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● TITLE: Relativistic combination of any number of collinear velocities and generalization of Einstein's formula
● AUTHORS: Loewenthal, D., Robinson, E.A.
● SOURCE: J. Math. Anal. Appl., v. 246, pp. 320-324 (2000).
● ABSTRACT: By a direct application of the theory of polynomials orthogonal on the unit circle, the Einstein relativistic combination of any number of collinear velocities is given in a surprisingly simple closed form. By doing so the Antippa additive formula is simplified. Insight is gained through treatment of the wave equations describing pressure and particle velocities for a layered model.
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● LOEWENTHAL'S RELATIVISTIC ADDITIVE FORMULA (for -c < vi < c ):
v/c = [ Πi=1...n(1+vi /c) - Πi=1...n(1-vi /c)] / [ Πi=1...n(1+vi /c) + Πi=1...n(1-vi /c)]
(where Π denotes successive multiplication).
Those who want to check for n=3 may calculate and compare the result with the formula in:
Lucas and Hodgson's "Spacetime and electromagnetism," p. 50, Clarendon, Oxford (1990)
or in: Vigoureux, "Use of Einstein's addition law in..." J. Opt. Soc. Amer. A. v. 9 , pp. 1313-1319 (1992).
● COMMENT: D. Loewenthal has submitted the last revised version of this paper just a few hours before his death.
● MEMORIAL/OBITUARY: Robinson and Treitl, Leading Edge, v. 19 (2000), no. 8924.
● REVIEWER: A. A. Ungar
● REVIEW SOURCE: MathSciNet
● REVIEW (Link to source in MathSciNet)
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