Le Sage Gravitation

The Le Sage's theory of gravitation is a simple mechanical gravitational declaration that the law of gravitation of Newton was justified. It was designed by Nicolas Fatio de Duillier (1690) and Georges-Louis Le Sage (1748).

Since Fatio's work was largely unknown and unpublished, it was Le Sage's version of the theory that became the subject of much interest towards the end of the 19th century in connection with the then newly developed kinetic theory of gases . Although some outside mainstream researchers continue to investigate the theory, it is considered obsolete and invalid, largely because of the objections raised by James Clerk Maxwell (1875) and Henri Poincaré (1908).

Basics of the theory

B1: Balance of forces
No movement

The basic assumption of the theory is the existence of a space that is largely isotropically filled by a radiation field that consists of various particles (corpuscles) or waves . These move in a straight line in all possible directions at a constant, very high speed. If a particle hits a body, it transmits an impulse to it. If there is only one body A, it is exposed to an even pressure, i.e. it is in an equilibrium of forces due to the impacts acting in all directions and will not move (see Figure B1).

B2: Shielding
Bodies “attract” each other

However, if there is a second body B, it acts like a screen, because A is hit by fewer particles from direction B than from the other side, and the same applies vice versa. A and B shade each other (B2) and this creates a negative pressure on the sides facing each other. This creates an apparently attractive force that acts exactly in the direction of the other body. The theory is therefore not based on the concept of attraction , but belongs to the class of pressure theories or kinetic explanations of gravity .

Nature of the collisions

B3: Opposite currents

If the collisions between body A and the particles are completely elastic , the intensity of the reflected particles would be just as high as that of the incoming particles, so that no force in direction A would result. The same thing would happen if there were a second body B, which would act as a screen for particles flying in direction A. The particles reflected between the bodies would completely cancel out the shadow effect. In order to allow a gravitational effect between the bodies, the kinetic energy of the particles must be completely or at least partially absorbed by the matter , or they must be modified in such a way that their momentum has decreased after the collision: Only then does the momentum of the incoming particles predominate versus the momentum of the particles reflected by the bodies (B3).

Proportionality to 1 / r²

B4: Increase and decrease in density in each section of the sphere

If one imagines a spherical surface (sphere) around a body, which has to be traversed by both the reflected and the incoming particles, it becomes evident that the size of the sphere increases proportionally to the square of the distance. The number of particles in question in these growing sections remains the same, however, and their density therefore decreases. According to the law of distance , the gravitational effect behaves inversely to the square of the distance to the respective masses (B4). This analogy to optical effects such as the decrease in radiation intensity with 1 / r² or the formation of shadows was already given by Fatio and Le Sage.

Proportionality to the mass

From what has been explained so far, there is only one force, the strength of which is proportional to the surface or the volume . In addition to the volume, gravity is also dependent on the density and thus on the mass . In order to achieve this observed proportionality to the mass , it was assumed that the matter consists largely of empty space and that the particles, assumed to be very small, can easily penetrate the body. This means that the particles penetrate the body, interact with all components of matter, are partially shielded or absorbed and then exit again weakened. As a result, assuming a corresponding penetration capability, a shadow effect of the body proportional to the mass is achieved at least within a certain measuring accuracy. The result (B5): Two bodies shadow each other and the result is an image analogous to B2.

B5: penetration, weakening and proportionality to the mass

Fatio

Nicolas Fatio

Nicolas Fatio de Duillier presented the first draft of his thoughts on gravity in a letter to Christiaan Huygens in 1690 . Immediately afterwards he read its contents at a meeting of the Royal Society in London . In the following years Fatio drafted several manuscripts of his main work De la Cause de la Pesanteur . He also wrote a didactic poem in Latin on the same subject in 1731. Some fragments of these manuscripts were later acquired by Le Sage, who tried to publish them but was unsuccessful. And so it was not until 1929 when Karl Bopp published a copy of a complete manuscript. Another version of the theory was published in 1949 by Bernard Gagnebin, who tried to reconstruct the work from the fragments of Le Sage. The following description is mainly based on the Bopp edition (which includes "Problems I – IV") and the representation of toe.

