发信人: Rg (RedGardenia), 信区: Physics
标 题: chapter two:Basic Physics
发信站: 哈工大紫丁香 (2002年08月15日12:49:29 星期四), 站内信件
2-1 Introduction
In this chapter, we shall examine the most fundamental ideas that
we have about physics—the nature of things as we see them at the
present time. We shall not discuss the history of how we know that
all these ideas are true; you will learn these details in due
time. The things with which we concern ourselves in science appear
in myriad forms, and with a multitude of attributes. For example,
if we stand on the shore and look at the sea, we see the water,
the waves breaking, the foam, the sloshing motion of the water,
the sound, the air, the winds and the clouds, the sun and the blue
sky, and light; there is sand and there are rocks of various
hardness and permanence, color and texture. There are animals and
seaweed, hunger and disease, and the observer on the beach; there
may be even happiness and thought. Any other spot in nature has a
similar variety of things and influences. It is always as
complicated as that, no matter where it is. Curiosity demands that
we ask questions, that we try to put things together and try to
understand this multitude of aspects as perhaps resulting from the
action of a relatively small number of elemental things and forces
acting in an infinite variety of combinations. For example: Is the
sand other than the rocks? That is, is the sand perhaps nothing
but a great number of very tiny stones? Is the moon a great rock?
If we understood rocks, would we also understand the sand and the
moon? Is the wind a sloshing of the air analogous to the sloshing
motion of the water in the sea? What common features do different
movements have? What is common to different kinds of sound? How
many different colors are there? And so on. In this way we try
gradually to analyze all things, to put together things which at
first sight look different, with the hope that we may be able to
reduce the number of different things and thereby understand them
better. A few hundred years ago, a method was devised to find
partial answers to such questions. Observation, reason, and
experiment make up what we call the scientific method. We shall
have to limit ourselves to a bare description of our basic view of
what is sometimes called fundamental physics, or fundamental ideas
which have arisen from the application of the scientific method.
What do we mean by "understanding" something? We can imagine that
this complicated array of moving things which constitutes "the
world" is something like a great chess game being played by the
gods, and we are observers of the game. We do not know what the
rules of the game are; all we are allowed to do is to watch the
playing. Of course, if we watch long enough, we may eventually
catch on to a few of the rules. The rules of the game are what we
mean by fundamental physics. Even if we knew every rule, however,
we might not be able to understand why a particular move is made
in the game, merely because it is too complicated and our minds
are limited. If you play chess you must know that it is easy to
learn all the rules, and yet it is often very hard to select the
best move or to understand why a player moves as he does. So it is
in nature, only much more so; but we may be able at least to find
all the rules. Actually, we do not have all the rules now. (Every
once in a while something like castling is going on that we still
do not understand.) Aside from not knowing all of the rules, what
we really can explain in terms of those rules is very limited,
because almost all situations are so enormously complicated that
we cannot follow the plays of the game using the rules, much less
tell what is going to happen next. We must, therefore, limit
ourselves to the more basic question of the rules of the game. If
we know the rules, we consider that we "understand" the world. How
can we tell whether the rules which we "guess" at are really right
if we cannot analyze the game very well? There are, roughly
speaking, three ways. First, there may be situations where nature
has arranged, or we arrange nature, to be simple and to have so
few parts that we can predict exactly what will happen, and thus
we can check how our rules work. (In one corner of the board there
may be only a few chess pieces at work, and that we can figure out
exactly.) A second good way to check rules is in terms of less
specific rules derived from them. For example, the rule on the
move of a bishop on a chessboard is that it moves only on the
diagonal. One can deduce, no matter how many moves may be made,
that a certain bishop will always be on a red square. So, without
being able to follow the details, we can always check our idea
about the bishop's motion by finding out whether it is always on a
red square. Of course it will be, for a long time, until all of a
sudden we find that it is on a black square (what happened of
course, is that in the meantime it was captured, another pawn
crossed for queening, and it turned into a bishop on a black
square). That is the way it is in physics. For a long time we will
have a rule that works excellently in an over-all way, even when
we cannot follow the details, and then some time we may discover a
new rule. From the point of view of basic physics, the most
interesting phenomena are of course in the new places, the places
where the rules do not work—not the places where they do work!
That is the way in which we discover new rules. The third way to
tell whether our ideas are right is relatively crude but probably
the most powerful of them all. That is, by rough approximation.
