]
Now wait, the cure for this one is the following.
It would be possible to say if it were possible
to state ahead of time how much love is not
enough, and how much love is overindulgent
exactly, then there would be a perfectly legitimate
theory, against which you could make tests.
It is usually said when this is pointed out,
how much love and so on, oh, you're dealing
with psychological matters, and things can't
be defined so precisely.
Yes, but then you can't claim to know anything
about it.
[APPLAUSE]
Now, we have examples, you'll be are horrified
to hear, in physics of exactly the same kind.
We have these approximate symmetries.
It works something like this.
You have approximate symmetry, you suppose
it's perfect.
Calculate the consequences, it's easy if you
suppose it's perfect.
You compare with experiment, of course it
doesn't agree.
The symmetry you're supposed to expect is
approximate.
So if the agreement is pretty good, you say,
nice.
If the agreement is very poor, you say, well
this particular thing must be especially sensitive
to the failure of the symmetry.
Now you laugh, but we have to make progress
in that way.
In the beginning, when our subject is first
new, and these particles are new to us, this
jockeying around, this is a feeling way of
guessing at the result.
And this is the beginning of any science.
And the same thing is true of psychology as
it is of the symmetry propositions in physics.
So don't laugh too hard, it's necessary in
the very beginning to be very careful.
It's easy to fall over the deep end by this
kind of a vague theory.
It's hard to prove it wrong.
It takes a certain skill and experience to
not walk off the plank on the game.
In this process of guessing, computing consequences,
and comparing to experiment, we can get stuck
at various stages.
For example, we may in the guess stage get
stuck.
We have no ideas, we can't guess an idea.
Or we may get in the computing stage stuck.
For example, Yukawa guessed an idea for the
nuclear forces in 1934.
Nobody could compute the consequences, because
the mathematics was too difficult.
So therefore, they couldn't compare it with
experiments successfully.
And the theory remained-- for a long time,
until we discovered all this junk.
And this junk was not contemplated by Yukawa,
and therefore, it's undoubtedly not as simple,
as least, as the way Yukawa did it.
Another place you can get stuck is at the
experimental end.
For example, the quantum theory of gravitation
is going very slowly, if at all, because there's
no use.
All the experiments that you can do never
involve quantum mechanics and gravitation
at the same time, because the gravity force
is so weak, compared to electrical forces.
Now I want to concentrate from now on-- because
I'm a theoretical physicist, I'm more delighted
with this end of the problem-- as to how do
you make the guesses.
Now it's strictly, as I said before, not of
any importance where the guess comes from.
It's only important that it should agree with
experiment and that it should be as definite
as possible.
But you say that is very simple.
We've set up a machine, a great computing
machine, which has a random wheel in it, that
makes a succession of guesses.
And each time it guesses a hypothesis about
how nature should work, it computes immediately
the consequences and makes a comparison to
a list of experimental results it has at the
other end.
In other words, guessing is a dumb man's job.
Actually, it's quite the opposite.
And I will try to explain why.
[LAUGHTER]
The first problem is how to start.
You say, I'll start with all the known principles.
But the principles that are all known are
inconsistent with each other.
So something has to be removed.
So we get a lot of letters from people.
We're always getting letters from people who
are insisting that we ought to make holes
in our guesses.
You make a hole to make room for a new guess.
Somebody says, do you know, you people always
say space is continuous.
But how do you know when you get to a small
enough dimension that there really are enough
points in between, it isn't just a lot of
dots separated by little distances?
Or they say, you know, those quantum mechanical
amplitudes you just told me about, they're
so complicated and absurd.
What makes you think those are right?
Maybe they aren't right.
I get a lot of letters with such content.
But I must say that such remarks are perfectly
obvious and are perfectly clear to anybody
who's working on this problem.
And it doesn't do any good to point this out.
The problem is not what might be wrong, but
what might be substituted precisely in place
of it.
If you say anything precise, for example in
the case of a continuous space, suppose the
precise proposition is that space really consists
of a series of dots only.
