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Vectorial Composition of Velocities in Relativity

Published online by Cambridge University Press:  14 March 2022

Boris Leaf
Boris Leaf*
Affiliation:
Kansas State College, Manhattan, Kansas
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Extract

The Einstein law of velocity addition is well-known. Consider three inertial reference frames S, K, and M, with X axes parallel in the same sense. Let K have velocity v1 along the X axis of S, and M have velocity v2 along the X axis of K. Then, according to the Einstein formula, the velocity v3 of M along the X axis of S is

If v2 is the velocity of an object at rest in M as measured by an observer in K, then v3 is the velocity of the same object as measured by an observer in S. The formula is valid for a change in reference frame of the observer.

Type
Research Article
Information
Philosophy of Science , Volume 22 , Issue 4 , October 1955 , pp. 321 - 324
Copyright
Copyright © Philosophy of Science Association 1955

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References

1 M. von Laue, Die Relativitätstheorie, Vol. I, 5th Edition, Vieweg & Sohn, Braunschweig (1952), pp. 40–41.

2 R. C. Tolman, The Theory of the Relativity of Motion, University of California Press, Berkeley (1917), p. 36.

3 A. Grünbaum, Philosophy of Science, 21, 252 (1954).

4 A. Grünbaum, Philosophy of Science, 32, 53 (1955).

5 B. Leaf, The Physical Review, 90, 1092 (1953).

6 Unfortunately, Grünbaum commits this error at the top of p. 252 of his paper cited earlier3 when he uses vector composition to determine the time interval recorded by his clock U 2 in inertial frame K during the motion of U 3 from B to A in S. He reports the interval instead of . Contrary to his result, both of his clocks U 3 and U β should read the same time, , upon their arrival at A.

7 B. Leaf, Philosophy of Science, 22, 45 (1955).