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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 |
--- Trang 156 --- |
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 |
--- Trang 157 --- |
= 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 |
--- Trang 158 --- |
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 |
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