Paul Gerber

Paul Gerber (* 1854; † 1909) was a German physicist. He studied in Berlin from 1872-1875. In 1877 he became a teacher at the Realgymnasium (high school) in Stargard in Pommern. Gerber is known for his controversial work on the speed of gravity and the Perihelion shift of Mercury's orbit.

Gravitation

Basic concept

Based on the electrodynamic laws of Wilhelm Eduard Weber, Carl Friedrich Gauß, Bernhard Riemann, between 1870-1900 many scientists tried to combine gravitation with a finite propagation speed and tried to explain the Perihelion shift of Mercury's orbit.Zenneck 1901, 46ff] Oppenheim 1920, 153ff] In 1890 Lévy succeeded in doing so by combining the laws of Weber and Riemann, whereby the speed of gravity is equal to the speed of light in his theory.Levy 1890] However, because the basic laws of Weber and others were wrong (for example, Weber's law was superseded by Maxwell's equations), those hypothesis were rejected.

A variation of those superseded theories was Gerber's theory, which was developed by him in 1898 and 1902.Gerber 1898, 1902] By assuming a finite speed of gravity, he developed the following expression for the gravitational potential::$V=frac\; \{mu\}\; \{r\; left(1-\; frac\; \{1\}\; \{c\}\; frac\; \{dr\}\; \{dt\}\; ight)^2\}$Using the Binomial theorem to second order it follows::$V=frac\; \{mu\}\; \{r\}\; left\; [1+frac\; \{2\}\; \{c\}\; frac\; \{dr\}\; \{dt\}\; +\; frac\; \{3\}\; \{c^2\}\; left(frac\; \{dr\}\; \{dt\}\; ight)^2\; ight]$According to Gerber, the relation of the speed of gravity (c) and the Perihelion shift (Ψ) is::$c^2=frac\; \{6pimu\}\; \{a(1-epsilon^2)Psi\}$where:$mu=frac\; \{4pi^2a^3\}\; \{\; au^2\}$, ε=Eccentricity, a=Semi-major axis, τ=Orbital period.So Gerber was able to calculate a speed of gravity of ca. 305 000 km/s, nearly the speed of light.Zenneck 1901, 49ff] Oppenheim 1920, 156f]

Controversy

Gerber's formula gives for the Perihelion shift::$Psi=24pi^3frac\; \{a^2\}\; \{\; au^2\; c^2(1-epsilon^2)\}$It was noted by the Einstein- and relativity critic Ernst Gehrcke in 1916,Gehrcke (1916)] that this formula is mathematically identical to Albert Einstein's formula (1915) for general relativity.Einstein (1915 and (1916), 822] :$epsilon=24pi^3frac\; \{a^2\}\; \{T^2c^2(1-e^2)\}$, where e=Eccentricity, a=Semi-major axis, T=Orbital period.So Gehrcke initiated a reprint of Gerber's 1902-paper in the Annalen der Physik in 1917, where he questioned the priority of Einstein and tried to prove a possible Plagiarism by him.Gerber 1917] However, according to Albrecht FölsingFölsing 1993, Chap. 5] and Roseveare,Roseveare 1982, Chap. 6] those claims were rejected, because soon after Gerber's paper was reprinted, scientists like Hugo von Seeliger,Seeliger (1917)] Max von LaueLaue (1917, 1920)] published some papers, where it was shown that Gerber's theory is inconsistent and his formula is not the consequence of his premises. Also Roseveare argued that Gerber's theory is inconsistent and that the value for the deflection of light in the gravitational field of the sun in Gerber's theory was too high by the factor 3/2. And Einstein wrote in 1920:Einstein 1920]

ources

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*Cite journal
last=Einstein, A.
year=1915
title=Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie
journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften
issue=2
pages =831–839

*Cite journal
last=Einstein, A.
year=1916
title=Die Grundlage der allgemeinen Relativitätstheorie
journal=Annalen der Physik
volume =49
pages =769–822
url=http://www.physik.uni-augsburg.de/annalen/history/papers/1916_49_769-822.pdf
doi=10.1002/andp.19163540702

