The Feynman Lectures on Physics

It doesn't make a difference how beautiful your guess is. It doesn't make a difference how smart you are, who made the guess, or what his name is. If it disagrees with experiment, it's wrong.

How I'm rushing through this! How much each sentence in this brief story contains. "The stars are made of the same atoms as the earth." I usually pick one small topic like this to give a lecture on. Poets say science takes away from the beauty of the stars—mere globs of gas atoms. Nothing is "mere." I too can see the stars on a desert night, and feel them. But do I see less or more ? The vastness of the heavens stretches my imagina-tion—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part—perhaps my stuff was belched from some forgotten star, as one is belching there. Or see them with the greater eye of Palomar, rushing all apart from some common starting point when they were perhaps all together. What is the pattern, or the meaning, or the why ? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined! Why do the poets of the present not speak of it ? What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms.

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.

In its efforts to learn as much as possible about nature, modern physics has found that certain things can never be "known" with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.

Every object is a mixture of lots of things, so we can deal with it only as a series of approximations and idealizations.

Another most interesting change in the ideas and philosophy of sciencebrought about by quantum mechanics is this: it is not possible to predict exactlywhat will happen in any circumstance. For example, it is possible to arrange anatom which is ready to emit light, and we can measure when it has emitted lightby 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, whichone 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 fundamentallyimpossible to make a precise prediction of exactly what will happen in a givenexperiment.

What is this "zero mass"? The masses given here are the masses of theparticles at rest. The fact that a particle has zero mass means, in a way, that itcannot be at rest. A photon is never at rest, it is always moving at 186,000 miles asecond.

More was discovered about the electrical force. The natural interpretationof electrical interaction is that two objects simply attract each other: plus againstminus. 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 thepositive charge, in some sense, distorts, or creates a "condition" in space, so thatwhen we put the negative charge in, it feels a force. This potentiality for produc-ing a force is called an electric field.

What about the inside of the earth? A great deal is known about the speed ofearthquake waves through the earth and the density of distribution of the earth.However, physicists have been unable to get a good theory as to how dense asubstance should be at the pressures that would be expected at the center of theearth. In other words, we cannot figure out the properties of matter very well inthese circumstances. We do much less well with the earth than we do with theconditions of matter in the stars. The mathematics involved seems a little toodifficult, so far, but perhaps it will not be too long before someone realizes thatit is an important problem, and really work it out. The other aspect, of course, isthat even if we did know the density, we cannot figure out the circulating currents.Nor can we really work out the properties of rocks at high pressure. We cannottell how fast the rocks should "give"; that must all be worked out by experiment.

All things, even ourselves, are made of fine-grained, enormouslystrongly 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 easierto rub off minuses), and in those circumstances we find the force of electricityunbalanced, and we can then see the effects of these electrical attractions.

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 toput the jigsaw puzzle together. Whether there are a finite number of pieces, andwhether there is even a border to the puzzle, is of course unknown. It will neverbe known until we finish the picture, if ever. What we wish to do here is to see towhat extent this amalgamation process has gone on, and what the situation is atpresent, 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 elementsare there ?

We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection!

The gravitational attraction relative to the electrical repulsion between two electrons is 1 divided by 4.17 times ten to the 42nd power!As an example of something , let us consider the time it takes light to go across a proton, 10 to the negative 24 second. If we compare this time with the age of the universe , 2 times 10 to the tenth power years, the answer is 10 to the negative 42nd power. It has about the same number of zeros going off it, so it has been proposed that the gravitational constant is related to the age of the universe.

The best teaching can be done only when there is a direct individual relationship between a student and a good teacher—a situation in which the student discusses the ideas, thinks about the things, and talks aboutthe things. It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned.

As an example of something , let us consider the time it takes light to go across a proton, 10 to the negative 24 second. If we compare this time with the age of the universe , 2 times 10 to the tenth power years, the answer is 10 to the negative 42nd power. It has about the same number of zeros going off it, so it has been proposed that the gravitational constant is related to the age of the universe.

For example, the force of electricity between two charged objects looks just like the law of gravitation: the force of electricity is a constant, with a minus sign, times the product of the charges, and varies inversely as the square of the distance. It is in the opposite direction-likes repel. But is it still not very remarkable that the two laws involve the same function of distance? Perhaps gravitation and electricity are much more closely related than we think. Many attempts have been made to unify them; the so called unified-field theory is only a very elegant attempt to combine electricity and gravitation; but, in comparing gravitation and electricity , the most interesting thing is the relative strengths of the forces. Any theory that contains them both must also deduce how strong the gravity is.

