'An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation,' pp. 447-450 in Reviews of Modern Physics, vol. 21, no. 3, July-September, 1949

GÖDEL ON TIME TRAVEL. First edition, journal issue, in original printed wrappers, of Gödel's 'time-travel paper,' 'one of the most important [papers] on relativity since my own original paper appeared' (Einstein to Morgenstern, 1952). "In the 1920s and 1930s, the Friedmann-Robertson-Walker cosmological models had been introduced as the simplest solutions of the equations of Einstein's general theory of relativity that were consistent with the observed red-shift of distant galaxies. These models were spatially homogenous and isotropic, and were expanding but were non-rotating. Gödel was the first to consider models that were rotating. The possible rotation of the universe has a special significance in general relativity because one of the influences that led Einstein to the theory in 1915 was Mach's principle. The exact formulation of the principle is rather obscure, but it is generally interpreted as denying the existence of absolute space. In other words, matter has inertia only relative to other matter in the universe. The principle is generally taken to imply that the local inertial frame defined by gyroscopes should be non-rotating with respect to the frame defined by distant galaxies. Gödel showed that it was possible to have solutions of the Einstein field equations in which the galaxies were rotating with respect to the local inertial frame. He therefore demonstrated that general relativity does not incorporate Mach's principle . In [the offered paper] Gödel presented a rotating solution that was not expanding but was the same at all points of space and time. This solution was the first to be discovered that had the curious property that in it it was possible to travel into the past. This leads to the paradoxes such as 'What happens if you go back and kill your father when he was a baby?' It is generally agreed that this cannot happen in a solution that represents our universe, but Gödel was the first to show that it was not forbidden by the Einstein equations. His solution generated a lot of discussion of the relation between general relativity and the concept of causality" (Stephen Hawking, p. 189 in Kurt Gödel: Collected Works: Volume II: Publications 1938-1974). "Gödel's brilliant burst into the world of physics in 1949 came as a surprise to those who knew him "only" as one of the greatest logicians of all time and thus as a very pure mathematician. However, to his colleagues at the Institute for Advanced Study (IAS) in Princeton, it was less surprising. At IAS, he had famously befriended Einstein, and much earlier, before switching over to mathematics, he had even entered the University of Vienna (in 1924) as a physics student and attended lectures by Hans Thirring, one of the earliest protagonists of Einstein's theories. Moreover, although this was not apparent from his published work, Gödel had maintained a lifelong interest in physics, attending the physics seminars at IAS and keeping abreast of ongoing developments. Then came the crucial trigger: the year 1949 brought Einstein's seventieth birthday, and Gödel was expected to contribute to the planned Festschrift for his friend. Not for the first time did pressure prove conducive to invention" (Rindler, p. 185). Gödel's Festschrift contribution, 'A Remark about the Relationship between Relativity Theory and Idealistic Philosophy' (pp. 557-562 in Albert Einstein: Philosopher-Scientist, P.A. Schilpp (ed.), 1949), appeared almost simultaneously with the offered paper. It treated the philosophical implications of Gödel's model, while the offered work provides the technical derivation from the Einstein field equations. "Gödel stated that he was motivated to invent his model universe from sympathy for Kant's philosophy of time. It was to serve as the first counterexample on the cosmic scale to the objective view of time, which treats time as an infinity of layers "now" coming into existence successively. By 1905, Einstein had already shown this view to be problematic.…