While we may not be able to tell why Alekhine moves this
particular piece, perhaps we can roughly understand that he is
gathering his pieces around the king to protect it, more or less,
since that is the sensible thing to do in the circumstances. In
the same way, we can often understand nature, more or less,
without being able to see what every little piece is doing, in
terms of our understanding of the game. At first the phenomena of
nature were roughly divided into classes, like heat, electricity,
mechanics, magnetism, properties of substances, chemical
phenomena, light or optics, x-rays, nuclear physics, gravitation,
meson phenomena, etc. However, the aim is to see complete nature
as different aspects of one set of phenomena. That is the problem
in basic theoretical physics, today—to find the laws behind
experiment; to amalgamate these classes. Historically, we have
always been able to amalgamate them, but as time goes on new
things are found. We were amalgamating very well, when all of a
sudden x-rays were found. Then we amalgamated some more, and
mesons were found. Therefore, at any stage of the game, it always
looks rather messy. A great deal is amalgamated, but there are
always many wires or threads hanging out in all directions. That
is the situation today, which we shall try to describe. Some
historic examples of amalgamation are the following. First, take
heat and mechanics. When atoms are in motion, the more motion, the
more heat the system contains, and so heat and all temperature
effects can be represented by the laws of mechanics. Another
tremendous amalgamation was the discovery of the relation between
electricity, magnetism, and light, which were found to be
different aspects of the same thing, which we call today the
electromagnetic field. Another amalgamation is the unification of
chemical phenomena, the various properties of various substances,
and the behavior of atomic particles, which is in the quantum
mechanics of chemistry. The question is, of course, is it going to
be possible to amalgamate everything, and merely discover that
this world represents different aspects of one thing? Nobody
knows. All we know is that as we go along, we find that we can
amalgamate pieces, and then we find some pieces that do not fit,
and we keep trying to put the jigsaw puzzle together. Whether
there are a finite number of pieces, and whether there is even a
border to the puzzle, is of course unknown. It will never be known
until we finish the picture, if ever. What we wish to do here is
to see to what extent this amalgamation process has gone on, and
what the situation is at present, in understanding basic phenomena
in terms of the smallest set of principles. To express it in a
simple manner, what are things made of and how few elements are
there ?
2-2 Physics before 1920
It is a little difficult to begin at once with the present view,
so we shall first see how things looked in about 1920 and then
take a few things out of that picture. Before 1920, our world
picture was something like this: The "stage" on which the universe
goes is the three-dimensional space of geometry, as described by
Euclid, and things change in a medium called time. The elements on
the stage are particles, for example the atoms, which have some
properties. First, the property of inertia: if a particle is
moving it keeps on going in the same direction unless forces act
upon it. The second element, then, is forces, which were then
thought to be of two varieties: First, an enormously complicated,
detailed kind of interaction force which held the various atoms in
different combinations in a complicated way, which determined
whether salt would dissolve faster or slower when we raise the
temperature. The other force that was known was a long-range
interaction—a smooth and quiet attraction—which varied inversely
as the square of the distance, and was called gravitation. This
law was known and was very simple. Why things remain in motion
when they are moving, or why there is a law of gravitation was, of
course, not known. A description of nature is what we are
concerned with here. From this point of view, then, a gas, and
indeed all matter, is a myriad of moving particles. Thus many of
the things we saw while standing at the seashore can immediately
be connected. First the pressure: this comes from the collisions
of the atoms with the walls or whatever; the drift of the atoms,
if they are all moving in one direction on the average, is wind;
the random internal motions are the heat. There are waves of
excess density, where too many particles have collected, and so as
they Tush off they push up piles of particles farther out, and so
on. This wave of excess density is sound. It is a tremendous
achievement to be able to understand so much. Some of these things
were described in the previous chapter. What kinds of particles
are there? There were considered to be 92 at that time: 92
different kinds of atoms were ultimately discovered. They had
different names associated with their chemical properties. The
next part of the problem was, what are the short-range forces ?
Why does carbon attract one oxygen or perhaps two oxygens, but not
three oxygens? What is the machinery of interaction between atoms?
Is it gravitation? The answer is no. Gravity is entirely too weak.
