Le Sage's theory of gravitation

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.

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.

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).

[2] So it lasted until 1929,[3] when the only complete copy of Fatio's manuscript was published by Karl Bopp, and in 1949[4] Gagnebin used the collected fragments in possession of Le Sage to reconstruct the paper.

Nevertheless, Fatio's theory remained largely unknown with a few exceptions like Cramer and Le Sage, because he never was able to formally publish his works and he fell under the influence of a group of religious fanatics called the "French prophets" (which belonged to the camisards) and therefore his public reputation was ruined.

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.

John Playfair described Boscovich's arguments by saying: An immense multitude of atoms, thus destined to pursue their never ending journey through the infinity of space, without changing their direction, or returning to the place from which they came, is a supposition very little countenanced by the usual economy of nature.

Lichtenberg originally believed (like Descartes) that every explanation of natural phenomena must be based on rectilinear motion and impulsion, and Le Sage's theory fulfilled these conditions.

[18] Partly in consideration of Le Sage's theory, Pierre-Simon Laplace undertook to determine the necessary speed of gravity in order to be consistent with astronomical observations.

He calculated that the speed must be “at least a hundred millions of times greater than that of light”, in order to avoid unacceptably large inequalities due to aberration effects in the lunar motion.

Addressing this problem, Armand Jean Leray[20] 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.

So Kelvin reiterated an idea that Fatio had originally proposed in the 1690s for attempting to deal with the thermodynamic problem inherent in Le Sage's theory.

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.

After his brief paper in 1873 noted above, he never returned to the subject, except to make the following comment: This kinetic theory of matter is a dream, and can be nothing else, until it can explain chemical affinity, electricity, magnetism, gravitation, and the inertia of masses (that is, crowds) of vortices.

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.

[26] After describing the basic concept of the theory he wrote (with sarcasm according to Aronson):[27] Here, then, seems to be a path leading towards an explanation of the law of gravitation, which, if it can be shown to be in other respects consistent with facts, may turn out to be a royal road into the very arcana of science.

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.

Lorentz showed that an attractive force between charged particles (which might be taken to model the elementary subunits of matter) would indeed arise, but only if the incident energy were entirely absorbed.

If the mechanism of gravitation consisted in vibrations which cross the aether with the velocity of light, the attraction ought to be modified by the motion of the celestial bodies to a much larger extent than astronomical observations make it possible to admit.In 1922[34] Lorentz first examined Martin Knudsen's investigation on rarefied gases and in connection with that he discussed Le Sage's particle model, followed by a summary of his own electromagnetic Le Sage model – but he repeated his conclusion from 1900: Without absorption no gravitational effect.

In 1913 David Hilbert referred to Lorentz's theory and criticised it by arguing that no force in the form 1/r2 can arise, if the mutual distance of the atoms is large enough when compared with their wavelength.

In 1905, George Darwin subsequently calculated the gravitational force between two bodies at extremely close range to determine if geometrical effects would lead to a deviation from Newton's law.

He concluded that only in the instance of perfectly inelastic collisions (zero reflection) would Newton's law stand up, thus reinforcing the thermodynamic problem of Le Sage's theory.

Also, such a theory is only valid if the normal and the tangential components of impact are totally inelastic (contrary to Le Sage's scattering mechanism), and the elementary particles are exactly of the same size.

After describing a similar re-radiation model like Thomson, he concluded: "Such are the complicated hypotheses to which we are led when we seek to make Le Sage's theory tenable".

Poincaré then went on to consider Le Sage's theory in the context of the "new dynamics" that had been developed at the end of the 19th and the beginning of the 20th centuries, specifically recognizing the relativity principle.

This makes Le Sage theory fundamentally incompatible with the modern science of mechanics based on special relativity, according to which no particle (or wave) can exceed the speed of light.

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.

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.

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.

[59][60] There are occasional attempts to re-habilitate the theory outside the mainstream, including those of Radzievskii and Kagalnikova (1960),[61] Shneiderov (1961),[62] Buonomano and Engels (1976),[63] Adamut (1982),[64] Popescu (1982),[65] Jaakkola (1996),[66] Tom Van Flandern (1999),[67] and Edwards (2014).