D O C . 4 4 T H E T H E O R Y O F R E L AT I V I T Y 5 5 perform no circular motions. And such a coordinate system, whose state of motion is such that the law of inertia holds relative to it, will thus be called a “Galilean co- ordinate system.” Now we have nearly finished laying the foundations for the so-called “principle of relativity” (in the strict sense). For reasons of clarity, let us start from the exam- ple of the uniformly moving train. We will call its motion a uniform translation (“uniform” because its velocity and direction remain constant “translation” be- cause the cars change their place along the track without rotating). Now if a raven is flying through the air rectilinearly and uniformly—as seen from the train tracks—then—as seen from the moving train—its motion is also linear . and uni- form. Expressed in an abstract way: if a mass m (“the raven”) is moving linearly and uniformly with respect to a coordinate system K (“the train track”), then it is also moving linearly and uniformly with respect to a second coordinate system K I (“the train”), provided that the latter is performing uniform translation relative to K. If K were a Galilean coordinate system (a system relative to which the law of inertia (I) holds), then every coordinate system K I that is in a state of linear trans- lation relative to K is likewise a Galilean coordinate system. If we take a further step in this generalization, then we arrive at the “principle of relativity” (II) in the strict sense: If K I (“the train”) is a coordinate system that is moving uniformly and without rotations relative to K (the track”), then all events in nature proceed with respect to K I according to precisely the same general laws as with respect to K. This result is by no means as self-evident as it now hopefully appears indeed, recent developments in electrodynamics and optics have placed the validity of the principle of relativity under scrutiny, and the answer appeared to be quite possibly “no.” Within the field of mechanics, at least, the validity of the principle of relativ- ity is supported, e.g., by the fact that mechanics predicts the real motions of the heavenly bodies with admirable precision. A serious difficulty, however, immediately arises as soon as one attempts to rec- oncile the principle of relativity (II) with the law of propagation of light (the law of constancy of the velocity of light). This law states, as is well known (III), that light propagates at a velocity of c = 300,000 km per second along straight lines in empty space. Naturally, we must also refer the process of light propagation to a rigid frame of reference (coordinate system). Let us thus imagine that along our already often-used train track, a light beam is sent at its velocity of c = 300,000 km per second relative to the track. Let our train travel along the track in the same direction at the velocity v. The “propagation [p. 6]
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