How can one derive mathematically a constant as large as 10^40? Some 20 years ago Dirac made an interesting proposal. He suggested that the figure 10^40 is in fact not a constant, but a variable that changes with time and is connected with the age of the universe. According to the evolutionary cosmology, which holds that the universe originated with a "big bang," the universe is now about 5 × 10^9 years, or 10^17 seconds, old. Of course, a year or a second is an arbitrary unit, and we would prefer an elementary time interval that can be derived from the basic properties of matter and light. A reasonable one is the length of time required by light to travel a distance equal to the radius of an elementary particle. Since all the particles have radii of about 3 × 10^-13 centimeter, and since the velocity of light is 3 × 10^10 centimeters per second, this elementary time unit is 3 × 10^-13 divided by 3 × 10^10, or 10^-23 second. To express the age of the universe in this elementary time unit we divide its age in seconds, 10^17, by 10^-23 and obtain the number 10^40! Thus, said Dirac, the large ratio of electric to gravitational forces is characteristic of the present age of the universe. When the universe was half as old as it is now, this ratio was also half of its present value. Since there are good reasons to assume that the elementary electric charge does not change with time, Dirac concluded that the gravitational constant must be decreasing, and that this decrease may be associated with the expansion of the universe and the steady rarefaction of the material that fills it.
If the gravitational constant really has been decreasing, or in other words if the force of gravity has been growing weaker, then our solar system must have been expanding along with the universe. In earlier times the earth would have been nearer the sun and therefore hotter than it is now. When Dirac put forward the idea, the solar system was thought to be about three billion years old. Edward Teller, now at the University of California, pointed out that on such a time scale the earth would have been 50 degrees hotter than the boiling point of water during the Cambrian era, when well-developed marine life existed. Now it seems that the solar system may be five billion or more years old, in which case the Cambrian oceans, though hot, would not have been vaporized. So the objection loses its force, provided that Cambrian plants and animals could live in very hot water.
In one of his stories H. G. Wells describes a British ' inventor, Mr. Cavor, who found a material, called cavorite, that was impenetrable to the force of gravity. Just as sheet copper can shield an object against electric forces and sheet iron can shield against magnetism, a sheet of cavorite placed under a material body would shield it from the gravitational pull of the earth. Mr. Cavor built a large gondola surrounded by cavorite shutters. One night when the moon was high, he got into the ship, closed the shutters facing the ground and opened those facing the moon. Cut off from terrestrial gravity and subjected only to the attraction of the moon, the gondola soared into space and eventually deposited Mr. Cavor on the surface of our satellite.
Why is such an invention impossible? Or is it? There is a profound similarity between Newton's law of universal gravity and the laws that govern the interactions of electric charges and magnetic poles. If one can shield electric and magnetic forces, why not gravity? To answer this question we must consider the mechanism of electric and magnetic shielding. Each atom or molecule in any piece of matter is a system of positive and negative electric charges; in conducting metals there are numbers of negative electrons that are free to move through the crystal lattice of positively charged ions. Then a metal is placed in an electric field, the free electrons move to one side of the material, giving it a negative charge and leaving the opposite side positive. This polarization produces a new electric field, which is directed opposite to the original field. Thus the two can cancel each other. Similarly, magnetic shielding depends on the fact that the atoms of magnetic materials are tiny magnets, with north and south poles that line up so as to produce a field that opposes an external magnetic field. Here also the shielding effect arises from polarization of atomic particles.