When I was in junior high school I used to amuse myself by swinging on the rings in gym. (I was lighter then, and more foolhardy.) On one occasion I grew weary of the exercise, so at the end of one swing I let go.
It was my feeling at the time, as I distinctly remember, that I would continue my semicircular path and go swoop ing upward until gravity took hold; and that I would then come down light as gossamer, landing on my toes after a perfect entrechat.
That is not the way it happened. My path followed nearly a straight line, tangent to the semicircle of swing at the point at which I let go. I landed good and hard on one side..
After my head cleared, I stood up* and to this day that is the hardest fall I have ever taken.
I might have drawn a great deal of intellectual good out of this incident. I might have pondered on the effects of inertia; puzzled out methods of sumn-ting vectors; or de duced some facts about differential calculus.
However, I will be frank with you. What really im pressed itself upon me was the fact that the force of gravity was both mighty and dangerous and that if you weren't watching every minute, it would clobber you.
Presumably, I had learned that, somewhat less dras tically, early in life; and presumably, every human being who ever got onto his hind legs at the age of a year or less and promptly toppled, learned the same fact.
People react oddly. After I stood up, I completely ignored my badly sprained (and possibly broken, though it later turned out not to be) right wrist imd lifted my untouched left wrist to my ear.
What worried me was whether my wristwatch were still running.
In fact, I have been told that infants have an instinctive fear of falling, and that this arose out of the survival value of having such an instinctive fear during the tree-living aeons of our simian ancestry.
We can say, then, that gravitational force is the first force with which each individual human being comes in contact. Nor can we ever manage to forget its existenc6, since it must be battled at every step, breath, and heart beat. Never for one moment must we cease exerting a counterforce.
It is also comforting that this mighty and overwhelming force protects us at all times. It holds us to our planet and doesn't allow us to shoot off into space. It holds our air and water to the planet too, for our perpetual use. And it holds the Earth itself in its orbit about the Sun, so that we always get the light and warmth we need.
What with all this, it generally comes as a rather sur prising shock to many people to learn that gravitation is not the strongest force in the universe. Suppose, for in stance, we compare it with the electromagnetic force that allows a magnet to attract iron or a proton to attract an electron. (The electromagnetic force also exhibits repul sion, which gravitational force does not, but that is a detail that need not distress us at this moment.)
How can we go about comparing the relative strengths of the electromagnetic force and the gravitational force? . Let's begin by considering two objects alone in the uni verse. The gravitational force between them, as was dis covered by Newton, can be expressed by the following equation (see also Chapter 7):
Gmr amp;
Fg = (Equation 1) d2 where F, is the gravitational force between the objects; m is the mass of one object; the mass of the other; d the distance between them; and G a universal "gravitational constant."
We must be careful about our units of measurement. If we measure mass in grams, distance in centimeters, and G in somewhat more complicated units, we will end up by determining the gravitational force in something called "dynes." (Before I'm through this chapter, the dynes will cancel out, so we need not, for present purposes, consider the dyne anything more than a one-syllable noise. It will be explained, however, in Chapter 13.)
Now let's get to work. The value of G is fixed (as far ,as we know) everywhere in the universe. Its value in the units I am using is 6.67 x 10-8. If you prefer long zero riddled decimals to exponential figures, you can express
G as 0.0000000667.
Let's suppose, next, that we are considering two objects of identical mass. This means that m = m'. so that mm' becomes mm, or M2. Furthermore, let's suppose the parti cles to be exactly I centimeter apart, center to center. In that case d = 1, and d2 = 1 also. Therefore, Equation 1 simplifies to the following:
F, = 0.0000000667 m2 (Equation 2)
We can now proceed to the electromagnetic force, which we can symbolize as F,.
Exactly one hundred years after Newton worked out the equation for gravitational forces, the French physicist Charles Augustin de Coulomb (1736-1806) was able'to show that a very similar equation could be used to deter mine the electromagnetic force between two electrically charged objects.
- Let us suppose, then, that the two objects for which we have been trying to calculate gravitational forces also carry electric charges, so that they also experience an electro magnetic force. In order to make sure that the electromag netic force is an attracting one and is therefore directly comparable to the gravitational force, let us suppose that one object carries a positive electric charge and the other a negative one. (The principle would remain even if we used like electric charges and measured the force of clec tromagnetic repulsion, but why introduce distractions?)