Some aspects of the theory

Fatio's pyramid (problem I)

B6: Fatio's pyramid

Fatio assumed that the universe was filled with tiny particles that move indiscriminately and in a straight line with very great speed in all directions . To illustrate his thoughts, he used the following picture: Let there be an object C on which there is an infinitely small area zz . Let this area zz be the center of a circle . Within this circle Fatio drew the pyramid PzzQ , in which some particles flow in the direction zz , and also some particles, which have already been reflected by C , flow in the opposite direction. Fatio assumed that the average speed and thus also the impulses of the reflected particles were lower than those of the incoming particles. The result is a current that drives all bodies towards zz . On the one hand the speed of the current remains constant, on the other hand its density increases in closer proximity to zz . Therefore, due to the geometric relationships, its intensity is proportional to 1 / r² , where r is the distance from zz . Infinitely because many such pyramids around C are conceivable, this proportionality applies to the entire area around C .

Reduced speed

To justify the claim that the particles move at a reduced speed after reflection, Fatio made the following suggestions:

• Ordinary matter, or particles, or both, are inelastic .
• The collisions are perfectly elastic, but the particles are not absolutely hard, which is why they vibrate and lose speed after the collision .
• The particles begin to rotate due to friction and also lose speed.

These passages are the most incomprehensible parts of Fatio's theory because he never clearly decides what kind of collision to prefer. In the last version of the theory from 1743, however, he shortened these passages and attributed perfect elasticity or perfect elasticity to the particles on the one hand , and incomplete elasticity to matter on the other , so that the particles are reflected at a lower speed. The loss of speed was set extremely low by Fatio in order not to let the gravitational force decrease noticeably over longer periods of time. In addition, Fatio was confronted with another problem: What happens when the particles collide with one another? Inelastic collisions would, even if no normal matter is present, lead to a constant decrease in speed and therefore also weaken the gravitational force. To avoid this problem, Fatio assumed that the diameter of the particles is very small compared to their mutual distance, and therefore encounters with one another are very rare.

compression

In order to dispel the objection that the lower particle speed could cause a congestion around the body, Fatio explained that the reflected particles are actually slower than the incoming ones. Therefore, the particles flowing in from the outside have a greater speed, but also a greater distance from one another. Conversely, the reflected particles are slower, but this is compensated for by a constant compression . The compression is therefore constant and there is no congestion. Fatio went on to explain that, by increasing the speed and elasticity of the particles, this compression can be made as small as desired.

Permeability of matter

Crystal lattice ( icosahedron )

In order to explain the proportionality to the mass, Fatio had to postulate that normal matter is evenly permeable to the particles in all directions. He sketched 3 models for this:

• He assumed that matter was an accumulation of small spheres , the diameter of which is negligibly small compared to the distance between them. But he rejected this explanation because the spheres must tend to get closer and closer to each other.
• Then he assumed that spheres were connected by rods and formed a crystal lattice or network . However, he also rejected this model, because if different networks were combined, uniform penetration would no longer be possible in the places where the spheres are very close to one another.
• Finally he removed the balls as well, leaving only the rods of the net, making the diameter of the rods infinitesimal compared to their spacing. He thought he could guarantee maximum penetrability.

Pressure of the particles (problem II)

As early as 1690, Fatio assumed that the pressure exerted by the particles on a flat surface accounts for the sixth part of the pressure that would exist if all particles were oriented perpendicular to the plane. Fatio provided evidence of this claim by calculating the pressure exerted by the particles on a certain point. is exercised. He finally arrived at the formula , where is the density and the speed of the particles. This solution is very similar to the formula known in kinetic gas theory that was found by Daniel Bernoulli in 1738. This was the first time the close relationship between the two theories had been demonstrated, and before the latter was even developed. However, Bernoulli's value is twice as large, because Fatio did not start with the impulse in the reflection , but instead . Its result would therefore only be valid for completely inelastic collisions. Fatio used his solution not only to explain gravity, but also to explain the behavior of gases. He constructed a thermometer that should measure the state of motion of the air molecules and thus the heat . However, in contrast to Bernoulli , Fatio did not identify the movement of air molecules with heat, but rather blamed another fluid for it. However, it is not known whether Bernoulli was influenced by Fatio. ${\displaystyle p=\rho v^{2}zz/6}$ ${\displaystyle \rho }$ ${\displaystyle v}$ ${\displaystyle p=\rho v^{2}/3}$ ${\displaystyle 2mv}$ ${\displaystyle mv}$

