9 5 4 A P P E N D I X F invariance in all systems, no matter what their movements might be. In other words, the form must be maintained not only for linear, right-angle transformations but for any others, as well. That means establishing the impossibility of recognizing, unmistakably, the motion of a body, rectilinear and uniform or not, through any sort of experiments performed on it. To affirm such a principle, however, seems to contradict the results of the experiment, since the existence of acceleration is evident in measurable internal effects. For example, let us think about what happens to the passengers when a train stops abruptly, or the possibility of predicting the rotational movement of the Earth (Foucault’s experiment). That is to say, while classical mechanics gives uniform, rectilinear movements a relative character, it endows that variable motion with a sort of absolute reality, contrary to what the generalized principle attempts to do. The possibility of determining accelerated movement comes from the existence of the so-called terms of inertia (Coriolis force), which classical mechanics always considered to be fictitious forces that “do not originate from external actions, although they are equivalent to them in their effects … which makes the possibility mentioned less likely, since it would be impossible to determine if the phenomena are the result of a change of velocity or a convenient force field. One explanation would be as plausible as the other.” What we have just said takes on transcendental importance, especially in regard to grav- itation. The effects we attributed to this could also easily be attributed to accelerated move- ment of the system. Free bodies in space, no matter what their nature or mass, would all fall at the same time, if, assuming gravity did not exist, we observed them from a system moving relative to them with motion that had the same acceleration as the fall. This, let us repeat once more, makes the possibility of recognizing accelerated movement less plausible. Thus, it is impossible to claim the existence of experimental facts that contradict the gen- eralized principle. Besides, since a privileged system of reference among those moving rel- atively with rectilinear, uniform motion cannot exist, it would be incomprehensible for all of them to form a set of privileged systems. Additionally, there is no reason to justify the possibility that the form of natural laws depends on the system they refer to. These consid- erations, together with the impossibility of unmistakably identifying the accelerated move- ment of a system, allow us to postulate the generalization of the principle of relativity. The equivalence between a gravitational field and an acceleration, while serving as a basis for establishing the general principle, allows us to understand the effects of gravity. That equivalence means “that the perspective nature offers an observer at rest in a grav- itational field is the same one it offers in a field free from that condition to an observer mov- ing at a certain acceleration.” Geometry and Time in a Gravitational Field Given that acceleration in the aforementioned sense is the equivalent of gravitation—Dr. Einstein said—we will refer to them interchangeably here in both cases. Let us see, he con- tinued, how spatial and temporal indications should be interpreted in general relativity. Let