And the space between them doesn't mean anything.
And the dots are in a cubic array.
Then we can prove that immediately is wrong,
that doesn't work.
You see, the problem is not to change or to
say something might be wrong but to replace
it by something.
And that is not so easy.
As soon as any real, definite idea is substituted,
it becomes almost immediately apparent that
it doesn't work.
Secondly, there's an infinite number of possibilities
of these the simple types.
It's something like this.
You're sitting, working very hard.
You work for a long time, trying to open a
safe.
And some Joe comes along, who doesn't know
anything about what you're doing or anything,
except that you're trying to open a safe.
He says, you know, why don't you try the combination
10-20-30?
Because you're busy, you're trying a lot of
things.
Maybe you already tried 10-20-30.
Maybe you know that the middle number is already
32 and not 20.
Maybe you know that as a matter of fact this
is a five digit combination.
[LAUGHTER]
So these letters don't do any good.
And so please don't send me any letters, trying
to tell me how the thing is going to work.
I read them to make sure--
[LAUGHTER]
--That I haven't already thought of that.
But it takes too long to answer them, because
they're usually in the class try 10-20-30.
And as usual, nature's imagination far surpasses
our own.
As we've seen from the other theories, they
are really quite subtle and deep.
And to get such a subtle and deep guess is
not so easy.
One must be really clever to guess.
And it's not possible to do it blindly, by
machine.
So I wanted to discuss the art of guessing
nature's laws.
It's an art.
How is it done?
One way, you might think, well, look at history.
How did the other guys do it?
So we look at history.
Let's first start out with Newton.
He has in a situation where he had incomplete
knowledge.
And he was able to get the laws, by putting
together ideas, which all were relatively
close to experiment.
There wasn't a great distance between the
observations on the test.
That's the first, but now it doesn't work
so good.
Now the next guy who did something-- well,
another man who did something great was Maxwell,
who obtained the laws of electricity and magnetism.
But what he did was this.
He put together all the laws of electricity,
due to Faraday and other people who came before
him.
And he looked at them, and he realized that
they were mutually inconsistent.
They were mathematically inconsistent.
In order to straighten it out, he had to add
one term to an equation.
By the way, he did this by inventing a model
for himself of idle wheels and gears and so
on in space.
And then he found that what the new law was.
And nobody paid much attention, because they
didn't believe in the idle wheels.
We don't believe in the idle wheels today.
But the equations that he obtained were correct.
So the logic may be wrong, but the answer
is all right.
In the case of relativity, the discovery of
relativity was completely different.
There was an accumulation of paradoxes.
The known laws gave inconsistent results.
And it was a new kind of thinking, a thinking
in terms of discussing the possible symmetries
of laws.
And it was especially difficult, because it
was the first time realized how long something
like Newton's laws could be right and still,
ultimately, be wrong.
And second, that ordinary ideas of time and
space that seems so instinctive could be wrong.
Quantum mechanics was discovered in two independent
ways, which is a lesson.
There, again, and even more so, an enormous
number of paradoxes were discovered experimentally.
Things that absolutely couldn't be explained
in any way by what was known.
Not that the knowledge was incomplete, but
the knowledge was too complete.
Your prediction was this should happen, it
didn't.
The two different roots were one by Schrodinger,
who guessed the equations.
Another by Heisenberg, who argued that you
must analyze what's measurable.
So it's two different philosophical methods
reduced to the same discovery in the end.
More recently, the discovery of the laws of
this interaction, which are still only partly
known, had quite a somewhat different situation.
Again, there was a-- this time, it was a case
of incomplete knowledge.
And only the equation was guessed.
The special difficulty this time was that
the experiments were all wrong.
All the experiments were wrong.
How can you guess the right answer?
When you calculate the results it disagrees
with the experiment, and you have the courage
to say, the experiments must be wrong.
I'll explain where the courage comes from
in a minute.
[LAUGHTER]
Today, we haven't any paradoxes, maybe.
We have this infinity that comes if we put
all the laws together.
