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Über die Schwere des Lichtes in der Newtonschen und in der Einsteinschen Gravitationstheorie
Author(s) -
Treder H.J.
Publication year - 1970
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19704800309
Subject(s) - physics , general relativity , mathematical physics , gravitation , gravitational field , einstein , theory of relativity , field (mathematics) , field equation , astrophysics , classical mechanics , mathematics , pure mathematics
The gravity theories of Newton and Einstein are giving opposite sentences about the velocity of light in gravitational field. According to the Newtonian theory the velocity v in gravitational field is greater than the velocity c in a field‐free space: v > c . According to general relativity theory we have a smaller velocity: v < c . For a spherical symmetric gravitational field Newton's theory gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 + \frac{{fM}}{{c^2 r}}} \right) $\end{document} but Einstein's theory of 1911 gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - \frac{{fM}}{{c^2 r}}} \right) $\end{document} and general relativity gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - 2\frac{{fM}}{{rc^2 }}} \right) $\end{document} . Therefore, the radarecho‐measurations of Shapiro are the experimentum crucis for Einstein's against Newton's theory.