Infinity (problem III)

In this section, Fatio examined the concept of infinity in the context of his theory. Fatio justified many of his considerations with the fact that various phenomena are infinitely smaller and larger than others and that many problematic effects of the theory can thereby be reduced to an immeasurable value. For example, the diameter of the rods is infinitely smaller than their distance from one another; or the speed of the particles is infinitely greater than that of matter; or the difference in speed between reflected and non-reflected particles is infinitely small.

Resistance of the medium (problem IV)

This is the most mathematically demanding part of Fatio's theory. Here he tried to calculate the flow resistance of the particle flows for moving bodies. Let it be the speed of the body, the speed of the particles and the density of the medium of propagation . In the case of and, Fatio calculated a resistance of . In the case and the resistance behaves like . Following Newton, who demanded an extremely low density of any medium due to the unobserved resistance in the direction of movement, Fatio reduced the density and concluded that this could be compensated by changing inversely proportional to the square root of the density . This follows from Fatio's printing formula . According to Zehe, Fatio's attempt to keep the resistance in the direction of movement low in relation to the gravitational force was successful, because the resistance in Fatio's model is proportional to , but the gravitational force is proportional to . ${\displaystyle u}$ ${\displaystyle v}$ ${\displaystyle \rho }$ ${\displaystyle v\ll u}$ ${\displaystyle \rho =\mathrm {const} }$ ${\displaystyle \rho u^{2}}$ ${\displaystyle v\gg u}$ ${\displaystyle \rho =\mathrm {const} }$ ${\displaystyle 4/3\rho uv}$ ${\displaystyle v}$ ${\displaystyle \rho v^{2}/6}$ ${\displaystyle v}$ ${\displaystyle uv}$ ${\displaystyle v^{2}}$

Reception of the theory

B8: Halley, Huygens and Newton signatures on Fatio's manuscript

Fatio was in contact with some of the most famous scientists of his time. Some of them, such as Edmond Halley , Christiaan Huygens, and Isaac Newton , signed his manuscript.

Newton and Fatio had a close personal relationship between 1690 and 1693, with Newton's comments on Fatio's theory being very different. On the one hand, Newton wrote in 1692 in his own copy of the Principia, copied by Fatio:

“With this type of hypothesis there is only one that can explain the severity, and that was the first Mr. Fatio, a gifted mathematician. And in order to be able to set it up [the hypothesis], a vacuum is necessary, since the thin particles have to be carried by straight, extremely rapid and uniformly continued movements in all directions and they are only allowed to feel resistance where they hit coarser particles bump."

- Isaac Newton

On the other hand, David Gregory noted in his diary: “Mr. Newton and Mr. Halley laugh at Mr. Fatio's explanation of gravity ”. This was supposedly recorded in 1691. However, the ink and pen used are very different from the rest of the sheet. This suggests that the entry was made later. But Fatio also recognized that Newton was more inclined to see the true cause of gravity in God's will. From 1694, the relationship between the two cooled down.

Christiaan Huygens was the first to be informed of Fatio's theory, but he never accepted it and continued to work on his own aether vortex theory. Fatio believed he had convinced Huygens of the consistency of his theory, but Huygens denied this in a letter to Gottfried Wilhelm Leibniz . There was also a brief correspondence between Fatio and Leibniz, mainly on mathematical questions, but also on Fatio's theory. Leibniz criticized this because Fatio assumed an empty space between the particles, an assumption that Leibniz rejected for philosophical reasons. Jakob I Bernoulli, in turn, showed great interest in Fatio's theory and urged him to write it down in a complete manuscript, which was actually done by Fatio. Bernoulli had a copy made of it, which is in the University Library of Basel and forms the basis for the Bopp edition.

