Atticus Rare Books

Beiträge zur Einsteinschen Gravitationstheorie [Comments on Einstein’s Theory of Gravity] (Flamm, pp. 448-454) WITH Zur Theorie des Zeeman-Effets der Wasserstofflinien, mit einem Angang ueber den Stark-Effekt (Sommerfeld, pp. 491-507) in Physikalische Zeitschrift 17, 1916

Flamm, Ludwig with Sommerfeld, Arnold

Leipzig: S. Hirzel, 1916. 1st Edition. FIRST EDITION, FULL VOLUME, OF LUDWIG FLAMM’S REALIZATION THAT EINSTEIN’S FIELD EQUATIONS ALLOWED A SECOND SOLUTION. FLAMM'S SOLUTION IS NOW KNOWN AS A ‘WHITE HOLE’. Flamm’s paper also first theorized the existence of wormholes (though not by name).

In 1916, Ludwig Flamm, an obscure Austrian physicist, was examining Karl Schwarzchild’s solution to Einstein's field equations. Schwarzchild’s metric admits negative and positive square root solutions for Einstein’s geometry and describes the gravitational field around “a spherically symmetric non-rotating mass. If the mass is adequately dense, the solution describes a particular form of the phenomenon now called a black hole – the Schwarzschild black hole” (306physics).

“Flamm realized that Einstein's equations allowed a second solution, [now] known as a white hole, and that the two solutions, describing two different regions of space time were connected by a space time conduit. Because Einstein’s theory has nothing to say about where these regions of space time might be in the real world, the black hole "entrance" and white hole "exit" could be in different parts of the same universe or in different universes” (ibid). A white hole is a region of spacetime that is the theoretical time reversal of a black hole; in essence, a black hole running backward in time. While black holes act as vacuums that draw in all matter crossing their event horizon, white holes are “a region of spacetime that cannot be entered from the outside but from which matter and light may escape” (meaning that contrary to black holes, white holes eject matter from their event horizon) (History of Physics: The Wenner Collection).

Flamm’s ideas were largely ignored in 1916, but in 1935, Einstein and Nathan Rosen used the general theory of relativity to explore Flamm’s theories further. They theorized "intra- or inter-universe connections… whose actual purpose was to try to explain fundamental particles, such as electrons, in terms of space-time tunnels threaded by electric lines of force” (David Darling Encyclopedia). Together they proposed the concept of bridges connecting two differing points in space-time -- a solution now known as the Einstein-Rosen bridge. What Einstein and Rosen called ‘bridges’, the physicist John Wheeler would later call wormholes. [Note that we offer Wheeler’s 1955 paper on the subject separately: “Geons” in Physical Review 97, 3, January 15, 1955].

"Further theoretical work showed that the Einstein-Rosen 'wormhole' is not, contrary to outward appearances, a stable structure. For an observer trying to pass through, the wormhole opens up and closes too quickly for even a photon to get through. Later work suggested that exotic forms of energy threaded through a wormhole might keep it open but it remains unclear whether such arrangements are physically feasible" (“The Birth of Wormholes”, APS Focus 15, 11, 3.25.2005).

ALSO INCLUDED IN THIS VOLUME: Arnold Sommerfeld’s explanation of the Zeeman effect and the Stark effect based on the Bohr model of the atom. Item #1071

CONDITION & DETAILS: Leipzig: S. Hirzel. Full volume, complete. 4to (11 x 8 inches; 275 x 200mm). A few institutional stamps to the preliminaries. Illustrated with plates and in-text photos and figures throughout. Tightly bound in black cloth, gilt-lettered at the spine. A bit of rubbing at the edge tips. Bright and clean throughout. Very good.

Price: $375.00