According to Coulomb, the electromagnetic force be 102 tween the two objects would be expressed by the foflo ' wmg equation:
F. (Equation 3) d2 where q is the charge on one object, q' on the other, and d is the distance between them.
If we let distance be measured in centimeters and elec tric charge in units called "electrostatic units" (usually abbreviated "esu7'), it is not necessary to insert a term analogous to the gravitational constant, provided the ob jects are separated by a vacuum. And, of course, since I started by assuming the objects were alone in the universe, there is necessarily a vacuunf between them.
Furthermore, if we use the units just mentioned, the value of the electromagnetic force will come out in dynes.
But lefs simplify matters by supposing that the positive electric charge on one object is exactly equal to the nega tive electric charge on the other, so that q = q,* which means that the objects . qq = qq = q2. Again, we can allow to be separated by just one centimeter, center to center, so that d2 = 1. Consequently, Equation 3 becomes:
Fe = q2 (Equation 4)
Let's summarize. We have two objects separated by one centimeter, center to center, each object possessing identi cal charge (positive in one case and negative in the other) and identical mass (no qualifications). There is both a gravitational and an electromagnetic attraction, between them.
The next problem is to determine how much stronger the electromagnetic force is than the gravitational force (or how much weaker, if that is how it turns out). To do * We could make one of them negative to allow for the fact that one object carries a negative electric charge. Then we could say that a negative value for- the electromagnetic force implies an attraction and a positive value a repulsion. However, for our pur poses, none of this folderol is needed. Since electromagnetic at traction and repulsion are but opposite manifestations of the same phenomenon, we shall ignore signs.
this we must determine the ratio of the forces by dividing
(let us say) Equation 4 by Equation 2. The result is:
F, q2 (Equation 5)
F, 0.0000000667 M2
A decimal is an inconvenient thing to have in a denomi nator, but we can move it up into the numerator by taking its reciprocal (that is, by dividing it into 1). Since 1 di vided by 0.0000000667 is equal to 1.5 x 101, or 15,000, 000, we can rewrite Equation 5 as:
F, _ 15,000,000 q2 (Equation 6)
Fg m2 or, still more simply, as:
F,. = 15,000,000 (VM)2 (Equat;on 7)
Since both F, and F, are measured in dynes, then in taking the ratio we find we are dividing dynes by dynes.
The units, therefore, cancel out, and we are left with a "pure number." We are going to find, in other words, that one force is stronger than the other by a fixed amount; an amount that will be the same whatever units we use or whatever units an intelligent entity on the fifth planet of the star Fomalhaut wants to use. We will have, therefore, a universal constant.
In order to determine the ratio 0 the two es, we see from Equation 7 that we must first determine the value of qlm; that is, the charge of an object divided by its mass. Let's consider charge first.
AJI objects are made up of subatomic particles of a number of varieties. These particles fall into exactly three classes, however, with respect to electric charge:
1) Class A are those particles which, like the neutron and the neutrino, have no charge at all. Their charge is 0.
2) Class B are those particles which, like the proton and the positron, carry a positive electric charge. But all particles which carry a positive electric charge invariably carry the same quantity of positive electric charge what ever their differences in other respects (at least as far as we know). Their charge can therefore be specified as +I.
3) Class C are those particles which, like the electron and the anti-proton, carry a negative electric charge.
Again, this charge is always the same in quantity. Their charge is - 1.
You see, then, that an object of any size can have a net electric charge of zero, provided it happens to be made up of neutral particles and/or equal numbers of positive and negative particles.
For such an object q = 0, and no matter how large its mass, the value of qlm is also zero. For such bodies, Equation 7 tells us, FIF, is zero. The gravitational force is never zero (as long as the objects have any mass at all) and it is, therefore, under these conditions, infinitely stronger than the electromagnetic force and need be the only one considered.
This is just about the case for actual bodies. The over all net charge of the Earth and the Sun is virtually zero, and in plotting the EartWs orbit it is only necessary to con sider the gravitational attraction between the two bodies.
Still, the case where F. = 0 and, therefore, FIF,, = 0 is clearly only one extreme of the situation and not a par ticularly interesting one. What about the other extreme?
Instead of an object with no charge, what about an object with maximum charge?
If we are going to make charge maximum, let's first eliminate neutral particles which add mass without charge.
Let's suppose, instead, that we have a piece of matter com posed exclusively of charged particles. Naturally it is of no use to include charged particles of both varieties, since then one " of charge would cancel the other and total charge would be less than maximum.
We will want one object then, composed exclusively of positively charged particles- and another exclusively of negatively charged particles. We can't possibly do better than that as a general thing.
