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Anatoly Vlasov heritage: 60-year-old controversy

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Abstract

We analyzed remarkable stories linked to the famous Anatoly Vlasov equations in plasma physics. Their creation, modification, and application are interesting from the scientific viewpoint. We also show the relations between those equations dealing with electromagnetism and analogous Jeans equations describing, in particular, gravitational instability in astrophysics. The second half of the essay is devoted to the controversies and political struggle in Soviet (before 1991) and Russian (after 1991) physical communities related to Vlasov’s personality, career, and posthumous recognition. The never-ending destructive influence of the Russian totalitarianism on science is demonstrated.

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Notes

  1. Ukrainian experimentalist Komnik (A. G. heard his regrets personally) excluded some strange original results from his book describing electrical conductivity of thin metallic films [154]. However, the excluded logarithmic temperature dependencies correspond to genuine quantum mechanical interference effects and were discovered theoretically somewhat later [4, 15].

  2. Biography of Anatoliy Vlasov can be found in [30].

  3. Recall the name of the continent in the Western Hemisphere.

  4. Lord Rayleigh [187] obtained the same plasma frequency while analyzing the properties of the J. J. Thomson plum pudding model atom [255]. Namely, Lord Rayleigh assumed that positive and negative entities in an atom are equal in all respects accept the ability to move: negative charges were considered mobile. It is exactly the behavior of light electrons against heavy ions in gas-discharge and metal plasmas.

  5. According to Earnshaw’s theorem, even quasi-neutrality would not ensure the stability of classical macroscopic systems [75]. Nevertheless, the situation in the quantum mechanical and relativistic world is different. If one considers corresponding complications, the problem of matter stability becomes much more involved [178].

  6. To formulate self-consistent kinetic equations without collisions (the Boltzmann-like equations without the Stoß term, which is responsible for collisions) but for any long-range field, one can follow Vlasov’s way of treating electromagnetic interaction. However, to call them Vlasov–Newton, Vlasov–Einstein, and Vlasov–Maxwell equations [262] reflects the imperial hubris and misinterpreted patriotism. Such equations were first proposed to describe the evolution of a collective of stars in the Newtonian universe, whereas the long-range field was represented by the gravitational potential. It was done by the eminent British physicist and astronomer James Jeans, who applied the Boltzmann approach considering stars as particles [127, 140, 141].

  7. Ginzburg et al. [105]; hereafter, for the sake of brevity, we shall refer to the authors as a “gang of four,” similarly to the authors of the famous highly cited article by Abrahams et al. [4] devoted to the weal localization in two-dimensional disordered systems that was so coined later on [3, 165].

  8. An overview of the problem of Landau damping in plasma physics and astrophysics can be found in [34, 204, 231].

  9. Vlasov wanted to bypass the calculation of the Gibbs partition function, from which one can find all the thermodynamic functions of the system. If his approximation had worked, it would have been a great success, since calculation of the partition function is always difficult and, in most cases, impossible. However, Vlasov failed. For example, the gang of four [105, p. 249] pointed out that, according to Vlasov theory, the period of the crystal lattice should strongly depend on temperature, which contradicts the experiment and discredits the theory within which this result was obtained.

  10. The adiabatic (Laplacian) and isothermal (Newtonian) speeds of sound are related as \((c_{\text{p}}/c_{\text{v}})^{1/2}\), where \(c_{\text{p}}\) and \(c_{\text{v}}\) are gas specific heat capacities at constant pressure and volume, respectively [170]. Naturally, this ratio depends on the parameters of a particular substance, but for real gases, the order of magnitude of the speed of sound remains the same whatever the process of sound propagation [168, 225].

  11. See, e. g., [170, p. 3]. In essence, Euler’s equation is a formulation of Newton’s second law for the fluid motion [10]. The biography of the great Swiss mathematician Leonhard Euler and the analysis of his differential equations can be found in [226, 254].

  12. For the Jeans instability in the quasi-static Einstein–de Sitter model, see: [49, 55, pp. 174–178; 148, p. 146]. Studies of instabilities in the Friedmann–Lemaître model are discussed, in particular, in [55, pp. 178–184; 113, pp. 13–20; 118, 179, 180, 181, 279, pp. 285–309].