But imagine a force analogous to gravity, varying inversely with
the square of the distance, but enormously more powerful and
having one difference. In gravity everything attracts everything
else, but now imagine that there are two kinds of "things," and
that this new force (which is the electrical force, of course) has
the property that likes repel but unlikes attract. The "thing"
that carries this strong interaction is called charge. Then what
do we have? Suppose that we have two unlikes that attract each
other, a plus and a minus, and that they stick very close
together. Suppose we have another charge some distance away. Would
it feel any attraction? It would feel practically none, because if
the first two are equal in size, the attraction for the one and
the repulsion for the other balance out. Therefore there is very
little force at any appreciable distance. On the other hand, if we
get very close with the extra charge, attraction arises, because
the repulsion of likes and attraction of unlikes will tend to
bring unlikes closer together and push likes farther apart. Then
the repulsion will be less than the attraction. This is the reason
why the atoms, which are constituted out of plus and minus
electric charges, feel very little force when they are separated
by appreciable distance (aside from gravity). When they come close
together, they can "see inside" each other and rearrange their
charges, with the result that they have a very strong interaction.
The ultimate basis of an interaction between the atoms is
electrical. Since this force is so enormous, all the plusses and
all minuses will normally come together in as intimate a
combination as they can. All things, even ourselves, are made of
fine-grained, enormously strongly interacting plus and minus
parts, all neatly balanced out. Once in a while, by accident, we
may rub off a few minuses or a few plusses (usually it is easier
to rub off minuses), and in those circumstances we find the force
of electricity unbalanced, and we can then see the effects of
these electrical attractions.
To give an idea of how much stronger electricity is than
gravitation, consider two grains of sand, a millimeter across,
thirty meters apart. If the force between them were not balanced,
if everything attracted everything else instead of likes
repelling, so that there were no cancellation, how much force
would there be? There would be a force of three million tons
between the two! You see, there is very, very little excess or
deficit of the number of negative or positive charges necessary to
produce appreciable electrical effects. This is, of course, the
reason why you cannot see the difference between an electrically
charged or uncharged thing—so few particles are involved that
they hardly make a difference in the weight or size of an object.
With this picture the atoms were easier to understand. They were
thought to have a "nucleus" at the center, which is positively
electrically charged and very massive, and the nucleus is
surrounded by a certain number of "electrons" which are very light
and negatively charged. Now we go a little ahead in our story to
remark that in the nucleus itself there were found two kinds of
particles, protons and neutrons, almost of the same weight and
very heavy. The protons are electrically charged and the neutrons
are neutral. If we have an atom with six protons inside its
nucleus, and this is surrounded by six electrons (the negative
particles in the ordinary world of matter are all electrons, and
these are very light compared with the protons and neutrons which
make nuclei), this would be atom number six in the chemical table,
and it is called carbon. Atom number eight is called oxygen, etc.,
because the chemical properties depend upon the electrons on the
outside, and in fact only upon how many electrons there are. So
the chemical properties of a substance depend only on a number,
the number of electrons. (The whole list of elements of the
chemists really could have been called 1, 2, 3, 4, 5, etc. Instead
of saying "carbon," we could say "element six," meaning six
electrons, but of course, when the elements were first discovered,
it was not known that they could be numbered that way, and
secondly, it would make everything look rather complicated. It is
better to have names and symbols for these things, rather than to
call everything by number.) More was discovered about the
electrical force. The natural interpretation of electrical
interaction is that two objects simply attract each other: plus
against minus. However, this was discovered to be an inadequate
idea to represent it. A more adequate representation of the
situation is to say that the existence of the positive charge, in
some sense, distorts, or creates a "condition" in space, so that
when we put the negative charge in, it feels a force. This
potentiality for producing a force is called an electric field.
