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The Weyl definition of redshifts. (English) Zbl 1272.83017

Summary: In 1923, H. Weyl [Raum, Zeit, Materie. Vorlesungen über allgemeine Relativitätstheorie. Berlin: J. Springer, IX u. 300 S. (1921; JFM 48.0984.01); Berlin-Heidelberg-New York: Springer-Verlag, VIII, 338 S. (1970; Zbl 0186.28602); 7th ed. Heidelberger Taschenbücher, 251. Berlin etc.: Springer-Verlag. xiii, 349 S. (1988; Zbl 0642.53001)] published a (not widely known) protocol for the calculation of redshifts. It is completely independent of the origin of the shift and treats it as a pure Doppler shift. The method is comprehensive and depends solely on the relation between the world lines of source and observer. It has the merit of simplicity of statement and generality. We illustrate the protocol by application to several standard situations. As a matter of historical interest, we include, in an appendix, the earliest known application of the Doppler principle. This was by Rømer who used it to calculate the speed of light.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83-03 History of relativity and gravitational theory
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
85A04 General questions in astronomy and astrophysics
85A05 Galactic and stellar dynamics
83A05 Special relativity
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