But the rug-sweeping people are so clever
that one sometimes thinks that's not a serious
paradox.
The fact that there are all these particles
doesn't tell us anything, except that our
knowledge is incomplete.
I'm sure that history does not repeat itself
in physics, as you see from this list.
And the reason is this.
Any scheme-- like think of symmetry laws,
or put the equations in mathematical form,
or any of these schemes, guess equations,
and so on-- are known to everybody now.
And they're tried all the time.
So if the place where you get stuck is not
that, you try that right away.
We try looking for symmetries, we try all
the things that have been tried before.
But we're stuck.
So it must be another way next time.
So each time that we get in this log jam of
too many problems, it's because the methods
that we're using are just like the ones we
used before.
We try all that right away.
But the new scheme, the new discovery is going
to be made in a completely different way.
So history doesn't help us very much.
I'd like to talk a little bit about this Heisenberg's
idea.
But you shouldn't talk about what you can't
measure, because a lot of people talk about
that without understanding it very well.
They say in physics you shouldn't talk about
what you can't measure.
If what you mean by this, if you interpret
this in this sense, that the constructs are
inventions that you make that you talk about,
it must be such a kind that the consequences
that you compute must be comparable to experiment.
That is, that you don't compute a consequence
like a moo must be three goos.
When nobody knows what a moo and a goo is,
that's no good.
[LAUGHTER]
If the consequences can be compared to experiment,
then that's all that's necessary.
It is not necessary that moos and goos can't
appear in the guess.
That's perfectly all right.
You can have as much junk in the guess as
you want, provided that you can compare it
to experiment.
That's not fully appreciated, because it's
usually said, for example, people usually
complain of the unwarranted extension of the
ideas of particles and paths and so forth,
into the atomic realm.
Not so at all.
There's nothing unwarranted about the extension.
We must, and we should, and we always do extend
as far as we can beyond what we already know,
those things, those ideas that we've already
obtained.
We extend the ideas beyond their range.
Dangerous, yes, uncertain, yes.
But the only way to make progress.
It's necessary to make science useful, although
it's uncertain.
It's only useful if it makes predictions.
It's only useful if it tells you about some
experiment that hasn't been done.
It's no good if it just tells you what just
went on.
So it's necessary to extend the ideas beyond
where they've been tested.
For example, in the law of gravitation, which
was developed to understand the motion of
the planets, if Newton simply said, I now
understand the planet, and didn't try to compare
it to the earth's pull, we can't, if we're
not allowed to say, maybe what holds the galaxies
together is gravitation.
We must try that.
It's no good to say, well, when you get to
the size of galaxies, since you don't know
anything about anything, it could happen.
Yes, I know.
But there's no science here, there's no understanding,
ultimately, of the galaxies.
If on the other hand you assume that the entire
behavior is due to only known laws, this assumption
is very limited and very definite and easily
broken by experiment.
All we're looking for is just such hypotheses.
Very definite, easy to compare to experiment.
And the fact is that the way the galaxies
behaved so far doesn't seem to be against
the proposition.
It would be easily disproved, if it were false.
But it's very useful to make hypotheses.
I give another example, even more interesting
and important.
Probably the most powerful assumption in all
of biology, the single assumption that makes
the progress of biology the greatest is the
assumption that everything the animals do,
the atoms can do.
That the things that are seen in the biological
world are the results of the behavior of physical
and chemical phenomena, with no extra something.
You could always say, when we come to living
things, anything can happen.
If you do that, you never understand the living
thing.
It's very hard to believe that the wiggling
of the temple of the octopus is nothing but
some fooling around of atoms, according to
the known physical laws.
But if investigated with this hypothesis,
one is able to make guesses quite accurately
as to how it works.
And one makes great progress in understanding
the thing.
So far, the tentacle hasn't been cut off.
What I mean is it hasn't been found that this
idea is wrong.
It's therefore not unscientific to take a
guess, although many people who are not in
science think it is.
For instance, I had a conversation about flying
saucers some years ago with laymen.