When we put an electron in an electric field, we say it is
"pulled." We then have two rules: (a) charges make a field, and
(b) charges in fields have forces on them and move. The reason for
this will become clear when we discuss the following phenomena: If
we were to charge a body, say a comb, electrically, and then place
a charged piece of paper at a distance and move the comb back and
forth, the paper will respond by always pointing to the comb. If
we shake it faster, it will be discovered that the paper is a
little behind, there is a delay in the action. (At the first
stage, when we move the comb rather slowly, we find a complication
which is magnetism. Magnetic influences have to do with charges in
relative motion, so magnetic forces and electric forces can really
be attributed to one field, as two different aspects of exactly
the same thing. A changing electric field cannot exist without
magnetism.) If we move the charged paper farther out, the delay is
greater. Then an interesting thing is observed. Although the
forces between two charged objects should go inversely as the
square of the distance, it is found, when we shake a charge, that
the influence extends very much farther out than we would guess at
first sight. That is, the effect falls off more slowly than the
inverse square. Here is an analogy: If we are in a pool of water
and there is a floating cork very close by, we can move it
"directly" by pushing the water with another cork. If you looked
only at the two corks, all you would see would be that one moved
immediately in response to the motion of the other—there is some
kind of "interaction" between them. Of course, what we really do
is to disturb the water; the water then disturbs the other cork.
We could make up a "law" that if you pushedthe water a little bit,
an object close by in the water would move. If it were farther
away, of course, the second cork would scarcely move, for we move
the water locally. On the other hand, if we jiggle the cork a new
phenomenon is involved, in which the motion of the water moves the
water there, etc., and waves travel away, so that by jiggling,
there is an influence wry much farther out, an oscillatory
influence, that cannot be understood from the direct interaction.
Therefore theidea of direct interaction must be replaced with the
existence of the water, or-inthe electrical case, with what we
call the electromagnetic field. The electromagnetic field can
carry waves; some of these waves are light, others are used in
radio broadcasts, but the general name is electromagnetic waves.
These oscillatory waves can have various frequencies. The only
thing that is really different from one wave to another is the
frequency of oscillation. If we shake a charge back and forth more
and more rapidly, and look at the effects, we get a whole series
of different kinds of effects, which are all unified by specifying
but one number, the number of oscillations per second. The usual
"pickup" that we get from electric currents in the circuits in the
walls of a building have a frequency of about one hundred cycles
per second. If we increase the frequency to 500 or 1000 kilocycles
(1 kilocycle = 1000 cycles) per second, we are "on the air," for
this is the frequency range which is used for radio broadcasts.
(Of course it has nothing to do with the air! We can have radio
broadcasts without any air.) If we again increase the frequency,
we come into the range that is used for FM and TV. Going still
further, we use certain short waves, for example for radar. Still
higher, and we do not need an instrument to "see" the stuff, we
can see it with the human eye. In the range of frequency from 5 X
1014 to 5 X 1015 cycles per second our eyes would see the
oscillation of the charged comb, if we could shake it that fast,
as red, blue, or violet light, depending on the frequency.
Frequencies below this range are called infrared, and above it,
ultraviolet. The fact that we can see in a particular frequency
range makes that part of the electromagnetic spectrum no more
impressive than the other parts from a physicist's standpoint, but
from a human standpoint, of course, it is more interesting. If we
go up even higher in frequency, we get x-rays. X-rays are nothing
but very high-frequency light. If we go still higher, we get gamma
rays. These two terms, x-rays and gamma rays, are used almost
synonymously. Usually electromagnetic rays coming from nuclei are
called gamma rays, while those of high energy from atoms are
called x-rays, but at the same frequency they are
indistinguishable physically, no matter what their source. If we
go to still higher frequencies, say to 1024 cycles per second, we
find that we can make those waves artificially, for example with
the synchrotron here at Caltech. We can find electromagnetic waves
with stupendously high frequencies—with even a thousand times
more rapid oscillation—in the waves found in cosmic rays. These
waves cannot be controlled by us.
2-3 Quantum physics
Having described the idea of the electromagnetic field, and that
this field can carry waves, we soon learn that these waves
actually behave in a strange way which seems very unwavelike. At
higher frequencies they behave much more like particles! It is
quantum mechanics, discovered just after 1920, which explains this
strange behavior. In the years before 1920, the picture of space
as a three-dimensional space, and of time as a separate thing, was
changed by Einstein, first into a combination which we call
space-time, and then still further into a curved space-time to
represent gravitation. So the "stage" is changed into space-time,
and gravitation is presumably a modification of space-time. Then
it was also found that the rules for the motions of particles were
incorrect. The mechanical rules of "inertia" and "forces" are
wrong—Newton's laws are wrong—in the world of atoms. Instead, it
was discovered that things on a small scale behave nothing like
things on a large scale. That is what makes physics difficult—and
very interesting. It is hard because the way things behave on a
small scale is so "unnatural"; we have no direct experience with
it. Here things behave like nothing we know of, so that it is
impossible to describe this behavior in any other than analytic
ways. It is difficult, and takes a lot of imagination. Quantum
mechanics has many aspects. In the first place, the idea that a
particle has a definite location and a definite speed is no longer
allowed; that is wrong. To give an example of how wrong classical
physics is, there is a rule in quantum mechanics that says that
one cannot know both where something is and how fast it is moving.