And yet while all the charged particles have identical charges of either + 1 or - 1, as the case may be, they pos sess different masses. What we want are charged particles of, the smallest possible mass. In that case the largest pos sible individual charge is hung upon the smallest possible mass, and the ratio qlm is at a maximum.
It so happens that the negatively charged particle of smallest mass is the electron and the positively charged particle of smallest mass is the positron. For those bodies, the ratio qltn is greater than for any other known object (nor have we any reason, as yet, for suspecting that any object of higher qlm remains to be discovered).
Suppose, then, we start with two bodies, one of which contains a certain number of electrons and the other the same number of positrons. There will be a certain electro magnetic force between them and also a certain gravi tational force.
If you triple the number of electrons in the first body and triple the number of positrons in the other, the total charge triples for each body and the total electromagnetic force, therefore, becomes 3 times 3, or 9 times greater.
However, the total mass also triples for each bod and the y total gravitational force also becomes 3 times 3, or 9 times greater. While each force increases, they do so to an equal extent, and the ratio of the two remains the same.
In fact the ratio of the two forces remains the same, even if the charge and/or mass on one body is not equal to the charge and/or mass on the other; or if the charge and/or mass of one body is changed by an amount different from the charge in the other.
Since we are concerned only with the ratio of the two forces, the electromagnetic and the gravitational, and since this remains the same, however much the number of electrons in one body and the number of positrons in the other are changed, why bother with any but the simplest possible number-one?
In other words, let's consider a Single electron and a simple positron separated by exactly I centimeter. This system will give us the maximum value'for the ratio of electromagnetic force to gravitational force.
It so happens that the electron and the positron have equal masses. That mass, in grams (which are the mass units we are using in this calculation) is 9.1 X 10-28 or, if you prefer, 0.00000000000000000000000000091.
The electric charge of the electron is equal to that of the positron (though different in sign). In electrostatic units (the charge-units being used in this calculation), the value is 4.8 x 10-111, or 0.00000000048.
To get the value qlm for the electron (or the positron) we must divide the charge by the mass. If we divide 4.8 x 10-10 by 9.1 X 10-28, we get the answer 5.3 x 1017 or 530,000,000,000,000,000.
But, as Equation 7 tells us, we must square the ratio qlm. We multiply 5.3 x 1017 by itself and obtain for (qlm)2 the value of 2.8 x 101,1, or 280,000,000,000,000, 000,000,000,000,000,000,000.
Again, consulting Equation 7, we find we must multiply this number by 15,000,000, and then we finally have the ratio we are looking for. Carrying through this multiplica tion gives us 4.2 x 1042, or 4,200,000,000,000,000,000, 000,000,000,000,000,000,000,000.
We can come to the conclusion, then, that the electro magnetic force is, under the most favorable conditions, over four million trillion trillion trillion times as strong as the gravitational force.
To be sure, under normal conditions there are no elec tron/positron systems in our surroundings, for positron virtually do not exist. Instead our universe (as far as we know) is held together electromagnetically by electron/ proton attractions. The proton is 1836 times as massive as the electron, so that the gravitational attraction is increased without a concomitant increase in electromagnetic attrac tion. In this case the ratio F,IF, is only 2.3 x 10il".
There are two other major forces in the physical world.
There is the nuclear strong interaction force which is over a hundred times as strong as even the electromagnetic force; and the nuclear weak interaction force, which is considerably weaker than the electromagnetic force. All three, however, are far, far strcinger than the gravitational force.
In fact, the force of gravity-though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate-is by far the weakest known force in nature. It is first and rearmost!
What makes the gravitational force seem so strong?
First, the two nuclear forces;ire short-range forces which make themselves felt only over distances about the width of an atomic nucleus. The electromagnetic force and the gravitational force are the only two long-range forces.
Of these, the electromagnetic force cancels itself out (with slight and temporary local exceptions) because both an attraction and a repulsion exist.
This leaves gravitational force alone in the field.
What's more, the most conspicuous bodies in the uni verse happen to be conglomerations of vast mass, and we live on the surface of one of these conglomerations.
Even so, there are hints that give away the real weak ness of gravitational force. Your weak muscle can lift a fifty-pound weight with the whole mass of the earth pull ing, gravitationally, in the other direction. A to magnet will lift a pin against the entire counterpufl of the earth.
Oh, gravity is weak all right. But let's see if we can dramatize that weakness further.
Suppose that the Earth were an assemblage of nothing but its mass in positrons, while the Sun were an assem blage of nothing but its mass in electrons. The force of at traction between them would be vastly greater than the feeble gravitational force that holds them together now.
