Einstein’s next attempt was therefore to weld Newton’s law into the general fabric, a result he achieved about 1914. The mathematical generalisation which would allow this result to be obtained seems almost obvious to-day, since (as will be explained in Chapter XXV) it reduces to assuming that in the neighbourhood of matter, four-dimensional space-time loses its flatness and becomes non-Euclidean or curved. However, it appears to have been through the medium of physical observation that Einstein was led to his superb generalisation, so we shall proceed to follow the historical order by explaining the significance of his postulate of equivalence. [Pg 250] CHAPTER XXIV THE POSTULATE OF EQUIVALENCE EINSTEIN’S Postulate of Equivalence consists essentially in an identification of forces of gravitation and forces of inertia. This identification he considered permissible because of certain well-known empirical facts which we shall discuss presently. Let us first recall that a field of force is exemplified by a region of space, at each and every point of which a definite force would be found to be acting on a test-body with which the field might be explored. Several different types of fields were known to classical science. Electric fields acted on electrified bodies, magnetic fields acted on magnets, and both inertial and gravitational fields acted on material bodies in general, whether electrified or not. For the present we shall be concerned solely with the inertial and gravitational fields. These two species of fields of force were regarded by classical science as of a totally different nature. There appeared to be very good reasons for this distinction. Suppose, for instance, that a train is slowing down. If we are standing in the train, we shall feel a force pulling us towards the engine and it may require a certain effort on our part to resist its pull. As such, the force is obviously real, in that it is experienced. But suppose now that an observer on the embankment views these same happenings. He will argue as follows: No force is pulling the passenger; but as the train is slowing down and as the passenger’s body tends to maintain a constant velocity along a straight line, in conformity with the laws of motion (law of inertia), the net result is that he will overtake the engine unless he holds on to the seat. Thus we see that according to whether we judge these same happenings from the standpoint of the train or of the embankment, the force exists or becomes a fiction.