The uncertainty of the momentum and the uncertainty of the
position are complementary, and the product of the two is
constant. We can write the law like this: Dx Dp 3 h/2p, but we
shall explain it in more detail later. This rule is the
explanation of a very mysterious paradox: if the atoms are made
out of plus and minus charges, why don't the minus charges simply
sit on top of the plus charges (they attract each other) and get
so close as to completely cancel them out? Why are atoms so big?
Why is the nucleus at the center with the electrons around it? It
was first thought that this was because the nucleus was so big;
but no, the nucleus is very small. An atom has a diameter of about
10-8 cm. The nucleus has a diameter of about 10-13 cm. If we had
an atom and wished to see the nucleus, we would have to magnify it
until the whole atom was the size of a large room, and then the
nucleus would be a bare speck which you could just about make out
with the eye, but very nearly all the weight of the atom is in
that infinitesimal nucleus. What keeps the electrons from simply
falling in? This principle: If they were in the nucleus, we would
know their position precisely, and the uncertainty principle would
then require that they have a very large (but uncertain) momentum,
i.e., a very large kinetic energy. With this energy they would
break away from the nucleus. They make a compromise: they leave
themselves a little room for this uncertainty and then jiggle with
a certain amount of minimum motion in accordance with this rule.
(Remember that when a crystal is cooled to absolute zero, we said
that the atoms do not stop moving, they still jiggle. Why? If they
stopped moving, we would know where they were and that they had
zero motion, and that is against the uncertainty principle. We
cannot know where they are and how fast they are moving, so they
must be continually wiggling in there!) Another most interesting
change in the ideas and philosophy of science brought about by
quantum mechanics is this: it is not possible to predict exactly
what will happen in any circumstance. For example, it is possible
to arrange an atom which is ready to emit light, and we can
measure when it has emitted light by picking up a photon particle,
which we shall describe shortly. We cannot, however, predict when
it is going to emit the light or, with several atoms, which one is
going to. You may say that this is because there are some internal
"wheels" which we have not looked at closely enough. No, there are
no internal wheels; nature, as we understand it today, behaves in
such a way that it is fundamentally impossible to make a precise
prediction of exactly what will happen in a given experiment. This
is a horrible thing; in fact, philosophers have said before that
one of the fundamental requisites of science is that whenever you
set up the sameconditions, the same thing must happen. This is
simply not true, it is not a fundamental condition of science. The
fact is that the same thing does not happen, that we can find only
an average, statistically, as to what happens. Nevertheless,
science has not completely collapsed. Philosophers, incidentally,
say a great deal about what is absolutely necessary for science,
and it is always, so far as one can see, rather naive, and
probably wrong. For example, some philosopher or other said it is
fundamental to the scientific effort that if an experiment is
performed in, say, Stockholm, and then the same experiment is done
in, say, Quito, the same results must occur. That is quite false.
It is not necessary that science do that; it may be a fact of
experience, but it is not necessary. For example, if one of the
experiments is to look out at the sky and see the aurora borealis
in Stockholm, you do not see it in Quito; that is a different
phenomenon. "But," you say, "that is something that has to do with
the outside; can you close yourself up in a box in Stockholm and
pull down the shade and get any difference?" Surely. If we take a
pendulum on a universal joint, and pull it out and let go, then
the pendulum will swing almost in a plane, but not quite. Slowly
the plane keeps changing in Stockholm, but not in Quito. The
blinds are down, too. The fact that this happened does not bring
on the destruction of science. What is the fundamental hypothesis
of science, the fundamental philosophy? We stated it in the first
chapter: the sole test of the validity of any idea is experiment.