*Cite journal
author=Einstein, A.
year=1920
title=Meine Antwort - Über die anti-relativitätstheoretische G.m b.H
journal=Berliner Tageblatt
volume=402
url=http://www.olaf-eitner.de/EIGENES/POTSDAM/EINSTEIN/artikel1.htm

*Cite journal
author=Gehrcke, E.
year=1916
title=Zur Kritik und Geschichte der neueren Gravitationstheorien
journal=Annalen der Physik
volume=51
pages =119–124
url=http://gallica.bnf.fr/ark:/12148/bpt6k15353s/f125.chemindefer
doi=10.1002/andp.19163561704

*Cite journal
author=Gerber, P.
year=1898
title=Die räumliche und zeitliche Ausbreitung der Gravitation
journal=Zeitschrift für Mathematik und Physik
volume=43
pages =93–104
url=http://www.mahag.com/fremd/gerber.htm

*Cite journal
author=Gerber, P.
year=1902
title=Die Fortpflanzungsgeschwindigkeit der Gravitation
journal=Programmabhandlung des städtischen Realgymnasiums zu Stargard i. Pomm.

*Cite journal
author=Gerber, P.
year=1917
title=Die Fortpflanzungsgeschwindigkeit der Gravitation
journal=Annalen der Physik
volume=52
pages =415–444
doi=10.1002/andp.19173570404 (Reprint of Gerber 1902)

*Cite journal
author=Laue, M.
year=1917
title=Die Fortpflanzungsgeschwindigkeit der Gravitation. Bemerkungen zur gleichnamigen Abhandlung von P. Gerber
journal=Annalen der Physik
volume=53
pages =214–216
url=http://gallica.bnf.fr/ark:/12148/bpt6k15355g/f219.chemindefer
doi=10.1002/andp.19173581103

*Cite journal
author=Laue, M.
year=1920
title= Historisch-Kritisches über die Perihelbewegung des Merkur
journal=Naturwissenschaften
volume=8
issue=37
pages =735-736
doi=10.1007/BF02449026

*Cite journal
author=Lévy
year=1890
title=Sur l'application des lois électrodynamiques au mouvement des planètes
journal=Comptes Rendus
volume=110
pages =545–551
url=http://gallica.bnf.fr/ark:/12148/bpt6k30663/f587.table

*Cite journal
author=Oppenheim, S.
year=1917
title=Zur Frage nach der Fortpflanzungsgeschwindigkeit der Gravitation
journal=Annalen der Physik
volume=53
pages =163–168
url=http://gallica.bnf.fr/ark:/12148/bpt6k15355g/f168.chemindefer
doi=10.1002/andp.19173581005

*Cite journal
author=Seeliger, H.
year=1917
title=Bermerkungen zu P. Gerbers Aufsatz: "Die Fortpflanzungsgeschwindigkeit der Gravitation"
journal=Annalen der Physik
volume=53
pages =31–32
url=http://gallica.bnf.fr/ark:/12148/bpt6k15355g/f37.chemindefer
doi=10.1002/andp.19173580904

;Secondary sources
*Cite book
author=Fölsing, A.
year=1993/1998
title=Albert Einstein: a biography
location=New York
publisher=Penguin
isbn=0140237194

*Cite journal
author=Oppenheim, S.
year=1920
title=Kritik des newtonschen Gravitationsgesetzes
journal=Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen
volume=6.2.2
pages =80–158
url=http://www.archive.org/details/encyklomath2206encyrich

*Cite book
author=Roseveare, N. T
year=1982
title=Mercury's perihelion, from Leverrier to Einstein
location=Oxford
publisher=University Press
isbn=0198581742

*Cite journal
author=Zenneck, J.
year=1901
title=Gravitation
journal=Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen
volume=5.1
pages =25–67
url=http://dz-srv1.sub.uni-goettingen.de/sub/digbib/loader?did=D189514

;Notes

External links

*MathPages: [http://www.mathpages.com/home/kmath527/kmath527.htm Gerber's Gravity]