Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-08T06:56:53.974Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).