In spite of everything, Fatio's theory remained largely unknown, with a few exceptions such as Cramer and Le Sage, because he was never able to publish his work and he also came under the influence of a fanatical section of the Camisards and thereby completely lost his public reputation.

Cramer, Redeker

In 1731 the Swiss mathematician Gabriel Cramer published a dissertation , at the end of which a summary of a theory appears which is identical to that of Fatio (including network structure, light analogy and shading, etc.), but without his name being listed. However, Fatio was aware that Cramer had access to a copy of his manuscript, so he accused him of merely repeating his theory without understanding it. It was also Cramer who later brought Fatio's theory to Le Sage's attention. In 1736, Franz Albert Redeker, a German doctor , had also put forward a very similar theory.

Le Sage

Georges-Louis Le Sage

The first elaboration of the theory, Essai sur l'origine des forces mortes , was sent by Le Sage to the Academy of Sciences in Paris in 1748, but was rejected and never published. In 1749, after working out his own thoughts, he was instructed by his teacher Cramer about the existence of Fatio's theory and in 1751 he learned about Redeker's theory. In 1756 Le Saga's thoughts were published for the first time in a journal and in 1758 he sent Essai de Chymie Méchanique, a more detailed version of his theory, to a competition held by the Academy of Sciences. In this work he tried to explain both the nature of gravity and that of chemical affinities. He won the award together with a competitor and thereby secured the attention of prominent contemporaries such as Leonhard Euler . A significantly expanded edition of this essay was printed in a few copies in 1761. However, a work more accessible to the wider public, Lucrece Neutonia , was not published until 1784. The most extensive compilation of the theory, Physique Mécanique des Georges-Louis Le Sage , was published posthumously by Pierre Prévost in 1818 .

Basic concept

Le Sage discussed the theory in great detail, but he did not add anything fundamentally new to it, and although he was in possession of some of Fatio's papers, according to Zehe, he often did not reach his level.

• Le Sage called his gravitational particles ultramundane corpuscles because he believed that they came from far outside known space. The distribution of these currents is extremely isotropic and the laws of propagation correspond to those of light .
• He argued that completely elastic matter-particle collisions would not generate any gravitational force. So he suggested that the particles and the constituents of matter are absolutely hard , which in his opinion implies a complicated form of impact, namely completely inelastic perpendicular to the surface of normal matter, and completely elastic tangential to the surface. He went on to say that the reflected particles would therefore only have an average of 2/3 the speed of before. In order to avoid inelastic collisions between the particles, he assumed, like Fatio, that their diameter was much smaller than their mutual distance.
• The resistance of the particle currents is proportional to uv (where v is the speed of the particles and u that of the body), whereas gravity is proportional to v² . It follows that the drag / gravity ratio can be made as small as desired by increasing v . For some time he assumed that the particles would move at c (= speed of light ), but later he increased the value considerably to 10 ⁵ · c .
• In order to maintain the proportionality to the mass, like Fatio he designed a hypothesis in which matter has a cage or lattice structure, the lattice atoms themselves only having a diameter that is 10 ⁷ times smaller than their mutual distance. The lattice atoms themselves are also permeable, with their rods being about ^10-20 times as long as they are wide. This allows the particles to penetrate practically unhindered.
• Le Sage also tried to use the shadowing mechanism to explain chemical effects by postulating the existence of many different types of ultramundane particles of different sizes (B9).

B9: Le Sage's own illustration of the ultramundane corpuscles

Reception of the theory

Le Sage's ideas were not received very positively in his day, except by some of his learned friends such as Pierre Prévost , Charles Bonnet , Jean-André Deluc, and Simon L'Huilier . These mentioned and described Le Sage's theory in their books and articles, which were used as secondary sources by their contemporaries - largely due to the lack of published papers by Le Sage himself.

