Feynman_Lectures_on_Physics_Volume_1_Chapter_02.pdf

Basic Physics

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 perma-

nence, 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 com-

plicated 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 dif-

ferent 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 under-

stand why a particular move is made in the game, merely because it is too com-

plicated 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 our-

selves to the more basic question of the rules of the game. If we know the rules,

we consider that we "understand" the world.

2-1 Introduction

2-2 Physics before 1920

2-3 Quantum physics

2-4 Nuclei and particles

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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 prob-

ably 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. How-

ever, 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 amalga-

mating 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 dif-

ferent 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 amalga-

mate 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

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 inter-

action force which held the various atoms in different combinations in a com-

plicated 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 direc-

tion 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 combina-

tion 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.

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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 elec-

trically 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 produc-

ing 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 be-

come 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 "inter-

action" 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 pushed

2-4

the 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 the-

idea of direct interaction must be replaced with the existence of the water, or-in-

the 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 10 1 4 to 5 X 10 1 5 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 10 24 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.

Table 2-1

The Electromagnetic Spectrum

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