Gravitation

Abstract

The Principle of Relativity requires that the fundamental laws of physics should be independent of the inertial frame of the observer. The inertial frame was supposed to be unaffected by external forces, and in the special theory of relativity this carried the implication that one inertial frame was unaccelerated relative to another. However, all observations on the earth’s surface are made in the presence of forces of several different kinds. Fortunately, for most observers the strongest of these forces — the force of gravity, and the force due to contact with the earth’s surface — are in approximate equilibrium with one another, and, at least over a limited area of the earth’s surface, the acceleration due to gravity does not vary much and affects all forms of matter in the same way. Also, according to Newtonian theory, the gravitational force exerted by two systems of mass m₁ and m₂ on one another is

$$ F = Gm_1 m_2 /r^2 $$

at distance r, where G ≈ 6.67 × 10^-8 in cgs units, and is completely negligible in most terrestrial applications, except where one of the systems is the earth itself! From this point of view, gravity is the weakest of known forces. For these reasons, the special theory of relativity provides an adequate basis for physical phenomena in a limited region of space and time. But for larger regions in the neighborhood of massive planets and stars it is necessary to develop a generalization to take account of the variations in the gravitational field.