Le Sage's Theory of Gravitation - Kinetic Theory

Kinetic Theory

Because the theories of Fatio, Cramer and Redeker were not widely known, Le Sage's exposition of the theory enjoyed a resurgence of interest in the latter half of the 19th century, coinciding with the development of the kinetic theory.

Leray

Since Le Sage's particles must lose speed when colliding with ordinary matter (in order to produce a net gravitational force), a huge amount of energy must be converted to internal energy modes. If those particles have no internal energy modes, the excess energy can only be absorbed by ordinary matter. Addressing this problem, Armand Jean Leray proposed a particle model (perfectly similar to Le Sage's) in which he asserted that the absorbed energy is used by the bodies to produce magnetism and heat. He suggested, that this might be an answer for the question of where the energy output of the stars comes from.

Kelvin and Tait

Le Sage's own theory became a subject of re-newed interest in the latter part of the 19th century following a paper published by Kelvin in 1873. Unlike Leray, who treated the heat problem imprecisely, Kelvin stated that the absorbed energy represents a very high heat, sufficient to vaporize any object in a fraction of a second. So Kelvin re-iterated an idea that Fatio had originally proposed in the 1690s for attempting to deal with the thermodynamic problem inherent in Le Sage's theory. He proposed that the excess heat might be absorbed by internal energy modes of the particles themselves, based on his proposal of the vortex-nature of matter. In other words, the original translational kinetic energy of the particles is transferred to internal energy modes, chiefly vibrational or rotational, of the particles. Appealing to Clausius's proposition that the energy in any particular mode of a gas molecule tends toward a fixed ratio of the total energy, Kelvin went on to suggest that the energized but slower moving particles would subsequently be restored to their original condition due to collisions (on the cosmological scale) with other particles. Kelvin also asserted that it would be possible to extract limitless amounts of free energy from the ultramundane flux, and described a perpetual motion machine to accomplish this. (The flaw in Kelvin's reasoning was that Clausius's proposition would apply only if ordinary matter was in thermodynamic equilibrium with the ultramundane flux - in which case there would no net gravitational effect.)

Subsequently, Peter Guthrie Tait called the Le Sage theory the only plausible explanation of gravitation which has been propounded at that time. He went on by saying:

Kelvin himself, however, was not optimistic that Le Sage's theory could ultimately give a satisfactory account of phenomena. After his brief paper in 1873 noted above, he never returned to the subject, except to make the following comment:

Preston

Samuel Tolver Preston illustrated that many of the postulates introduced by Le Sage concerning the gravitational particles, such as rectilinear motion, rare interactions, etc.., could be collected under the single notion that they behaved (on the cosmological scale) as the particles of a gas with an extremely long mean free path. Preston also accepted Kelvin's proposal of internal energy modes of the particles. He illustrated Kelvin's model by comparing it with the collision of a steel ring and an anvil - the anvil would not be shaken very much, but the steel ring would be in a state of vibration and therefore departs with diminished velocity. He also argued, that the mean free path of the particles is at least the distance between the planets - on longer distances the particles regain their translational energy due collisions with each other, so he concluded that on longer distances there would be no attraction between the bodies, independent of their size. Paul Drude suggested that this could possibly be a connection with some theories of Carl Gottfried Neumann and Hugo von Seeliger, who proposed some sort of absorption of gravity in open space.

Maxwell

A review of the Kelvin-Le Sage theory was published by James Clerk Maxwell in the Ninth Edition of the Encyclopædia Britannica under the title Atom in 1875. After describing the basic concept of the theory he wrote (with sarcasm according to Aronson):

Maxwell commented on Kelvin’s suggestion of different energy modes of the particles that this implies the gravitational particles are not simple primitive entities, but rather systems, with their own internal energy modes, which must be held together by (unexplained) forces of attraction. He argues that the temperature of bodies must tend to approach that at which the average kinetic energy of a molecule of the body would be equal to the average kinetic energy of an ultra-mundane particle and he states that the latter quantity must be much greater than the former and concludes that ordinary matter should be incinerated within seconds under the Le Sage bombardment. He wrote:

Maxwell also argued that the theory requires "an enormous expenditure of external power" and therefore violating the conservation of energy as the fundamental principle of nature. Preston responded to Maxwell's criticism by arguing that the kinetic energy of each individual simple particle could be made arbitrarily low by positing a sufficiently low mass (and higher number density) for the particles. But this issue later was discussed in a more detailed way by Poincaré, who showed that the thermodynamic problem within Le Sage models remained unresolved.

Isenkrahe, Ryšánek, du Bois-Reymond

Caspar Isenkrahe presented his model in a variety of publications between 1879-1915. His basic assumptions were very similar to those of Le Sage and Preston, but he gave a more detailed application of the kinetic theory. However, by asserting that the velocity of the corpuscles after collision was reduced without any corresponding increase in the energy of any other object, his model violated the conservation of energy. He noted that there is a connection between the weight of a body and its density (because any decrease in the density of an object reduces the internal shielding) so he went on to assert that warm bodies should be heavier than colder ones (related to the effect of thermal expansion).

In another model Adalbert Ryšánek in 1887 also gave a careful analysis, including an application of Maxwell's law of the particle velocities in a gas. He distinguished between a gravitational and a luminiferous aether. This separation of those two mediums was necessary, because according to his calculations the absence of any drag effect in the orbit of Neptune implies a lower limit for the particle velocity of 5 · 1019 cm/s. He (like Leray) argued that the absorbed energy is converted into heat, which might be transferred into the luminiferous aether and/or is used by the stars to maintain their energy output. However, these qualitative suggestions were unsupported by any quantitative evaluation of the amount of heat actually produced.

In 1888 Paul du Bois-Reymond argued against Le Sage's model, partly because the predicted force of gravity in Le Sage's theory is not strictly proportional to mass. In order to achieve exact mass proportionality as in Newton's theory (which implies no shielding or saturation effects and an infinitely porous structure of matter), the ultramundane flux must be infinitely intense. Du Bois-Reymond rejected this as absurd. In addition, du Bois-Reymond like Kant observed that Le Sage's theory cannot meet its goal, because it invokes concepts like "elasticity" and "absolute hardness" etc., which (in his opinion) can only be explained by means of attractive forces. The same problem arises for the cohesive forces in molecules. As a result, the basic intent of such models, which is to dispense with elementary forces of attraction, is impossible.