[LAUGHTER]
Because I'm scientific, I know all about flying
saucers.
So I said, I don't think there are flying
saucers.
So my antagonist said, is it impossible that
there are flying saucers?
Can you prove that it's impossible?
I said, no, I can't prove it's impossible,
it's just very unlikely.
That, they say, you are very unscientific.
If you can't prove it impossible, then how
could you say it's likely that it's unlikely?
Well, that's the way that it is scientific.
It is scientific only to say what's more likely
and less likely, and not to be proving all
the time, possible and impossible.
To define what I mean, I finally said to him,
listen.
I mean that from my knowledge of the world
that I see around me, I think that it is much
more likely that the reports of flying saucers
are the results of the known irrational characteristics
of terrestrial intelligence, rather than the
unknown, rational efforts of extraterrestrial
intelligence.
[LAUGHTER]
It's just more likely, that's all.
And it's a good guess.
And we always try to guess the most likely
explanation, keeping in the back of the mind
the fact that if it doesn't work, then we
must discuss the other possibilities.
Now, how to guess at what to keep and what
to throw away.
You see, we have all these nice principles
and known facts and so on.
But we're in some kind of trouble-- that we
get the inifinities or we don't get enough
of a description, we're missing some parts.
And sometimes that means that we have, probably,
to throw away some idea.
At least in the past it's always turned out
that some deeply held idea has to be thrown
away.
And the question is what to throw away and
what to keep.
If you throw it all away, it's going a little
far, and you don't got much to work with.
After all, the conservation of energy looks
good, it's nice.
I don't want to throw it away, and so on.
To guess what to keep and what to throw away
takes considerable skill.
Actually, it probably is merely a matter of
luck.
But it looks like it takes considerable skill.
For instance, probability amplitudes, they're
very strange.
And the first thing you'd think is that the
strange new ideas are clearly cockeyed.
And yet everything that can be deduced from
the idea of probability-- the existence of
quantum mechanical probability amplitude,
strange though they are, all the things that
depend on that work throughout all these strange
particles, work 100%.
Everything that depends on that seems to work.
So I don't believe that that idea is wrong,
and that when we find out what the inner guts
of this stuff is we'll find that idea is wrong.
I think that part's right.
I'm only guessing.
I'm telling you how I guess.
For instance, that space is continuous is,
I believe, wrong.
Because we get these infinities in other difficulties,
and we have some questions as to what determines
the sizes of all these particles, I rather
suspect that the simple ideas of geometry
extended down into infinitely small space
is wrong.
I don't believe that space-- I mean, I'm making
a hole.
I'm only making a guess, I'm not telling you
what to substitute.
If I did, I would finish this lecture with
a known law.
Some people have used the inconsistency of
all the principles to say that there's only
one possible consistent world.
That if we put all the principles together
and calculate it very exactly, we will not
only be able to reuse the principle, but discover
that these are the only things that can exist
and have the [INAUDIBLE].
And that seems to me like a big order.
I don't believe-- that's not like wagging
the tail by the dog.
That's right.
Wagging the dog by the tail.
I believe that you have to be given that certain
things exist, a few of them-- not all the
48 particles or the 50 some odd particles.
A few little principles, a few little things
exist, like electrons, and something, something
is given.
And then with all the principles, the great
complexities that come out could probably
be a definite consequence.
But I don't think you can get the whole thing
from just arguments about consistency.
Finally, we have another problem, which is
the question of the meaning of the partial
symmetries.
I think I better leave that one go, because
of a shortage of time.
Well, I'll say it quickly.
These symmetries-- like the neutron and proton
are nearly the same, but they're not, for
electricity, or that the law of reflection
symmetry is perfect, except for one kind of
a reaction-- are very annoying.
The thing is almost symmetrical, but not.
Now, two schools of thought exist.
One who say it's really simple, they're really
symmetrical.
But there's a little complication, which knocks
it a little bit cockeyed.
Then there's another school, which has only
one representative, myself.
