Page:The principle of relativity (1920).djvu/27

 Einstein's first theory is restricted in the sense that it only refers to uniform rectiliniar motion and has no application to any kind of accelerated movements. Einstein in his second theory extends the Relativity Principle to cases of accelerated motion. If Relativity is to be universally true, then even accelerated motion must be merely relative motion between matter and matter. Hence the Generalised Principle of Relativity asserts that "absolute" motion cannot be detected even with the help of gravitational laws. All movements must be referred to definite sets of co-ordinate axes. If there is any change of axes, the numerical magnitude of the movements will also change. But according to Newtonian dynamics, such alteration in physical movements can only be due to the effect of certain forces in the field. Thus any change of axes will introduce new "geometrical" forces in the field which are quite independent of the nature of the body acted on. Gravitational forces also have this same remarkable property, and gravitation itself may be of essentially the same nature as these "geometrical" forces introduced by a change of axes. This leads to Einstein's famous Principle of Equivalence. A gravitational field of force is strictly equivalent to one introduced by a transformation of co-ordinates and no possible experiment can distinguish between the two.

Thus it may become possible to "transform away" gravitational effects, at least for sufficiently small regions of space, by referring all movements to a new set of axes. This new "framework" may of course have all kinds of very complicated movements when referred to the old Galilean or "rectangular unaccelerated system of co-ordinates."

But there is no reason why we should look upon the Galilean system as more fundamental than any other. If it