Gravitational polarization, which could make possible shielding against the force of gravity, requires that matter be constituted of two kinds of particles : some with positive gravitational mass, which are attracted by the earth, and some with negative gravitational mass, which are repelled. Positive and negative electric charges and north and south magnetic poles are equally abundant in nature, but particles with negative gravitational mass are as yet unknown, at least within the structure of ordinary atoms and molecules. Therefore ordinary matter cannot be gravitationally polarized and cannot act as a gravity shield.
There is, however, another kind of matter-antimatter-that in many ways is the reverse of ordinary matter, including its electric and magnetic properties. Perhaps antiparticles also have negative mass. At first sight this might seem an easy point to decide. One has only to watch a horizontal beam of antineutrons, say, emerging from an accelerator and see whether the beam bends down or up in the gravitational field of the earth. In practice the experiment cannot be done. The particles produced by accelerators move almost at the speed of light; in a kilometer of horizontal travel gravity would bend them, whether up or down, only about 10^-12 centimeter, the diameter of an atomic nucleus. Nor can they be slowed down by letting them collide with the nuclei of a "moderator" material, as neutrons are slowed in atomic piles. If antiparticles collide with their ordinary counterparts, both disappear in material annihilation. Thus from the experimental point of view the question as to the sign of the gravitational mass of antiparticles remains painfully open.
From the theoretical point of view it is open too, since we do not have a theory that relates gravitational and electromagnetic interactions. If a future experiment should demonstrate that antiparticles do have a negative gravitational mass, it will deliver a mortal blow to the entire relativistic theory of gravity by disproving the principle of equivalence. An antiapple might fall up in a true gravitational field, but it could hardly do so in Einstein's accelerated spaceship. If it did, an outside observer would see it moving at twice the acceleration of the ship, with no force at all acting on it. The discovery of antigravity would therefore force upon us a choice between Newton's law of inertia and Einstein's equivalence principle. The author earnestly hopes that this will not come to pass.