In fact, in order to reduce the electromagnetic attraction to no more than the present gravitational one, the Earth and Sun would have to be separated by some 33,000,000,000, 000,000 light-years, or about five million times the diame ter of the known universe.
Or suppose you imagined in the place of the Sun a mil 108 lion tons of electrons (equal to the mass of a very small asteroid). And in the place of the Earth, imagine 31/3 tons of positrons.
The electromagnetic attraction between these two in significant masses, separated by the distance from the Earth to the Sun, would be equal to the gravitational at traction between the colossal masses of those two bodies right now.
In fact, if one could scatter a million tons of electrons on the Sun, and 31/3 tons of positrons on the Earth, you would double the Sun's attraction for the Earth and alter the nature of Earth's orbit considerably. And if you made it electrons, both on Sun and Earth, so as to introduce a repulsion, you would cancel the gravitational attraction al together and send old Earth on its way out of the Solar System.
Of course, all this is just paper calculation. The mere fact that electromagnetic forces are as strong as they are means that you cannot collect a significant number of like charged particles in one place. They would repel each other too strongly.
Suppose you divided the Sun into marble-sized fragments and strewed them through the Solar System at mutual rest.
Could you, by some manmade device, keep those fragments from falling together under the pull of gravity? Well, this is no greater a task than that of getting bold of a million tons of electrons and squeezing them together into a ball.
The same would hold true if you tried to separate a sizable quantity of positive charge from a sizable quantity of negative charge.
If the universe were composed of electrons and posi trons as the chief charged particles, the electromagnetic force would make it necessary for them to come together.
Since they are anti-particles, one being the precise reverse of the other, they would melt together, cancel each other, and go up in one cosmic flare of gamma rays.
Fortunately, the universe is composed of electrons and protons as the chief charged particles. Tbough their charges are exact opposites (-I for the former and +1 for the latter), this is not so of other properties-such as mass, for instance. Electrons and protons are not antiparticles, in other words, and cannot cancel each other.
Their opposite charges, however, set up a strong mutual attraction that cannot, within limits, be gainsaid. An elec tron and ia proton therefore approach closely and then maintain themselves at a wary distance, forming the hy drogen atom.
Individual protons can cling together despite electro magnetic repulsion because of the existence of a very short-range nuclear strong interaction force that sets up an attraction between neighboring protons that far over balances the electromagnetic repulsion. This makes atoms other than hydrogen possible.
In short: nuclear forces dominate the atomic nucleus; electromagnetic forces dominate the atom itself; and grav itational forces dominate the large astronomic bodies.
The weakness of the gravitational force is a source of frustration to physicists.
The different forces, you see, make themselves felt by transfers of particles. The nuclear strong interaction force, the strongest of all, makes itself evident by transfers of pions (pi-mesons), while the electromagnetic force (next strongest) does it by the transfer of photons. An analogous particle involved in weak interactions (third strongest) has recently been reported. It is called the "W particle" and as yet the report is a tentative one.
So far, so good. It seems, then, that if gravitation is a force in the same sense that the others are, it should make itself evident by transfers of particles.
Physicists have given this particle a name, the "graviton."
They have even decided on its properties, or lack of prop erties. It is electrically neutral and without mass. (Because it is without mass, it must travel at an unvarying velocity, that of light.) It is stable, too; that is, left to itself, it Will not break down to form other particles.
So far, it is rather like the neutrino, [See Chapter 13 of my book View from a Height, Doubleday, 1963.] hich is also stable, electrically neutral, and massless (hence traveling at the velocity of light).
The graviton and the neutrino differ in some respects, however. The neutrino comes in two varieties, an electron neutrino and a muon (mu-meson) neutrino, each with its anti-particle; so there are, all told, four distinct kinds of neutrinos. The graviton comes in but one variety and is its own anti-particle. There is but one kind of graviton.
Then, too, the graviton has a spin of a type that is as signed the number 2, while the neutrino along with most other subatomic particles have spins of 1/2. (There are also some mesons with a spin of 0 and the photon with a spin of 1.)
The graviton has not yet been detected. It is even more elusive than the neutrino. The neutrino, while massless and chargeless, nevertheless has a measurable energy con tent. Its existence was first suspected, indeed, because it carried off enough energy to make a sizable gap in the bookkeeping.
But gravitons?
Well, remember that factor of 10421
An individual graviton must be trillions of trillions of trillions of times less energetic than a neutrino. Considering how difficult it was to detect the neutrino, the detection of the graviton is a problem that will really test the nuclear physicist.