[LAUGHTER]
Which says, no, the thing may be complicated
and become simple only through the complication.
Like this.
The Greeks believed that the orbits of the
planets were circles.
And the orbits of the planets are nearly circles.
Actually, they're ellipses.
The next question is, well, they're not quite
symmetrical.
But they're almost circles, they're very close
to circles.
Why are they very close to circles?
Why are they nearly symmetrical?
Because of the long complicated effects of
tidal friction, a very complicated idea.
So it is possible that nature, in her heart,
is completely as unsymmetrical for these things.
But in the complexities of reality, it gets
approximately looking as if it's symmetrical.
Ellipses look almost like circles, it's another
possibly.
Nobody knows, it's just guess work.
Now another thing that people often say is
that for guessing, two identical theories--
two theories.
Suppose you have two theories, a and b, which
look completely different psychologically.
They have different ideas in them and so on.
But that all the consequences that are computed,
all the consequences that are computed are
exactly the same.
You may even say they even agree with experiment.
The point is thought that the two theories,
although they sound different at the beginning,
have all consequences the same.
It's easy, usually, to prove that mathematically,
by doing a little mathematics ahead of time,
to show that the logic from this one and this
one will always give corresponding consequences.
Suppose we have two such theories.
How are we going to decide which one is right?
No way, not by science.
Because they both agree with experiment to
the same extent, there's no way to distinguish
one from the other.
So two theories, although they may have deeply
different ideas behind them, may be mathematically
identical.
And usually people say, then, in science one
doesn't know how to distinguish them.
And that's right.
However, for psychological reasons, in order
to guess new theories, these two things are
very far from equivalent.
Because one gives a man different ideas than
the other.
By putting the theory in a certain kind of
framework, you get an idea of what to change,
which would be something, for instance, in
theory A that talks about something.
But you say I'll change that idea in here.
But to find out what the corresponding thing
you're going to change in here may be very
complicated.
It may not be a simple idea.
In other words, a simple change here, may
be a very different theory than a simple change
there.
In other words, although they are identical
before they are changed, there are certain
ways of changing one which look natural, which
don't look natural in the other.
Therefore, psychologically, we must keep all
the theories in our head.
And every theoretical physicist that's any
good knows six or seven different theoretical
representations for exactly the same physics,
and knows that they're all equivalent, and
that nobody's ever going to be able to decide
which one is right at that level.
But he keeps them in his head, hoping that
they'll give him different ideas for guessing.
Incidentally, that reminds me of another thing.
And that is that the philosophy, or the ideas
around the theory-- a lot of ideas, you say,
I believe there is a space time, or something
like that, in order to discuss your analyses--
that these ideas change enormously when there
are very tiny changes in the theory.
In other words, for instance, Newton's idea
about space and time agreed with experiment
very well.
But in order to get the correct motion of
the orbit of Mercury, which was a tiny, tiny
difference, the difference in the character
of the theory with which you started was enormous.
The reason is these are so simple and so perfect.
They produce definite results.
In order to get something that produced a
little different result, it has to be completely
different.
You can't make imperfections on a perfect
thing.
You have to have another perfect thing.
So the philosophical ideas between Newton's
theory of gravitation and Einstein's theory
of gravitation are enormous.
Their difference is rather enormous.
What are these philosophies?
These philosophies are really tricky ways
to compute consequences quickly.
A philosophy, which is sometimes called an
understanding of the law, is simply a way
that a person holds the laws in his mind,
so as to guess quickly at consequences.
Some people have said, and it's true, for
instance, in the case of Maxwell's equations
and other equations, never mind the philosophy,
never mind anything of this kind.
Just guess the equations.
The problem is only to compute the answers
so they agree with experiment, and is not
necessarily to have a philosophy or words
about the equation.
That's true, in a sense, yes and no.
It's good in the sense you may be, if you
only guess the equation, you're not prejudicing
yourself, and you'll guess better.
On the other hand, maybe the philosophy helped
you to guess.
It's very hard to say.