One very important feature of pseudo forces is that they are always proportional to the masses; the same is true of gravity. The possibility exists, therefore, that gravity is a pseudo force. Is it not possible that perhaps gravitation is due simply to the fact that we do not have the right coordinate system? After all, we can always get a force proportional to the mass if we imagine that a body is accelerating. For instance, a man shut up in a box that is standing still on the earth finds himself held to the floor of the box with a certain force that is proportional to his mass. But if there were no earth at all and the box were standing still, the man inside would float in space. On the other hand, if there were no earth at all and something were pulling the box along with an acceleration g, then the man in the box analyzing physics would find a pseudo force which would pull him to the floor, just as gravity does.

Universal gravitationWhat else can we understand when we understand gravity? Everyone knows the earth is round. Why is the earth round? That is easy ; it is due to gravitation. The earth can be understood to be round merely because everything attracts everything else and so it has attracted itself together as far as it can! If we go even further, the earth is not exactly a sphere because it is rotating and this brings in centrifugal effects which tend to oppose gravity near the equator. It turns out that the earth should be elliptical, and we even get the right shape forthe ellipse. We can thus deduce that the sun, the moon, and the earth should be (nearly) spheres just from the law of gravitation.

Newton proved to himself (and perhaps we shall be able to prove it soon) that the very fact that equal areas are swept out in equal tines is a precise sign post of the proposition that all deviations are precisely radial-that the law of areas is a direct consequence of the idea that all of the forces are directed exactly toward the sun.

Einstein put forward the famous hypothesis that accelerations give an imitation of gravitation, that the forces of acceleration (the pseudo forces) cannot be distinguished from those of gravity; it is not possible to tell how much of a given force is gravity and how much is pseudo force.

Thus Kepler's three laws are: I. Each planet moves around the sun in an ellipse, with the sun at one focus.II. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time.III. The squares of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits : T - a'3/2

By extending our techniques—and if necessary our definitions—still furtherwe can infer the time duration of still faster physical events. We can speak of theperiod of a nuclear vibration. We can speak of the lifetime of the newly discoveredstrange resonances (particles) mentioned in Chapter 2. Their complete life occupiesa time span of only 10-24 second, approximately the time it would take light(which moves at the fastest known speed) to cross the nucleus of hydrogen (thesmallest known object).

Galileo expressed the result of his observations inthis way: if the location of the ball is marked at 1, 2, 3, 4,... units of time fromthe instant of Its release, those marks are distant from the starting point in propor-tion to the numbers 1, 4, 9, 16, ... Today we would say the distance is propor-tional to the square of the time

If it can be controlled in thermonuclear reactions, it turnsout that the energy that can be obtained from 10 quarts of water per second is equalto all of the electrical power generated in the United States. With 150 gallons ofrunning water a minute, you have enough fuel to supply all the energy which isused in the United States today! Therefore it is up to the physicist to figure outhow to liberate us from the need for having energy. It can be done.

The general name of energy which has to do with location relative to some-thing else is called potential energy.

We call the sum of the weights times the heights gravitational potentialenergy—the energy which an object has because of its relationship in space, rela-tive to the earth.

To summarize: every reversiblemachine, no matter how it operates, which drops one pound one foot and liftsa three-pound weight always lifts it the same distance, X. This is clearly a universallaw of great utility.

In order to verify the conservation of energy, wemust be careful that we have not put any in or taken any out. Second, the energyhas a large number of different forms, and there is a formula for each one. Theseare: gravitational energy, kinetic energy, heat energy, elastic energy, electricalenergy, chemical energy, radiant energy, nuclear energy, mass energy. If we totalup the formulas for each of these contributions, it will not change except for energygoing in and out.It is important to realize that in physics today, we have no knowledge of whatenergy is. We do not have a picture that energy comes in little blobs of a definiteamount. It is not that way. However, there are formulas for calculating somenumerical quantity, and when we add it all together it gives "28"'—always thesame number. It is an abstract thing in that it does not tell us the mechanism orthe reasons for the various formulas.

Assuming, however, that there issome kind of memory thing, the brain is such an enormous mass of interconnect ing wires and nerves that it probably cannot be analyzed in a straightforwardmanner. There is an analog of this to computing machines and computing ele-ments, in that they also have a lot of lines, and they have some kind of element,analogous, perhaps, to the synapse, or connection of one nerve to another. Thisis a very interesting subject which we have not the time to discuss further—therelationship between thinking and computing machines. It must be appreciated,of course, that this subject will tell us very little about the real complexities ofordinary human behavior. All human beings are so different. It will be a longtime before we get there.