Le Sage's theory of gravitation From Wikipedia, the free encyclopedia
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In
1690[1] Nicolas Fatio de Duillier and in
1748[2] Georges-Louis Le Sage of
Geneva proposed a simple
mechanical explanation of gravitation. Because Fatio's work was not widely known and remained unpublished for a long time, it was Le Sage's exposition of the theory which became the subject of renewed interest in the late nineteenth century when it was studied in the context of the then newly discovered kinetic theory of gases.
[3] By the early twentieth century, the theory was generally considered discredited, most notably due to issues raised by
Maxwell[4] and
Poincaré.
[5] While Le Sage's theory is still studied by some researchers, it is not regarded as a viable theory within the mainstream scientific community.
Contents
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[edit] The basic Theory 
P1: Single Body
No net directional force
The theory posits that the
force of gravity is the result of tiny
particles moving at high speed in all directions, throughout the
universe. The intensity of the flux of particles is assumed to be the same in all directions, so an isolated object A is struck equally from all sides, resulting in only an inward-directed
pressure but no net directional force (P1).
P2: Two bodies "attract" each other
With a second object
B present, however, a fraction of the particles that would otherwise have struck A from the direction of B is intercepted, so B works as a shield, i.e. from the direction of B, A will be struck by fewer particles than from the opposite direction. Likewise B will be struck by fewer particles from the direction of A than from the opposite direction. One can say that A and B are "shadowing" each other, and the two bodies are pushed toward each other by the resulting imbalance of forces (P2). Thus the apparent attraction between bodies is, according to this theory, actually a diminished push from the direction of other bodies, so the theory is sometimes called
push gravity or
shadow gravity, although it is more widely referred to as
Lesage gravity.
[edit] Nature of Collisions 
P3: Opposite streams
If the collisions of body A and the gravific particles are fully
elastic, the intensity of the reflected particles would be as strong as of the incoming ones, so no net directional force would arise. The same is true if a second body B is introduced, where B acts as a shield against gravific particles in the direction of A. The gravific particle C which ordinarily would strike on A is blocked by B, but another particle D which ordinarily would not have struck A, is re-directed by the reflection on B, and therefore replaces C. Thus if the collisions are fully elastic, the reflected particles between A and B would fully compensate any shadowing effect. In order to account for a net gravitational force, it must be assumed that the collisions are not fully elastic, or at least that the reflected particles are slowed, so that their momentum is reduced after the impact. This would result in streams with diminished momentum departing from A, and streams with undiminished momentum arriving at A, so a net directional momentum toward the center of A would arise (P3). Under this assumption, the reflected particles in the two-body case will not fully compensate the shadowing effect, because the reflected flux is weaker than the incident flux.
[edit] The inverse square Law 
P4: Inverse square relation
Since it is assumed that some or all of the gravific particles converging on an object are either absorbed or slowed by the object, it follows that the intensity of the flux of gravific particles emanating from the direction of a massive object is less than the flux converging on the object. We can imagine this imbalance of momentum flow - and therefore of the force exerted on any other body in the vicinity - distributed over a spherical surface centered on the object (P4). The imbalance of momentum flow over an entire spherical surface enclosing the object is independent of the size of the enclosing sphere, whereas the surface area of the sphere increases in proportion to the square of the radius. Therefore, the momentum imbalance per unit area decreases inversely as the square of the distance.
[edit] Mass Proportionality
From the things outlined so far, there arises only a force which is proportional to the surface of the bodies. But gravity is proportional to the masses. To satisfy the need for mass proportionality, the theory posits that a) the basic elements of matter are very small so that gross matter consists mostly of empty space, and b) that the particles are so small, that only a small fraction of them would be intercepted by gross matter. The result is, that the "shadow" of each body is proportional to the surface of every single element of matter. If it is then assumed that the elementary opaque elements of all matter are identical (i.e., having the same ratio of density to area), it will follow that the shadow effect is, at least approximately, proportional to the mass (P5).
P5: Permeability, attenuation and mass proportionality
[edit] Le Sage
The first exposition of his theory, was sent by Le Sage to the Academy of Sciences at Paris in
1748, but it was never published.
[27] According to Le Sage,
after creating and sending his
essay he was informed on the theories of
Fatio,
Cramer and Redeker.
[28] In
1756 one of Le Sage's expositions of the theory was published,
[2] and in
1758 he sent a more detailed exposition to a competition to the Academy of Sciences in
Rouen.
[29] 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 was "Lucrèce Newtonien", in which the correspondence with Lucretius’ concepts was fully developed.
[30] Another exposition of the theory was published from Le Sage's notes posthumously by
Prévost in
1818,
[31] but it doesn't contain anything which wasn't published in the earlier papers.
[32] [edit] Le Sage's basic Concept
Le Sage discussed the theory in great detail and he proposed quantitative estimates for some of the theory's parameters.
