## Näherungsweise Integration der Feldgleichungen der Gravitation. Offprint from Sitzungsberichte der Königlich preussischen Akademie der Wissenschaften, XXXII.

Berlin: Königlich Akademie der Wissenschaften, 1916.

First edition, offprint issue, in the original printed wrappers, of the paper in which Einstein first proposed the existence of gravitational waves on the basis of general relativity, which he had completed just eight months earlier. “In June 1916 [Einstein] published a follow-up paper [the offered paper] to his recently formulated theory of the gravitational field in which he predicted the existence of gravitational waves traveling at the speed of light, in analogy with electromagnetic radiation (i.e. light, radio waves, etc.). In it he derived a formula for the emission of gravitational waves” (Blum, Lalli & Renn). Notwithstanding this paper, some physicists, including Einstein himself, later came to doubt the existence of gravitational waves (see below). These doubts were finally laid to rest when, on 14 September 2015, gravitational waves formed by the collision of two black holes 1.3 billion light years away were detected by both LIGO (Laser Interferometer Gravitational-wave Observatory) detectors in Louisiana and Washington State in the US. Regarding this discovery, Stephen Hawking wrote: “The discovery of gravitational waves by the LIGO team is an incredible achievement. It is the first observation of gravitational waves as predicted by Einstein and will allow us new insights into our universe.”

“Even before relativity, [Hendrik Antoon] Lorenz had conjectured in 1900 that gravitation ‘can be attributed to actions which do not propagate with a velocity larger than that of light.’ The term *gravitational wave* (onde gravifique) appeared for the first time in 1905, when [Henri] Poincaré discussed the extension of Lorenz invariance to gravitation. In June 1916 [in the offered paper], Einstein became the first to cast these qualitative ideas into explicit form” (Pais, p. 279). Remarkably, Einstein’s work on gravitational waves seems to have led to his realization that a quantum theory of gravity would be necessary, and then to new discoveries in quantum theory itself. “He also pointed out [in the same paper] that the existence of radiationless stable interatomic orbits is equally mysterious from the electromagnetic as from the gravitational point of view! ‘It seems that the quantum theory will have to modify not only Maxwell’s electrodynamics but also the new gravitational theory.’ Perhaps this renewed concern with quantum physics spurred him, a few months later, to make one of his great contributions to quantum electrodynamics: in the fall of 1916 he introduced the concepts of spontaneous and induced transitions and gave a new derivation of Planck’s radiation law” (*ibid*., p. 280).

“Einstein’s earliest calculations in general relativity were based on the theory’s Newtonian approximation. This was a natural choice, since it was vital to the theory’s acceptability to most physicists that it should be able to reproduce, in some plausible, if approximate, sense, the enormously successful predictions of Newton’s gravitational theory. In addition, this approximation scheme could then prove useful in identifying physical scenarios in which higher-order terms in the approximation scheme predicted measurable departures from the Newtonian prediction, the most famous case of this being the Mercury perihelion advance. Einstein’s early emphasis on the Newtonian approximation scheme may explain his comment to Karl Schwarzschild, in a letter of February 19, 1916, that gravitational waves did not exist within his new theory. Unfortunately, Einstein’s letter does not state the grounds for this belief …

“However, within a few months of this letter, Einstein was to change his mind, and not for the last time, on the existence of waves in his theory. Probably the occasion for this change of heart came about in his investigation of a new method of approximation, comparing his theory to Maxwellian electrodynamics … Following a suggestion of the astronomer Willem de Sitter (1872-1934), Einstein adopted a linearized approximation scheme of his equations, with a coordinate choice which cast the resulting linearized field equations in a form analogous to a familiar version of the Maxwell equations. Once this maneuver had been accomplished, it was trivial to solve the resulting wave equation, using techniques developed in the study of Maxwell’s equations. In this way one could demonstrate the existence of a solution of the linearized Einstein equations representing plane gravitational waves. The paper published by Einstein on this linearized approximation in 1916 [the offered paper] thus became the first mathematical theory of gravitational waves, and the approach it pioneered is still fundamental to the design of such existing gravitational wave detectors as the LIGO, VIRGO, and GEO600 detectors operating (respectively) in the United States, Italy, and Germany” (Kennefick, pp. 270-3).

Efforts to detect gravitational waves began in earnest in the 1960s. In June 1969, after almost a decade’s work, Joseph Weber reported that he had detected gravitational waves using a ‘Weber bar,’ a large, solid bar of metal isolated from outside vibrations. Weber found residual vibrations of the bar which he attributed to the presence of gravitational waves, but his results were challenged by other scientists partly because the intensity of the gravitational waves necessary to produce Weber’s results was much larger than expected. New evidence came from observations over three decades of the Hulse-Taylor binary, a pair of stars, one of which is a pulsar, which orbit each other rapidly at very short distance, which should cause them to radiate significant amounts of energy in the form of gravitational waves. This in turn should cause their period of rotation to increase over time; the observations of this slowing turned out to agree with Einstein’s predictions to within 0.2%. Russell Hulse and Joe Taylor were awarded the 1993 Nobel Prize in Physics for this work, the first indirect evidence of the existence of gravitational waves. The first *direct* observation of gravitational waves was made by the LIGO team in 2015.

Weil 86. Blum, Lalli & Renn, ‘One hundred years of gravitational waves: the long road from prediction to observation,’ Research Topic 43, Max Planck Institute for the History of Science, 11 February 2016; Kennefick, ‘Einstein, gravitational waves, and the theoretician’s regress,’ pp. 270-280 in *The Cambridge Companion to Einstein*, 2014; Pais, *Subtle is the Lord, *1982.

8vo (252 x 179 mm), pp. 688-696. Original printed wrappers, 5 cm pencil line across front wrapper, very mild sunning to wrappers, otherwise fine.

Item #4278

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Price:
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