  13. The inevitability of classical and quantum fluctuations and their important role against the background of average statistical (thermodynamic) characteristics of systems have long been known and are being widely studied now, in particular, in magnetic, superconducting, and ferroelectric materials, where, apart from the crystalline order, additional order parameters are observed with the loss of some symmetry. Of course, fluctuations there can be “touched,” if not by experimentalists themselves then at least with the help of simple devices. This distinguishes these “terrestrial” fluctuations favorably from theoretically assumed fluctuations in astrophysics, which are discussed here. One can read about fluctuations in plasma, condensed media, and devices in Refs. [108, 134, 168, 173, 197, 200, 211, 220, 244].

  14. The first attempts to overcome the inadequacy of the Newtonian theory to describe a spatially unlimited Universe uniformly filled with matter (“gravitational paradox”) belong to the outstanding German scientists Hugo von Seeliger and Carl Neumann [160, p. 53; 212, pp. 271–323; 213, pp. 65–71].

  15. The history of physics should include a description in terms of attributes and their carriers [96].

  16. Hideki Yukawa was a renowned Japanese researcher who made contributions to nuclear physics and field theory [194, 277].

  17. This problem was analyzed in detail but much later [9, 17, 51, 74, 85, 202, 206, 248, 249].

  18. Actually, Marxist in form, but meaningless in content, mumbling of Marxist philosophers (it would be more valid to add the prefix “pseudo”) easily turns into religious fundamentalism (which has nothing in common with the Christian theology of civilized Europe). For instance, such a metamorphosis occurred with the French revolutionary Roger Garaudy, who from a devoted Marxist became an Islamic fundamentalist and a professional outspoken anti-Semite [98].

  19. Anyway, those points, which were criticized by the gang of four, were not touched upon in the Bogolyubov monograph [41], so the Rukhadze attempt to rely on Bogolyubov’s authority is not justified.

  20. Ginzburg [102] quite frankly notes that the main trigger causing the appearance of the gang-of-four article was the role of Vlasov as the banner of the communist establishment of Moscow State University, which hunted physics and physicists and prepared the destruction of physics in the style of the destruction of genetics by the notorious academician Trofim Lysenko. If Vlasov’s dangerous public role had not been so evident, his mistakes would hardly have been noticed. At the same time, from the scientific viewpoint, as Ginzburg writes, the article of four authors was flawless. However, the crushing tone of the academicians’ article induced such emotions that it also cast doubt on the main results of Vlasov’s 1938 article, which were and are of great scientific importance. Still, the gang of four did not know (or forgot) about the priority of Jeans regarding the self-consistent field, so Vlasov managed to avoid criticism in this respect then and throughout his later life.

  21. Vladimir Moiseevich Agranovich is a well-known Ukrainian and Russian physicist. Since the 1990s, he has been working in the West; https://ru.wikipedia.org/wiki/Aгpaнoвич,_Bлaдимиp_Moиceeвич.

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Acknowledgements

We would like to thank the Ukrainian Armed Forces and our Western allies, who made possible the preparation of this paper. Alexander Gabovich is supported by Grant No. 1.4.B-197 of the Institute of Physics of the National Academy of Sciences of Ukraine. He is also grateful to the Max Planck Institute for the Physics of Complex Systems for the invitation to Dresden and Joint Ukrainian-Polish program (2022–2024), Grant No. 23. Vladimir Kuznetsov is supported by the Project Logical, Ontological and Axiological Dimensions of Scientific Cognition of the Program Priorities Directions of Scientific Studies of the National Academy of Sciences of Ukraine (2021). The preliminary version of this article was published in Russian in the International Network Journal 7 iskusstv (7i.7iskusstv.com/y2022/nomer5/gabovich/). We are very grateful to Evgeniy Berkovich, who gave us this platform.

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    Alexander M. Gabovich

  2. H. Skovoroda Institute of Philosophy, National Academy of Sciences of Ukraine, Trokhsvyatytelska Street 4, Kyiv, 01001, Ukraine

    Vladimir I. Kuznetsov

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Gabovich, A.M., Kuznetsov, V.I. Anatoly Vlasov heritage: 60-year-old controversy. EPJ H 48, 5 (2023). https://doi.org/10.1140/epjh/s13129-023-00051-6

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