Editor’s Note: Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation. Hans-J¨ urgen Schmidt Institut f¨ ur Mathematik, Universit¨at Potsdam, Germany Am Neuen Palais 10, D-14469 Potsdam,
[email protected] Abstract This is the Editor’s Note to the paper “Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation” by Academician A. D. Sakharov, Dokl. Akad. Nauk SSSR 170, 70 - 71 (1967). Soviet Physics - Doklady 12, 1040 - 1041 (May, 1968). (Original article submitted August 28, 1961.) Reprinted from Gen. Relat. Grav. 32 (2000) 361 - 363.
Ref. [1], entitled “On Sakharov’s Theory of Gravitation”, is one of the many papers (I have seen approximately one hundred of them) which took the paper by Sakharov reprinted here as the starting point for further investigation. The original paper covers only one and a half printed pages, and it is exciting to see how many different ideas so many authors have found in this short seminal paper by Sakharov.1 The main points of the contents are: – to consider gravitation as “elasticity” of space, see e.g. [1]; – to calculate the value of the gravitational constant G from the R2 -terms in the action, see e.g. [2]; – to explain that Λ, the cosmological constant, may have a small but nonzero value, and to this end, what are the cosmological consequences of the 1
The only inaccuracy I have found in the translation reprinted here is the following: After eq. (1), “forces” must replaced by “force”.
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curvature squared terms in the effective action (see footnote 2 in Sakharov’s paper) which lead to fourth-order field equations for the metrical tensor, see e.g. [3,4]; the inflationary cosmological model following from Sakharov’s theory of gravitation now carries the name “Starobinsky model”. – to evaluate how quantum fluctuations of the vacuum can influence the gravitational action, especially how curvature squared terms may cancel ultraviolet divergencies, see [5]. Sometimes, however, Sakharov’s paper was quoted – as an act of solidarity with him – also in contexts not much related to the contents of it. So, the present reprint should help to find out what is really contained in that paper.
References 1. Pessa, E. (1978). Gen. Relat. Grav. 9, 911. 2. Pollock, M. (1998). Int. J. Mod. Phys. D 7, 727. 3. Schmidt, H.-J. (1994). Phys. Rev. D 49, 6354; Erratum (1996). Phys. Rev. D 54, 7906. 4. Tapia, V., et al. (1996). Class. Quant. Grav. 13, 3261. 5. Weinberg, S. (1979). In General Relativity. An Einstein Centenary Survey, S. Hawking, W. Israel, eds. (Cambridge University Press, Cambridge), p. 790.
Brief biography, based on [1] and [2] Andrei Dmitrievich Sakharov was born on May 21, 1921 and died on December 14, 1989, both in Moscow. From 1938 Andrei Dmitrievich studied physics at Moscow University, which was evacuated to Ashkhabad in 1941. He graduated in 1942. Then he worked in the armament industry in Uljanovsk (the other name of this town at the Volga river is Simbirsk). In 1945 he returned to Moscow and worked on thermonuclear reactions, especially on the development of the hydrogen bomb. In 1953 he received his PhD degree and was elected Academician. From 1965 he published a series of papers on cosmology. He is best known for his prolonged campaign against the abuses of human rights and of the freedom of speech in the Soviet Union. These activities were honoured by the Nobel Prize for Peace in 1975. From that time until his official rehabilitation under M. Gorbachov in 1986, he was under house arrest in Gorki (now Nizhni Novgorod). After his return to Moscow, he participated in several conferences. 2
His collected scientific works are published by M. Dekker, New York, and Ref. [2] contains a short biography written by E. L. Feinberg.
References [1] Sakharov, A. (1990). Memoirs (A. Knopf Publ., New York). German translation: (1991). Mein Leben (R. Piper-Verlag, M¨ unchen). [2] Sakharov, A. (1990). In Priroda 8/90 (in Russian); German translation 1991 (Spektrum-Verlag, Heidelberg).
Acknowledgement I am grateful to Andrzej Krasinski for useful comments.
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