For those people who insist, however, that
the only thing that's important is that the
theory agrees with experiment, I would like
to make an imaginary discussion between a
Mayan astronomer and his student.
The Mayans were able to calculate with great
precision the predictions, for example, for
eclipses and the position of the moon in the
sky, the position of Venus, and so on.
However, it was all done by arithmetic.
You count certain numbers, you subtract some
numbers, and so on.
There was no discussion of what the moon was.
There wasn't even a discussion of the idea
that it went around.
It was only calculate the time when there
would be an eclipse, or the time when it would
rise-- their full moon-- and when it would
rise, half moon, and so on, just calculating,
only.
Suppose that a young man went to the astronomer
and said, I have an idea.
Maybe those things are going around, and there
are balls of rocks out there.
We could calculate how they move in a completely
different way than just calculate what time
they appear in the sky and so on.
So of course the Mayan astronomer would say,
yes, how accurate can you predict eclipses?
He said, I haven't developed the thing very
far.
But we can calculate eclipses more accurately
than you can with your model.
And so you must not pay attention to this,
because the mathematical scheme is better.
And it's a very strong tendency of people
to say against some idea, if someone comes
up with an idea, and says let's suppose the
world is this way.
And you say to him, well, what would you get
for the answer for such and such a problem?
And he says, I haven't developed it far enough.
And you say, well, we have already developed
it much further.
We can get the answers very accurately.
So it is a problem, as to whether or not to
worry about philosophies behind ideas.
Another thing, of course, I wanted you to
guess is to guess new principles.
For instance, in Einstein's gravitation, he
guessed, on top of all the other principles,
the principle that correspondent to the idea
that the forces are always proportional to
the masses.
He guessed the principle that if you are in
an accelerating car, you couldn't tell that
from being in a gravitational field.
And by adding that principle to all the other
principles was able to deduce correct laws
of gravitation.
Well, that outlines a number of possible ways
of guessing.
I would now like to come to some other points
about the final result.
First of all, when we're all finished, and
we have a mathematical theory by which we
can compute consequences, it really is an
amazing thing.
What do we do?
In order to figure out what an atom is going
to do in a given situation, we make up a whole
lot of rules with marks on paper, carry them
into a machine, which opens and closes switches
in some complicated way.
And the result will tell us what the atom
is going to do.
Now if the way that these switches open and
close, with some kind of a model of the atom--
in other words, if we thought the atom had
such switches in it-- then I would say, I
understand more or less what's going on.
But I find it quite amazing that it is possible
to predict what will happen by what we call
mathematics.
We're just simply following a whole lot of
rules, which have nothing to do, really, with
what's going on in the original thing.
In other words, the closing and opening of
switches in a computer is quite different,
I think, than what's happening in nature.
And that is, to me, very surprising.
Now finally, I would like to say one of the
most important things in his guess compute
consequences compare experiment business is
to know when you're right, that it's possible
to know when you're right way ahead of computing
all a consequences-- I mean of checking all
the consequences.
You can recognize truth by beauty and simplicity.
It's always easy when you've got the right
guess and make two or three little calculations
to make sure it isn't obviously wrong to know
that it's right.
When you get it right, it's obvious that it's
right.
At least if you have any experience.
Because most of what happens is that more
comes out than goes in, that your guess is,
in fact, that something is very simple.
And at the moment you guess that it's simpler
than you thought, then it turns out that it's
right, if it can't be immediately disproved.
Doesn't sound silly.
I mean, if you can't see immediately that
it's wrong, and it's simpler than it was before,
then it's right.
The inexperienced and crackpots and people
like that will make guesses that are simple,
all right, but you can immediately see that
they're wrong.
That doesn't count.
And others, the inexperienced students, make
guesses that are very complicated.
And it sort of looks like it's all right.
But I know that's not true, because the truth
always turns out to be simpler than you thought.
What we need is imagination.
But imagination is a terrible straitjacket.
We have to find a new view of the world that
has to agree with everything that's known,
but disagree in its predictions, some way.
