The Spatial and Temporal Propagation of Gravity

By Paul Gerber
1898

Einstein was the first one to explain the precession of perihelion of Mercury, we are told. But in 1898, Paul Gerber published a paper, in which he gave a clear explanation of the precession (Gerber, 1898). The core of that paper is the derivation of a formula that connects the speed of propagation of gravity to the amount of precession. More than a decade later, Einstein published the same formula. If so, why almost no one has heard of Paul Gerber?

In 19^th century, people recognized that electromagnetic force propagate at the speed of light. Some thought that gravitational force might propagate at a finite speed as well, possibly at the speed of light (Roseveare, 1982). If the gravitational force propagates at a finite speed, it might affect the movements of planets, especially when a planet is very close to the sun. Mercury is the planet closest to the sun. The movement of Mercury could not be completely accounted for by the standard Newtonian theory. Could the irregularity of Mercury’s movement be explained by the finiteness of speed of propagation of gravity?

Gerber assumed the speed of gravitational propagation is c, a finite number. Through a complex but logically clear derivation, he found the following formula

          c² = 24pi³a²/(T²(1-e²)fi)

Here a is semi-major axis of the orbit of Mercury, e is eccentricity, T is the period, and fi is residual precession of perihelion of Mercury. With available data, Gerber calculated the value of c to be 305500 km/sec. This is very close to the speed of light.

His work indicated that the speed of gravitational propagation is finite and equal to the speed of light. His work gave a clear explanation of precession of perihelion of Mercury. Why was he not given credit for this great achievement? Why haven’t we even heard of him?

Einstein made the following statement about Gerber’s work.

The experts are not only in agreement that Gerber’s derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber. Mr. Gerber’s work is therefore completely useless, an unsuccessful and erroneous theoretical attempt. I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of Mercury. I did not mention the work by Gerber initially, because I did not know about it when I wrote my work on the perihelion motion of Mercury; even if I had been aware of it, I would not have had any reason to mention it. (Einstein, 1920)

 First he made an indictment of Gerber’s work. “Gerber’s derivation is wrong through and through … the formula cannot be obtained as a consequence of the main assumption made by Gerber”. Anyone can go over the paper ourselves. The derivation is indeed quite long and complex. But the logic is very clear. It is hard to imagine that a “wrong through and through” method can derive a complex formula describing reality so perfectly.

Then Einstein proclaimed, “I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of Mercury.”

Finally, Einstein insisted, “I did not mention the work by Gerber initially, because I did not know about it when I wrote my work on the perihelion motion of Mercury; even if I had been aware of it, I would not have had any reason to mention it.”

With einstein’s authority, few people dare to mention Gerber’s work since.

Since Einstein's supporters did not concern themselves with Gerber's work it is not surprising that this result is not found in the literature ---  Gerber partisans would not proclaim their inferiority --- but one might have expected some notice of it … Nevertheless Gerber's law faded from view rather than being publicly refuted. (Roseveare, 1982, P 144)

It has been more than a century since Gerber published his great work. Yet his work and ideas are still languishing in obscurity. Even on rare occasions when he is mentioned, his is presented in a way that Einstein’s work is regarded as the standard. The following is a sentence from Wikipedia on the item Paul Gerber.

Gerber is known for his controversial work on the speed of gravity and the perihelion shift of Mercury's orbit.

Why is his work controversial? His work was published earlier than Einstein’s!

References

Einstein, A. (1920). "Meine Antwort - Über die anti-relativitätstheoretische G.m b.H". Berliner Tageblatt. 402. Archived from the original on 2009-12-14.

Gerber, P. (1898). "Die räumliche und zeitliche Ausbreitung der Gravitation" . Zeitschrift für Mathematik und Physik. 43: 93–104

Roseveare, N. T (1982). Mercury's perihelion, from Leverrier to Einstein. Oxford: University Press.