If it turns out that most experiments work out the same in Quito
as they do in Stockholm, then those "most experiments" will be
used to formulate some general law, and those experiments which do
not come out the same we will say were a result of the environment
near Stockholm. We will invent some way to summarize the results
of the experiment, and we do not have to be told ahead of time
what this way will look like. If we are told that the same
experiment will always produce the same result, that is all very
well, but if when we try it, it does not, then it does not. We
just have to take what we see, and then formulate all the rest of
our ideas in terms of our actual experience. Returning again to
quantum mechanics and fundamental physics, we cannot go into
details of the quantum-mechanical principles at this time, of
course, because these are rather difficult to understand. We shall
assume that they are there, and go on to describe what some of the
consequences are. One of the consequences is that things which we
used to consider as waves also behave like particles, and
particles behave like waves; in fact everything behaves the same
way. There is no distinction between a wave and a particle. So
quantum mechanics unifies the idea of the field and its waves, and
the particles, all into one. Now it is true that when the
frequency is low, the field aspect of the phenomenon is more
evident, or more useful as an approximate description in terms of
everyday experiences. But as the frequency increases, the particle
aspects of the phenomenon become more evident with the equipment
with which we usually make the measurements. In fact, although we
mentioned many frequencies, no phenomenon directly involving a
frequency has yet been detected above approximately 1012 cycles
per second. We only deduce the higher frequencies from the energy
of the particles, by a rule which assumes that the particle-wave
idea of quantum mechanics is valid. Thus we have a new view of
electromagnetic interaction. We have a new kind of particle to add
to the electron, the proton, and the neutron. That new particle is
called a photon. The new view of the interaction of electrons and
protons that is electromagnetic theory, but with everything
quantum-mechanically correct, is called quantum electrodynamics.
This fundamental theory of the interaction of light and matter, or
electric field and charges, is our greatest success so far in
physics. In this one theory we have the basic rules for all
ordinary phenomena except for gravitation and nuclear processes.
For example, out of quantum electrodynamics come all known
electrical, mechanical, and chemical laws: the laws for the
collision of billiard balls, the motions of wires in magnetic
fields, the specific heat of carbon monoxide, the color of neon
signs, the density of salt, and the reactions of hydrogen and
oxygen to make water are all consequences of this one law. All
these details can be worked out if the situation is simple enough
for us to make an approximation, which is almost never, but often
we can understand moreor less what is happening. At the present
time no exceptions are found to the quantum-electrodynamic laws
outside the nucleus, and there we do not know whether there is an
exception because we simply do not know what is going on in the
nucleus. In principle, then, quantum electrodynamics is the theory
of all chemistry, and of life, if life is ultimately reduced to
chemistry and therefore just to physics because chemistry is
already reduced (the part of physics which is involved in
chemistry being already known). Furthermore, the same quantum
electrodynamics, this great thing, predicts a lot of new things.
In the first place, it tells the properties of very high-energy
photons, gamma rays, etc. It predicted another very remarkable
thing: besides the electron, there should be another particle of
the same mass, but of opposite charge, called a positron, and
these two, coming together, could annihilate each other with the
emission of light or gamma rays. (After all, light and gamma rays
are all the same, they are just different points on a frequency
scale.) The generalization of this, that for each particle there
is an antiparticle, turns out to be true. In the case of
electrons, the antiparticle has another name—it is called a
positron, but for most other particles, it is called antiso-
and-so, like antiproton or antineutron. In quantum
electrodynamics, two numbers are put in and most of the other
numbers in the world are supposed to come out. The two numbers
that are put in are called the mass of the electron and the charge
of the electron. Actually, that is not quite true, for we have a
whole set of numbers for chemistry which tells how heavy the
nuclei are. That leads us to the next part.