Otherwise it's not interesting.
And in that disagreement, agree with nature.
If you can find any other view of the world
which agrees over the entire range where things
have already been observed, but disagrees
somewhere else, you've made a great discovery.
Even if it doesn't agree with nature.
It's darn hard, it's almost impossible, but
not quite impossible, to find another theory,
which agrees with experiments over the entire
range in which the old theories have been
checked and yet gives different consequences
in some other range.
In other words, a new idea that is extremely
difficult, takes a fantastic imagination.
And what of the future of this adventure?
What will happen ultimately?
We are going along, guessing the laws.
How many laws are we going to have to guess?
I don't know.
Some of my-- let's say, some of my colleagues
say, science will go on.
But certainly, there will not be perpetual
novelty, say for 1,000 years.
This thing can't keep on going on, we're always
going to discover new laws, new laws, new
laws.
If we do, it will get boring that there are
so many levels, one underneath the other.
So the only way that it seems to me that it
can happen-- that what can happen in the future
first-- either that everything becomes known,
that all the laws become known.
That would mean that after you had enough
laws, you could compute consequences.
And they would always agree with experiment,
which would be the end of the line.
Or it might happen that the experiments get
harder and harder to make, more and more expensive,
that you get 99.9% of the phenomena.
But there's always some phenomenon which has
just been discovered that's very hard to measure,
which disagrees and gets harder and harder
to measure.
As you discover the explanation of that one,
there's always another one.
And it gets slower and slower and more and
more uninteresting.
That's another way that it could end.
But I think it has to end in one way or another.
And I think that we are very lucky to live
in the age in which we're still making the
discoveries.
It's an age which will never come again.
It's like the discoveries of America.
You only discover it once.
It was an exciting day, when there was investigations
of America.
But the age that we live in is the age in
which we are discovering the fundamental laws
of nature.
And that day will never come again.
I don't mean we're finished.
I mean, we're right in the process of making
such discoveries.
It's very exciting and marvelous, but this
excitement will have to go.
Of course, in the future there will be other
interests.
There will be interests on the connection
of one level of phenomena to another, phenomena
in biology and so on, all kinds of things.
Or if you're talking about explorations, exploring
planets and other things.
But there will not still be the same thing
as we're doing now.
It will be just different interests.
Another thing that will happen is that if
all is known-- ultimately, if it turns out
all is known, it gets very dull-- the biggest
philosophy and the careful attention to all
these things that I've been talking about
will have gradually disappeared.
The philosophers, who are always on the outside,
making stupid remarks, will be able to close
in.
Because we can't push them away by saying,
well, if you were right, you'd be able to
guess all the rest of the laws.
Because when they're all there, they'll have
an explanation for it.
For instance, there are always explanations
as to why the world is three dimensional.
Well, there's only one world.
And it's hard to tell if that explanation
is right or not.
So if everything were known, there will be
some explanation about why those are the right
laws.
But that explanation will be in a frame that
we can't criticize by arguing that that type
of reasoning will not permit us to go further.
So there will be a degeneration of ideas,
just like the degeneration that great explorers
feel occurs when tourists begin moving in
on their territory.
[LAUGHTER]
[APPLAUSE]
I must say that in this age, people are experiencing
a delight, a tremendous delight.
The delight that you get when you guess how
nature will work in a new situation, never
seen before.
From experiments and information in a certain
range, you can guess what's going to happen
in the region where no one has ever explored
before.
It's a little different than regular exploration.
That is, there's enough clues on the land
discovered to guess what the land is going
to look like that hasn't been discovered.
And these guesses, incidentally, are often
very different than what you've already seen.
It takes a lot of thought.
What is it about nature that lets this happen,
that it's possible to guess from one part
what the rest is going to do?
That's an unscientific question, what is it
about nature.
I don't know how to answer.
And I'm going to give therefore an unscientific
answer.
I think it is because nature has a simplicity
and therefore a great beauty.
Thank you very much.
[APPLAUSE]
[BELLS RINGING]