- He called the gravitational particles "ultramundane corpuscles", because he supposed them to originate beyond our known universe. The distribution of the ultramundane flux is very isotropic and the laws of its propagation are very similar to that of light.
- Le Sage argued, that in case the matter-corpuscle-collisions are perfectly elastic, no gravitational force would arise. So he proposed that the corpuscles and the basic constituents of matter are "absolutely hard" and asserted that this implies a complicated form of interaction, completely inelastic in the direction normal to the surface of the ordinary matter, and perfectly elastic in the direction tangential to the surface. He then commented that this implies the mean speed of scattered corpuscles is 2/3 of their incident speed.[33] To avoid inelastic collisions between the corpuscles, he supposed that their diameter is very small relative to their mutual distance.
- That resistance of the flux is proportional to uv (where v is the velocity of the corpuscles and u that of gross matter) and gravity is proportional to v², so the ratio resistance/gravity can be made arbitrarily small by increasing v. Therefore he suggested that the ultramundane corpuscles might move at the speed of light, but after further consideration he corrected this value to 105 times the speed of light.[34]
- To maintain mass proportionality, ordinary matter consists of cage-like structures, in which their diameter is only the 107th part of their mutual distance. Also the "bars", which constitute the cages, were small (around 1020 times as long as thick) relative to the dimensions of the cages, so the corpuscles can travel through them nearly unhindered.[35]
Le Sage said that he was the first one, who drew all consequences from the theory and also
Prévost said that Le Sage's theory was more developed than Fatio's theory.
[36] However, by comparing the two theories and after a detailed analyses of Fatio's papers (which also were in possession of Le Sage) Zehe judged that Le Sage contributed nothing essentially new and he often didn't reach Fatio's level.
[37]
As mentioned above, Le Sage also attempted to use the shadowing mechanism to account for the forces of cohesion, and for forces of different strengths, by positing the existence of multiple species of ultramundane corpuscles of different sizes, as illustrated in Figure 9.
[edit] Reception of Le Sage's Theory
Le Sage’s ideas were not well-received during his day, except for some of his friends and associates like
Prévost,
Bonnet,
Deluc and
L'Huilier. They mentioned and described Le Sage's theory in their books and papers, which were used by their contemporaries as a secondary source for Le Sage's theory (because of the lack of published papers by Le Sage himself) .
[edit] Range of Gravity
In many corpuscular models, such as Kelvin's, the range of gravity is limited due to the nature of corpuscular interactions amongst themselves. The range is effectively determined by the rate that the proposed
internal modes of the corpuscles 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 corpuscular 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.
[edit] Absorbed Energy
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
[50] gave a simple proof of Maxwell's assertion:
Suppose that, contrary to Maxwell's hypothesis, the molecules of gross matter actually possess more energy than the corpuscles. In that case the corpuscles would, on the average, gain energy in the collision and the particles intercepted by body B would be replaced by more energetic ones rebounding from body B. Thus the effect of gravity would be reversed: there would be a mutual repulsion between all bodies of mundane matter, contrary to observation. If, on the other hand, the average kinetic energies of the corpuscles and of the molecules are the same, then no net transfer of energy would take place, and the collisions would be equivalent to elastic ones, which, as has been demonstrated, do not yield a gravitational force.
Likewise Isenkrahe's violation of the
energy conservation law is unacceptable, and Kelvin's application of Clausius' theorem leads (as noted by Kelvin himself) to some sort of
perpetual motion mechanism. The suggestion of a secondary re-radiation mechanism for wave models attracted the interest of JJ Thomson, but was not taken very seriously by either Maxwell or Poincaré, because it entails a gross violation of the second law of
thermodynamics (huge amounts of energy spontaneously being converted from a colder to a hotter form), which is one of the most solidly established of all physical laws.
The energy problem has also been considered in relation to the idea of mass accretion in connection with the
expanding earth theory. Among the early theorists to link mass increase in some sort of push gravity model to Earth expansion were
Yarkovsky and
Hilgenberg.
[90] Shneiderov, on the other hand, attempted to link earth expansion to internal heating caused by the collisions of Le Sage particles.
[91] 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.
[edit] Coupling to Energy
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.
[92] This means, for example, that when the atoms of a quantity of gas are moving more rapidly, the gravitation of that gas increases. Le Sage's theory does not predict any such effect, nor does any of the known variants of Le Sage's theory.
[edit] Recent activity
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 twentieth century Le Sage’s theory was eclipsed by Einstein’s theory of
general relativity.
Although it is not regarded as a viable theory within the mainstream scientific community, there are ongoing attempts to revitalize the theory outside the mainstream, including those of Radzievskii and Kagalnikova,
[93] Shneiderov,
[91] Buonomano and Engels,
[94] Adamut,
[95] Jaakkola,
[96] and
Van Flandern.
[97] A variety of Le Sage models and related topics are discussed in Edwards, et al.
[98] For a much more detailed report on this remarkable issue, enter 'Le Sage', in google. Regards, - RP http://foums.delphiforums.com/EinsteinGroupie