Space And Time in Contemporary Physics An Introduction to the Theory of Relativ
Space And Time in Contemporary Physics An Introduction to the Theory of Relativ
Moritz Schlick
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The velocity which it has at different points of its path, or the time at which it passes through these points. But if we add time # 4 as a third co- ordinate, the same motion will be represented by a three- dimensional curve, the form of which immediately gives us information about the character of the motion; for we can recognize directly from it which x belongs to any point Xi x 2 of the path, and we can also read off the velocity at any mo- ment from the inclination of the curve to the #i-#... 2 -plane. We shall follow Minkowski by appropriately calling this curve the world-lime of the point. A circular motion in the #i-# 2 -plane would be represented by a helical world-line in the #i-# 2 -3vmanifold. This trajectory of the point only arbitrarily expresses, as it were, one aspect of its motion, viz. The projection of the three-dimensional world-line on the #i-#2-plane. Now, if the motion of the point itself takes place in three-dimensional space, we obtain for its world- 52 General Postulate of Relativity of line a curve in the four-dimensional manifold of the x iy o?
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