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 7 and the spatial distance between two points on a rigid body, depend on the state of motion of the moving body. This statement resolves the dilemma of the incompati- bility of the principle of relativity and the law of light propagation, since the addi- tion theorem (IV) no longer holds. An additional question immediately arises: How can an event that I have fixed temporally and spatially (“spatiotemporally”) for a coordinate system K (“the track”) be determined also for a moving coordinate system K I (“the train”)? This is accomplished by the system of equations called the Lorentz transformations (which we cannot describe in detail here). From them, we find the no longer uncanny-appearing fact that moving clocks tick more slowly than clocks at rest, and that a rigid ruler that is moving lengthwise is shorter than the same ruler in the state of rest. The theory of special relativity, which grew out of electrodynamics and optics, has not changed the conclusions of the theory in those fields to any great extent but it has yielded a law of motion for the field of mechanics that has been verified experimentally, that deviates at high velocities from that of classical mechanics, and has simplified and unified the theoretical structure. With its help, for example, the law of conservation of mass and the law of conservation of energy could be combined into a single law, since the theory shows that the inertial mass of a body is not a fixed quantity, but rather changes along with changes in its energy. The the- ory of relativity also explains the mirror experiment of Michelson and Morley[2] in a much more satisfying manner than all the other attempts at explaining it, and without the need to introduce the contradictory and difficult ether theory. Let us make the content of the principle of special relativity clear once more: it states that if K is a Galilean coordinate system (with respect to which the law of inertia thus holds), then every other coordinate system K I is also Galilean, if it per- forms a linear, uniform, rotation-free motion with respect to the first system. The theory of special relativity does not differ from classical mechanics in its postulate of relativity, but rather in its postulate of the constancy of the velocity of light prop- agation in empty space (III) from which, together with the principle of relativity (II), follow the relativity of simultaneity as well as the Lorentz transformations and the laws for the behavior of moving rigid bodies and clocks associated with them. By “principle of general relativity” we will now understand (for the moment) the assertion that all frames of reference K, K I , etc. for the description of nature (i.e., for the formulation of general laws of nature) are equivalent, whatever their state of motion may be. The laws of physics must take a form such that they hold with respect to any arbitrarily moving frame of reference. Every child knows: a stone falls because it is attracted by the Earth, in fact with an acceleration that is independent of its specific weight. The Earth produces a [p. 7]
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