Кинетическая теория гравитации: от Фатио до Ле Сажа

Kinetic theory of gravity
Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra mundane corpuscles) impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together. This mechanical explanation for gravity never gained widespread acceptance.

Nicolas Fatio presented the first formulation of his thoughts on gravitation in a letter to Christiaan Huygens in the spring of 1690. Two days later Fatio read the content of the letter before the Royal Society in London. In the following years Fatio composed several draft manuscripts of his major work De la Cause de la Pesanteur, but none of this material was published in his lifetime. In 1731 Fatio also sent his theory as a Latin poem, in the style of Lucretius, to the Paris Academy of Science, but it was dismissed. Some fragments of these manuscripts and copies of the poem were later acquired by Le Sage who failed to find a publisher for Fatio's papers. So it lasted until 1929, when the only complete copy of Fatio's manuscript was published by Karl Bopp, and in 1949 Gagnebin used the collected fragments in possession of Le Sage to reconstruct the paper. The Gagnebin edition includes revisions made by Fatio as late as 1743, forty years after he composed the draft on which the Bopp edition was based. However, the second half of the Bopp edition contains the mathematically most advanced parts of Fatio's theory, and were not included by Gagnebin in his edition. For a detailed analysis of Fatio's work, and a comparison between the Bopp and the Gagnebin editions, see Zehe The following description is mainly based on the Bopp edition.

Fatio was in communication with some of the most famous scientists of his time. There was a strong personal relationship between Isaac Newton and Fatio in the years 1690 to 1693. Newton's statements on Fatio's theory differed widely. For example, after describing the necessary conditions for a mechanical explanation of gravity, he wrote in an (unpublished) note in his own printed copy of the Principia in 1692:The unique hypothesis by which gravity can be explained is however of this kind, and was first devised by the most ingenious geometer Mr. N. Fatio. at the end of which appeared a sketch of a theory very similar to Fatio's – including net structure of matter, analogy to light, shading – but without mentioning Fatio's name. It was known to Fatio that Cramer had access to a copy of his main paper, so he accused Cramer of only repeating his theory without understanding it. It was also Cramer who informed Le Sage about Fatio's theory in 1749. In 1736 the German physician Franz Albert Redeker also published a similar theory. Any connection between Redeker and Fatio is unknown.

The first exposition of his theory, Essai sur l'origine des forces mortes, was sent by Le Sage to the Academy of Sciences at Paris in 1748, but it was never published. and in 1758 he sent a more detailed exposition, Essai de Chymie Méchanique, to a competition to the Academy of Sciences in Rouen. In this paper he tried to explain both the nature of gravitation and chemical affinities. The exposition of the theory which became accessible to a broader public, Lucrèce Newtonien (1784), in which the correspondence with Lucretius’ concepts was fully developed. Another exposition of the theory was published from Le Sage's notes posthumously by Pierre Prévost in 1818.

Although matter is postulated to be very sparse in the Fatio–Le Sage theory, it cannot be perfectly transparent, because in that case no gravitational force would exist. However, the lack of perfect transparency leads to problems: with sufficient mass the amount of shading produced by two pieces of matter becomes less than the sum of the shading that each of them would produce separately, due to the overlap of their shadows (P10, above). This hypothetical effect, called gravitational shielding, implies that addition of matter does not result in a direct proportional increase in the gravitational mass. Therefore, in order to be viable, Fatio and Le Sage postulated that the shielding effect is so small as to be undetectable, which requires that the interaction cross section of matter must be extremely small (P10, below). This places an extremely high lower bound on the intensity of the flux required to produce the observed force of gravity. Any form of gravitational shielding would represent a violation of the equivalence principle, and would be inconsistent with the extremely precise null result observed in the Eötvös experiment and its successors all of which have instead confirmed the precise equivalence of active and passive gravitational mass with inertial mass that was predicted by general relativity. For more historical information on the connection between gravitational shielding and Le Sage gravity, see Martins, and Borzeszkowski et al. Since Isenkrahe's proposal on the connection between density, temperature and weight was based purely on the anticipated effects of changes in material density, and since temperature at a given density can be increased or decreased, Isenkrahe's comments do not imply any fundamental relation between temperature and gravitation. (There actually is a relation between temperature and gravitation, as well as between binding energy and gravitation, but these actual effects have nothing to do with Isenkrahe's proposal. See the section below on "Coupling to energy".) Regarding the prediction of a relation between gravitation and density, all experimental evidence indicates that there is no such relation.

In many particle models, such as Kelvin's, the range of gravity is limited due to the nature of particle interactions amongst themselves. The range is effectively determined by the rate that the proposed internal modes of the particles can eliminate the momentum defects (shadows) that are created by passing through matter. Such predictions as to the effective range of gravity will vary and are dependent upon the specific aspects and assumptions as to the modes of interactions that are available during particle interactions. However, for this class of models the observed large scale structure of the cosmos constrains such dispersion to those that will allow for the aggregation of such immense gravitational structures.

As noted in the historical section, a major problem for every Le Sage model is the energy and heat issue. As Maxwell and Poincaré showed, inelastic collisions lead to a vaporization of matter within fractions of a second and the suggested solutions were not convincing. For example, Aronson The idea of mass accretion and the expanding earth theory are not currently considered to be viable by mainstream scientists. This is because, among other reasons, according to the principle of mass–energy equivalence, if the Earth was absorbing the energy of the ultramundane flux at the rate necessary to produce the observed force of gravity (i. e. by using the values calculated by Poincaré), its mass would be doubling in each fraction of a second.

Based on observational evidence, it is now known that gravity interacts with all forms of energy, and not just with mass. The electrostatic binding energy of the nucleus, the energy of weak interactions in the nucleus, and the kinetic energy of electrons in atoms, all contribute to the gravitational mass of an atom, as has been confirmed to high precision in Eötvös type experiments. This means, for example, that when the atoms of a quantity of gas are moving more rapidly, the gravitation of that gas increases. Moreover, Lunar Laser Ranging experiments have shown that even gravitational binding energy itself also gravitates, with a strength consistent with the equivalence principle to high precision which furthermore demonstrates that any successful theory of gravitation must be nonlinear and self coupling. Le Sage's theory does not predict any of these aforementioned effects, nor do any of the known variants of Le Sage's theory.

The re examination of Le Sage's theory in the 19th century identified several closely interconnected problems with the theory. These relate to excessive heating, frictional drag, shielding, and gravitational aberration. The recognition of these problems, in conjunction with a general shift away from mechanical based theories, resulted in a progressive loss of interest in Le Sage's theory. Ultimately in the 20th century Le Sage's theory was eclipsed by Einstein's theory of general relativity. In 1965 Richard Feynman examined the Fatio/Lesage mechanism, primarily as an example of an attempt to explain a "complicated" physical law (in this case, Newton's inverse square law of gravity) in terms of simpler primitive operations without the use of complex mathematics, and also as an example of a failed theory. He notes that the mechanism of "bouncing particles" reproduces the inverse square force law and that "the strangeness of the mathematical relation will be very much reduced", but then remarks that the scheme "does not work", because of the drag it predicts would be experienced by moving bodies. There are occasional attempts to re habilitate the theory outside the mainstream, including those of Radzievskii and Kagalnikova (1960), Shneiderov (1961), Buonomano and Engels (1976), Adamut (1982), Popescu (1982), Jaakkola (1996), Tom Van Flandern (1999), and Edwards (2014). A variety of Le Sage models and related topics are discussed in Edwards, et al.

English summary of Prévost (1805).