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done is to describe 5ou the earth moves around the sun, but we have not said
tuhat makes ?t go. Newton made no hypotheses about this; he was satisfed to ñnd
tuhøt it dịd without getting into the machinery ofit. No one has sincc giuen ang
tmachiner. Tt 1s characteristic of the physical laws that they have this abstract
character. 'Phe law of conservation of energy is a theorem concerning quantities
that have to be calculated and added together, with no mention of the machinery,
and likewise the great laws of mechanics are quantitative mathematical laws Íor
which no machinery is available. Why can we use mathematics to describe nature
without a mechanism behind it? No one knows. We have to keep going because
we fnd out more that way.
Many mechanisms for gravitation have been suggested. Ït is interesting to
consider one of these, which many people have thought of rom time to time. At
first, one is quite excited and happy when he “discovers” it, but he soon finds
that i% is not correct. lt was first discovered about 1750. Suppose there were
many particles moving in space at a very high speed in all directions and being
only slightly absorbed in going through matter. When they are absorbed, they
give an impulse to the earth. However, since there are as many going one wawy
as another, the impulses all balance. But when the sun 1s nearby, the particles
coming toward the earth through the sun are partially absorbed, so fewer of them
are coming from the sun than are coming from the other side. Therefore, the
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earth feels a net impulse toward the sun and it does not take one long to see
that it is inversely as the square of the distance—because of the variation of the
solid angle that the sun subtends as we vary the distance. What is wrong with
that machinery? It involves some new consequences which are noø‡ fruec. This
particular idea has the following trouble: the earth, in moving around the sun,
would impinge on more particles which are coming from i§s forward side than
from its hind side (when you run in the rain, the rain in your face is stronger
than that on the back of your headl). Therefore there would be more impulse
given the earth from the front, and the earth would feel a resistance ‡o motion
and would be slowing up in its orbit. One can calculate how long i9 would take
for the earth to stop as a result of this resistance, and it would not take long
enough for the earth to still be in its orbit, so this mechanism does not work. No
machinery has ever been invented that “explains” gravity without also predicting
some other phenomenon that does øœø exist.
Next we shall discuss the possible relation of gravitation to other forces. Thhere
is no explanation of gravitation in terms of other forces at the present time. lt
1s not an aspect of electricity or anything like that, so we have no explanation.
However, gravitation and other forces are very similar, and it is interesting to
note analogies. Eor 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 produet 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 unifñed fñeld theory is only
a very elegant attempt to combine electricity and gravitation; but, in comparing
gravitation and electricity, the most interesting thing is the relatioe strengths of
the forces. Any theory that contains them both must also deduce how strong the
gTAVIEYy 1s.
TỶ we take, in some natural units, the repulsion of two electrons (nature's
universal charge) due to electricity, and the attraction of 6wo electrons due to
their masses, we can measure the ratio of electrical repulsion to the gravitational
attraction. “The ratio is independent of the distance and is a fundamental constant
of nature. The ratio is shown in Fig. 7-14. 'Phe gravitational attraction relative
to the electrical repulsion bebween two electrons is 1 divided by 4.17 x 102! The
question is, where does such a large number come from? lt is not accidental, like
the ratio of the volume of the earth to the volume of a fea. We have considered
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= 1⁄4 70, 2O, 000, ooo Sa,
-ạoe '098
"Sao Đ00 oøo,
Fig. 7-14. The relative strengths of electrical and gravitational inter-
actions between two electrons.
two natural aspects of the same thing, an electron. This fantastic number is a
natural constant, so it Involves something deep in nature. Where could such
a tremendous number come from? Some say that we shall one day fnd the
“universal equation,” and ïn it, one of the roots will be this number. ϧ is very
dificult to ñnd an equation for which such a fantastic number is a natural root.
Other possibilities have been thought of; one is to relate it to the age of the
universe. Clearly, we have to fnd øanother large number somewhere. But do
we mean the age of the universe in eørs? No, because years are not “natural”;
they were devised by men. As an example of something natural, let us consider
the time it takes light to go across a proton, 102? second. If we compare this
time with the aøe oƒ the niuerse, 2 x 1010 years, the answer is 1072. ]t has
about the same number of zeros going of it, so it has been proposed that the
gravitational constant is related to the age of the universe. If that were the case,
the gravitational constant would change with time, because as the universe got
older the ratio of the age of the universe to the time which it takes for light to go
across a proton would be gradually increasing. Is it possible that the gravitational
constant ¡s changing with time? Of course the changes would be so small that it
1s quite difficult to be sure.
One test which we can think of is to determine what would have been the
effect of the change during the past 10 years, which is approximately the age
from the earliest life on the earth to now, and one-tenth of the age of the universe.
In this time, the gravity constant would have increased by about 10 percent.
Tt turns out that if we consider the structure of the sun—the balance bebween
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the weight of its material and the rate at which radiant energy ¡is generated
Inside it —we can deduce that if the gravity were 10 percent stronger, the sun
would be much more than 10 percent brighter—by the sizth pouer of the gravity
constantl If we calculate what happens to the orbit of the earth when the gravity
is changing, we find that the earth was then cỉoser 7n. Altogether, the earth
would be about 100 degrees centigrade hotter, and all of the water would not
have been in the sea, but vapor in the aïr, so life would not have started in the
sea. So we do ro now believe that the gravity constant is changing with the age
of the universe. But such arguments as the one we have just given are not very
convincing, and the subject is not completely closed.
lt is a fact that the force of gravitation is proportional to the mass, the
quantity which is fundamentally a measure of 7nerf2aœ—of how hard ït is to hold