2-4 Nuclei and particles
What are the nuclei made of, and how are they held together? It is
found that the nuclei are held together by enormous forces. When
these are released, the energy released is tremendous compared
with chemical energy, in the same ratio as the atomic bomb
explosion is to a TNT explosion, because, of course, the atomic
bomb has to do with changes inside the nucleus, while the
explosion of TNT has to do with the changes of the electrons on
the outside of the atoms. The question is, what are the forces
which hold the protons and neutrons together in the nucleus? Just
as the electrical interaction can be connected to a particle, a
photon, Yukawa suggested that the forces between neutrons and
protons also have a field of some kind, and that when this field
jiggles it behaves like a particle. Thus there could be some other
particles in the world besides protons and neutrons, and he was
able to deduce the properties of these particles from the already
known characteristics of nuclear forces. For example, he predicted
they should have a mass of two or three hundred times that of an
electron; and lo and behold, in cosmic rays there was discovered a
particle of the right mass! But it later turned out to be the
wrong particle. It was called a m-meson, or muon. However, a
little while later, in 1947 or 1948, another particle was found,
the p-meson, or pion, which satisfied Yukawa's criterion. Besides
the proton and the neutron, then, in order to get nuclear forces
we must add the pion. Now, you say, "Oh great!, with this theory
we make quantum nucleodynamics using the pions just like Yukawa
wanted to do, and see if it works, and everything will be
explained." Bad luck. It turns out that the calculations that are
involved in this theory are so difficult that no one has ever been
able to figure out what the consequences of the theory are, or to
check it against experiment, and this has been going on now for
almost twenty years! So we are stuck with a theory, and we do not
know whether it is right or wrong, but we do know that it is a
little wrong, or at least incomplete. While we have been dawdling
around theoretically, trying to calculate the consequences of this
theory, the experimentalists have been discovering some things.
For example, they had already discovered this m-meson or muon, and
we do not yet know where it fits. Also, in cosmic rays, a large
number of other "extra" particles were found. It turns out that
today we have approximately thirty particles, and it is very
difficult to understand the relationships of all these particles,
and what nature, wants them for, or what the connections are from
one to another. We do not today understand these various particles
as different aspects of the same thing, and the fact that we have
so many unconnected particles is a representation of the fact that
we have so much unconnected information without a good theory.
After the great successes of quantum electrodynamics, there is a
certain amount of knowledge of nuclear physics which is rough
knowledge, sort of half experience and half theory, assuming a
type of force between protons and neutrons and seeing what will
happen, but not really understanding where the force comes from.
Aside from that, we have made very little progress. We have
collected an enormous number of chemical elements. In the chemical
case, there suddenly appeared a relationship among these elements
which was unexpected, and which is embodied in the periodic table
of Mendeleev. For example, sodium and potassium are about the same
in their chemical properties and are found in the same column in
the Mendeleev chart. We have been seeking a Mendeleev-type chart
for the new particles. One such chart of the new particles was
made independently by Gell-Mann in the U.S.A. and Nishijima in
Japan. The basis of their classification is a new number, like the
electric charge, which can be assigned to each particle, called
its "strangeness," S. This number is conserved, like the electric
charge, in reactions which take place by nuclear forces. In Table
2-2 are listed all the particles. We cannot discuss them much at
this stage, but the table will at least show you how much we do
not know. Underneath each particle its mass is given in a certain
unit, called the Mev. One Mev is equal to 1.782 X 10~27 gram. The
reason this unit was chosen is historical, and we shall not go
into it now. More massive particles are put higher up on the
chart; we see that a neutron and a proton have almost the same
mass. In vertical columns we have put the particles with the same
electrical charge, all neutral objects in one column, all
positively charged ones to the right of this one, and all
negatively charged objects to the left. Particles are shown with a
solid line and "resonances" with a dashed one. Several particles
have been omitted from the table. These include the important
zero-mass, zero-charge particles, the photon and the graviton,
which do not fall into the baryon-meson-lepton classification
scheme, and also some of the newer resonances (K*, <p, ri). The
antiparticles of the mesons are listed in the table, but the
antiparticles of the leptons and baryons would have to be listed
in another table which would look exactly like this one reflected
on the zero-charge column. Although all of the particles except
the electron, neutrino, photon, graviton, and proton are unstable,
decay products have been shown only for the resonances.
Strangeness assignments are not applicable for leptons, since they
do not interact strongly with nuclei. All particles which are
together with the neutrons and protons are called baryons, and the
following ones exist: There is a "lambda," with a mass of 1154
Mev, and three others, called sigmas, minus, neutral, and plus,
with several masses almost the same. There are groups or
multiplets with almost the same mass, within one or two percent.
