Again, just as matter cannot produce a field of force distributed in exactly the same way as a field generated by acceleration, so also is it impossible to produce by the sole virtue of acceleration a field of force distributed in exactly the same way as the gravitational field around matter. From this it follows that it is impossible, by merely selecting some suitably accelerated frame, to cancel in its entirety a field of force produced by matter. This statement may appear to be in conflict with the example of the falling elevator, in which it was explained that owing to the motion of the elevator the field of force produced by the earth vanished in its interior. However, there is [Pg 258] no conflict between the two statements, if we are careful to express ourselves with precision. In the falling elevator no field of force is experienced in the interior of the elevator, provided the extension of the elevator is small in comparison with the size of the earth. If the elevator were very large, if, for instance, it were a gigantic box completely surrounding the earth, no conceivable motion of the box could ever cause the gravitational field of the earth to vanish everywhere in the box’s interior. Suppose, for instance, that the roof of the box were accelerated towards the North Pole, its floor would then be moving with accelerated motion away from the South Pole. Hence, whereas an observer attached to the roof of the box would perceive no force of gravitation, an observer attached to the floor would experience a force of doubled intensity. In other words, it would be impossible to banish the force of gravitation in all parts of the box. Only when the box or elevator is small in comparison with the earth, so that within its confines the field produced by our planet is practically uniform, is it possible to cancel the earth’s field in the whole interior of the box. Even then, however, this cancellation would be rigorous only at a point, and would decrease in thoroughness as we moved away from this point. It follows that a falling elevator cannot be assimilated in all rigour to a Galilean frame, since in a Galilean frame, wherever we might be stationed, no forces would be experienced. Nevertheless, as in practice, the frames we consider are not supposed to extend for great distances in all directions, conditions enduring in a falling elevator would be identical to a very high order of precision with those existing in a Galilean frame. For this reason, rigid frames of small dimensions falling freely in a gravitational field are termed semi-Galilean.