Paul Gerber (physicist)

Carl Ludwig Paul Gerber (born January 1, 1854 in Berlin ; † August 13, 1909 in Freiburg im Breisgau ) was a German physicist . He was best known for his controversially discussed work on the speed of gravity and the perihelion rotation of Mercury (1898).

Life

Gerber studied in Berlin from 1872 to 1875. In 1877 he became a teacher at the secondary school in Stargard in Pomerania .

Gravity

Basics

Based on the fundamental electrodynamic laws of Wilhelm Eduard Weber , Carl Friedrich Gauß , Bernhard Riemann , the so-called ( Weber electrodynamics ), a number of attempts were made between 1890 and 1900 to combine gravitation with a finite speed of propagation and thereby the observed perihelion shift of the Determine Mercury. Maurice Lévy (1890) succeeded in deriving the correct perihelion rotation by combining Weber's and Riemann's constitution. However, since these underlying laws turned out to be unusable over time (e.g. Weber's electrodynamics were replaced by Maxwell's electrodynamics), these hypotheses were no longer pursued.

A variation of these efforts, obsolete from today's point of view (without, however, being based directly on Weber's electrodynamics) presented Gerber's theory set up in 1898 and 1902. Assuming that the gravitational potential spreads at a finite speed, he arrived at the following expression for the speed-dependent one Potential:

${\displaystyle V={\frac {\mu }{r\left(1-{\frac {1}{c}}{\frac {dr}{dt}}\right)^{2}}}}$

With the help of the binomial theorem up to the second power it follows:

${\displaystyle V={\frac {\mu }{r}}\left[1+{\frac {2}{c}}{\frac {dr}{dt}}+{\frac {3}{c^{2}}}\left({\frac {dr}{dt}}\right)^{2}\right]}$

The generalized force follows from this velocity-dependent potential as a functional derivative ${\displaystyle K}$

${\displaystyle K={\frac {dV}{dr}}-{\frac {d}{dt}}{\frac {dV}{d{\dot {r}}}}}$,

where the speed denotes. Gerber uses this force in Newton's equations of motion and, after some elementary transformations, comes to the result that the relationship between the speed of gravity (c) and the perihelion displacement (Ψ) applies: ${\displaystyle {\dot {r}}={\frac {dr}{dt}}}$

${\displaystyle c^{2}={\frac {6\pi \mu }{a(1-\epsilon ^{2})\Psi }}}$

Where

${\displaystyle \mu ={\frac {4\pi ^{2}a^{3}}{\tau ^{2}}}}$, and ε = eccentricity , a = major semi-axis , τ = period of revolution .

From this, Gerber calculated a speed of propagation of the potential of approx. 305,000 km / s, i.e. practically the speed of light.

controversy

Gerber's above formula now gives the perihelion shift:

${\displaystyle \Psi =24\pi ^{3}{\frac {a^{2}}{\tau ^{2}c^{2}(1-\epsilon ^{2})}}}$

In 1916, Ernst Gehrcke , opponent of Einstein and relativity, noticed that this expression is formally identical to Albert Einstein's approximated formula for general relativity (published in 1915).

${\displaystyle \epsilon =24\pi ^{3}{\frac {a^{2}}{T^{2}c^{2}(1-e^{2})}}}$, where e = eccentricity, a = major semi-axis, T = period of revolution.

Gehrcke therefore had Gerber's 1902 paper reprinted in Annalen der Physik (1917) with the intention of undermining Einstein's priority and pointing out possible plagiarism . According to Roseveare, Klaus Hentschel and Albrecht Fölsing , these allegations were immediately rejected, as counter- statements appeared shortly after Gerber's work was reprinted, according to which, despite the correct formula, Gerber's theory was unusable. For example, according to Hugo von Seeliger and Max von Laue , Gerber's results cannot be brought into agreement with the requirements of his own theory or even only “mathematical errors”. While Seeliger mocked the functional derivation of Gerber's potential as a recipe for deriving the velocity-dependent force in a two-page letter in the Annalen der Physik, Laue also criticized in a two-page letter in the same journal and later in Die Naturwissenschaften what he considered to be unphysical Gerber's potential, which does not have any Has similarity with retarding potentials. And Einstein wrote (in this partly polemical debate) in 1920:

“Mr. Gehrcke wants to make believe that the perihelion of Mercury can also be explained without the theory of relativity. There are two options. Either you invent special interplanetary masses. [...] Or you can refer to a work by Gerber, who already gave me the correct formula for the perihelion movement of Mercury. But experts not only agree that Gerber's derivation is thoroughly incorrect, but that the formula cannot be won at all as a consequence of the assumptions made by Gerber at the top. Herr Gerber's work is therefore completely worthless, a failed and irreparable theoretical attempt. I state that the general theory of relativity provided the first real explanation for the perihelion of Mercury. Originally I did not mention Gerber's work because I did not know it when I wrote my work on the perihelion movement of Mercury; But I would have had no reason to mention it if I had known about it. "

In the more recent past Roseveare also dealt with this theory and described Gerber's derivation as "unclear", but he himself believed that he had given a coherent derivation of Gerber's potential, although its accuracy is contested. But Roseveare also rejects Gerber's theory and particularly points out that, according to Gerber, the value for the deflection of light in the gravitational field is too high by a factor of 3/2 . The rotation of the perihelion also gives an incorrect value if the relativistic mass is taken into account.

swell

Wikisource: Paul Gerber  - Sources and full texts

Primary sources

• Einstein, A .: Explanation of the perihelion movement of Mercury from the general theory of relativity . In: Meeting reports of the Prussian Academy of Sciences . No. 2, 1915, pp. 831-839.
• Einstein, A .: The basis of the general theory of relativity . In: Annals of Physics . 49, 1916, pp. 769-822.
• Einstein, A .: My answer - About the anti-relativity theory Gm bH . In: Berliner Tageblatt . 402, 1920.
• Gehrcke, E .: On the criticism and history of the more recent gravitation theories . In: Annals of Physics . 51, 1916, pp. 119-124.
• Gerber, P .: The spatial and temporal spread of gravitation . In: Journal of Mathematics and Physics . 43, 1898, pp. 93-104.
• Gerber, P .: The speed of propagation of gravity . In: Annals of Physics . 52, pp. 415-444. . (Originally published in the program of the municipal high school in Stargard i. Pomm. , 1902)
• Laue, M .: The speed of propagation of gravitation. Comments on the treatise of the same name by P. Gerber . In: Annals of Physics . 53, 1917, pp. 214-216.
• Laue, M .: Historical and critical information about the perihelion movement of Mercury . In: Natural Sciences . 8, No. 37, 1920, pp. 735-736. doi : 10.1007 / BF02449026 .
• Lévy, M .: Sur l'application des lois électrodynamiques au mouvement des planètes . In: Comptes Rendus . 110, 1890, pp. 545-551.
• Oppenheim, S .: On the question of the speed of propagation of gravity . In: Annals of Physics . 53, 1917, pp. 163-168.
• Seeliger, H .: Comments on P. Gerber's paper: "The speed of propagation of gravitation" . In: Annals of Physics . 53, 1917, pp. 31-32.

Secondary sources

• Fölsing, A .: Albert Einstein. A biography . Suhrkamp, ​​Frankfurt am Main 1993.

• Hentschel, Klaus: Interpretations and misinterpretations of the special and general relativity theory by Albert Einstein's contemporaries , Basel: Birkhäuser, 1990 (= Science Networks, 6), pp. 150–162.

• Oppenheim, S .: Critique of Newton's Law of Gravitation . In: Encyclopedia of Mathematical Sciences, including its applications . 6.2.2, 1920, pp. 80-158.
• Roseveare, N.T . : Mercury's perihelion from Leverrier to Einstein . University Press, Oxford 1982.
• Zenneck, J .: Gravitation . In: Encyclopedia of Mathematical Sciences, including its applications . 5.1, 1901, pp. 25-67.

Individual evidence

Individual references to primary sources (A)

1. ^ Levy 1890
2. ^ Gerber 1898, 1902
3. ↑ Gehrcke (1916)
4. ↑ Einstein (1915) and (1916), 822
5. ↑ Gerber 1917
6. ↑ Seeliger (1917)
7. ↑ Laue (1917, 1920)
8. ↑ Einstein 1920

Individual references to secondary sources (B)

1. ↑ Zenneck 1901, 46ff
2. ↑ Oppenheim 1920, 153ff
3. ↑ ^{a b c} Roseveare 1982, chap. 6th
4. ↑ Zenneck 1901, 49ff
5. ↑ Oppenheim 1920, 156f
6. ↑ Hentschel 1990, pp. 150ff.
7. ↑ Fölsing 1993, chap. 5

Others

1. ↑ MathPages: Gerber's Gravity , Gerber's Light Deflection