Each particle in a multiple! has the same strangeness. The first
multiple! is the proton-neutron doublet, and then there is a
singlet (the lambda) then the sigma triplet, and finally the xi
doublet. Very recently, in 1961, even a few more particles were
found. Or are they particles? They live so short a time, they
disintegrate almost instantaneously, as soon as they are formed,
that we do not know whether they should be considered as new
particles, or some kind of "resonance" interaction of a certain
definite energy between the A and T products into which they
disintegrate. In addition to the baryons the other particles which
are involved in the nuclear interaction are called mesons. There
are first the pions, which come in three varieties, positive,
negative, and neutral; they form another multiplet. We have also
found some new things called A'-mesons, and they occur as a
doublet, K+ and K°. Also, every particle has its antiparticle,
unless a particle is its own antiparticle. For example, the ir~
and the 7T4' are antiparticles, but the TT" is its own
antiparticle. The K~ and ^+ are antiparticles, and the K° and
K°. In addition, in 1961 we also found some more mesons or maybe
mesons which disintegrate almost immediately. A thing called w
which goes into three pions has a mass 780 on this scale, and
somewhat less certain is an object which disintegrates into two
pions. These particles, called mesons and baryons, and the
antiparticles of the mesons are on the same chart, but the
antiparticles of the baryons must be put on another chart,
"reflected" through the charge-zero column. Just as Mendeleev's
chart was very good, except for the fact that there were a number
of rare earth elements which were hanging out loose from it, so we
have a number of things hanging out loose from this
chart梡articles which do not interact strongly in nuclei, have
nothing to do with a nuclear interaction, and do not have a strong
interaction (I mean the powerful kind of interaction of nuclear
energy). These are called leptons, and they are the following:
there is the electron, which has a very small mass on this scale,
only 0.510 Mev. Then there is that other, the ^-meson, the muon,
which has a mass much higher, 206 times as heavy as an electron.
So far as we can tell, by all experiments so far, the difference
between the electron and the muon is nothing but the mass.
Everything works exactly the same for the muon as for the
electron, except that one is heavier than the other. Why is there
another one heavier; what is the use for it? We do not know. In
addition, there is a lepton which is neutral, called a neutrino,
and this particle has zero mass. In fact, it is now known that
there are two different kinds of neutrinos, one related to
electrons and the other related to muons. Finally, we have two
other particles which do not interact strongly with the nuclear
ones: one is a photon, and perhaps, if the field of gravity also
has a quantum- mechanical analog (a quantum theory of gravitation
has not yet been worked out), then there will be a particle, a
graviton, which will have zero mass. What is this "zero mass"? The
masses given here are the masses of the particles at rest. The
fact that a particle has zero mass means, in a way, that it cannot
be at rest. A photon is never at rest, it is always moving at
186,000 miles a second. We will understand more what mass means
when we understand the theory of relativity, which will come in
due time. Thus we are confronted with a large number of particles,
which together seem to be the fundamental constituents of matter.
Fortunately, these particles are not all different in their
interactions with one another. In fact, there seem to be just four
kinds of interaction between particles which, in the order of
decreasing strength, are the nuclear force, electrical
interactions, the beta-decay interaction, < and gravity. The
photon is coupled to all charged particles and the strength of the
interaction is measured by some number, which is 1/137. The
detailed law of this coupling is known, that is quantum
electrodynamics. ?Gravity is coupled to all energy, but its
coupling is extremely weak, much weaker than that of electricity.
This law is also known. Then there are the so-called weak decays?
beta decay, which causes the neutron to disintegrate into proton,
electron, and neutrino, relatively slowly. This law is only partly
known. The so-called strong interaction, the meson-baryon
interaction, has a strength of 1 in this scale, and the law is
completely unknown, although there are a number of known rules,
such as that the number of baryons does not change in any
reaction.This then, is the horrible condition of our physics
today. To summarize it, I would say this: outside the nucleus, we
seem to know all; inside it, quantum mechanics is valid—the
principles of quantum mechanics have not been found to fail. The
stage on which we put all of our knowledge, we would say, is
relativistic space-time; perhaps gravity is involved in
space-time. We do not know how the universe got started, and we
have never made experiments which check our ideas of space and
time accurately, below some tiny distance, so we only know that
our ideas work above that distance. We should also add that the
rules of the game are the quantum-mechanical principles, and those
principles apply, so far as we can tell, to the new particles as
well as to the old. The origin of the forces in nuclei leads us to
new particles, but unfortunately they appear in great profusion
and we lack a complete understanding of their interrelationship,
although we already know that there are some very surprising
relationships among them. We seem gradually to be groping toward
an understanding of the world of subatomic particles, but we
really do not know how far we have yet to go in this task.
--
这个世界不是缺少美；
而是缺少发现美的眼睛！
上帝呀，请赐予我吧！
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