Zusammenfassung
During his time at the Institute for Advanced Study, Kurt Gödel became a close friend of Albert Einstein, and in particular studied the theory of relativity. One result of this study was the discovery of the so-called Gödel universe (strictly speaking, it is about a whole class of universes; the singular form stands here as a collective noun.), a model of Einstein’s field equations of general relativity in which no absolute time can be defined. Theoretically, time travel would be possible in such a universe.
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Notes
- 1.
Strictly speaking, it is about a whole class of universes; the singular form stands here as a collective noun.
- 2.
“Can we really infer the nonexistence of time in this world from its absence from a merely possible universe? In a word, yes. Or so Gödel argues” (Yourgrau, 2005, p. 130).
- 3.
Compare Gödel (1956, p. 412).
- 4.
Oskar Morgenstern in a letter to Bruno Kriesky, the Austrian Federal Minister of Foreign Affairs, Oct. 25, 1965, (Morgenstern, 2002): “Einstein often told me that in the last years of his life he always sought Gödel’s company in order to be able to discuss with him. Once he said to me that his own work no longer meant much, that he merely came to the Institute building to have ‘the privilege of walking home with Gödel’”
- 5.
Note Minkowski’s astonishment at Einstein’s mathematical achievements, handed down by Max Born: Oh, Einstein, he was always skipping lectures—I wouldn’t have believed it of him. From Constance Reid comes the following quote of Minkowski (Reid, 1970, p. 112): Einstein’s presentation of his deep theory is mathematically awkward—I can say that because he got his mathematical education in Zurich from me.
- 6.
Gödel (1956, p. 412).
- 7.
Gödel (1956, p. 412).
- 8.
With this evaluation we are in contrast to Yourgrau, who writes: “First, he remarks that in an attempt to ‘specify’ the above definition of ‘cosmic’ or ‘absolute’ time, arbitrary elements come into play which can never be fully eliminated” (Yourgrau, 2002, p. 276, our emphasis). Here, we refer to footnote 9 in Gödel (1949a). There, however, Gödel only opposes a precise definition of absolute time in the sense of Jeans, and instead of “never” Gödel carefully speaks of “perhaps”, even if he subsequently considers the existence of such a precise definition as doubtful. Regardless of any precise definition of absolute time that Jeans may have had in mind, one certainly cannot imply to Gödel that all forms of physical completion of relativity could be accomplished only by arbitrary elements. This follows already from his own considerations, which will be briefly addressed below.
- 9.
Gödel says this explicitly at the end of the quotation given in footnote 12.
- 10.
From this perspective, Yourgrau’s harsh criticism of Hawking (Yourgrau, 2005, pp. 8 and 136) is both incomprehensible and unjustified.
- 11.
This remark can be found as an “addition by the author in the German translation to footnote 14” only in the German edition of the article.
- 12.
This can be found again in an “addition of the author to footnote 11 of the German edition”, which is introduced as follows (Gödel, 1956, p. 411): A second reason to exclude the above universes a priori could be found in the possibility of a “telegraphing into one’s own past”. However, the practical difficulties arising in this case are hardly likely to be less [than in the case of the previously discussed time travel]. By the way, the border between practical and principal difficulties is by no means immovable.
- 13.
Here, one may well feel reminded of the Aristotelian distinction between sublunary physics and celestial mechanics.
- 14.
The terminology used by Gödel is not unproblematic. In which concrete sense the presented position should correctly be called idealistic may be discussed. The tension is increased by the fact that Gödel himself is usually regarded as a realist; see, e.g. Yourgrau (2005, p. 171 f.).
- 15.
- 16.
Howard Stein (1990), in his introduction to the reprint of the article Gödel (1949a), explicitly regrets the lack of more material that would shed light on Gödel’s philosophical position, especially vis-á-vis Kant. We at least have more detailed drafts of this article, in which “idealistic philosophy” was replaced by “Kantian philosophy” in the title, and which are dated 1946–49 (Gödel, 1995).
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Kahle, R. (2023). The Philosophical Meaning of the Gödel Universe. In: Passon, O., Benzmüller, C., Falkenburg, B. (eds) On Gödel and the Nonexistence of Time – Gödel und die Nichtexistenz der Zeit. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-67045-3_3
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