Euler, Daniel Bernoulli, Boscovich

Leonhard Euler once noted in 1761 that Le Sage's model was infinitely better than the explanations of other authors, and that all objections had been resolved here. Later, however, he said that the light analogy was of no importance to him, since he believed in the wave nature of light. After further considerations, he generally rejected the model and wrote to Le Sage in 1765:

«Je sens encore une-grande répugnance pur cos corpuscules ultra mondains, et j'aimerais toujours mieux d'avouer mon ignorance sur la cause de la gravite, que de recourir a des hypothèses étranges. »

"You must excuse me if I have a great dislike for your ultramundane corpuscles, and I will always prefer to admit my ignorance of the cause of gravity than to resort to such strange hypotheses."

- Leonhard Euler

In 1767, Daniel Bernoulli was impressed by the similarity between Le Sage's model and his own thoughts on the kinetic theory of gases. However, Bernoulli himself was of the opinion that his own gas theory was only speculation, although this was even more true of Le Sage's theory. However, as it turned out in the 19th century, Bernoulli's gas theory was in principle correct. (P. 30)

Rugjer Josip Bošković explained in 1771 that Le Sage's theory was the first that could actually explain gravity by mechanical means. However, he rejected the model because of the enormous and unused quantity of ultramundane matter. In addition, Boscovich rejected the existence of direct contact effects and instead suggested repulsive and attractive long-range effects . John Playfair described Boscovich's arguments as follows:

“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. Whence is the supply of these innumerable torrents; must it not involve a perpetual exertion of creative power, infinite both in extent and in duration? "

“An immense number of atoms destined to pursue their never-ending journey through the infinity of space without changing direction or ever returning to their original location is an assumption that bears very little agreement with the usual economy of nature. Where is the source of these innumerable rivers; Doesn't that include a perpetual exercise of creative power, infinite in both extent and duration? "

- John Playfair

Lichtenberg, Schelling

Georg Christoph Lichtenberg originally believed, like René Descartes , that any explanation of natural phenomena must be based on linear motion and direct contact, and Le Sage's theory fulfilled these requirements. He referred to Le Sage's theory in his lectures on physics at the University of Göttingen and wrote about Le Sage's theory in 1790:

"If it is a dream, it is the greatest and most sublime that has ever been dreamed, and with which we can fill a gap in our books that can only be filled by a dream"

- Georg Christoph Lichtenberg

However, around 1796, Lichtenberg changed his mind after being confronted with the arguments of Immanuel Kant , who criticized any attempt to attribute attraction to repulsion. According to Kant, every form of matter is infinitely divisible, from which it follows that the mere existence of extended matter requires the existence of attractive forces which hold the individual parts together. However, this force cannot be justified by collisions with a surrounding matter, since the parts of this impacting matter themselves would have to be held together again. In order to avoid this circular argument, Kant postulated, in addition to a repulsive force, the necessity of a fundamental attractive force. Friedrich Wilhelm Joseph von Schelling, in turn, rejected Le Sage's model because of its mechanical materialism , whereas Schelling advocated a very idealistic philosophy.

Laplace

Partly taking into account Le Sage's theory, Pierre-Simon Laplace tried around 1805 to determine the speed with which such a medium must move in order to remain in harmony with astronomical observations. He calculated that the speed of gravity must be at least 100 million times greater than the speed of light in order to avoid irregularities in the lunar orbit. For Laplace and others this was a reason to assume that Newtonian gravity is based on action at a distance and that models of near action like that of Le Sage cannot work.

Kinetic theory

Since the theories of Fatio, Cramer and Redeker remained largely unknown, it was Le Sage's theory that was revitalized in the second half of the 19th century due to the development of the kinetic theory of gases by Clausius, Kelvin and Maxwell.

Leray

Since Le Sages particles lose speed after the collisions, a large amount of energy would have to be converted into internal energy modes of the body due to the law of conservation of energy . Addressing this problem, P. Leray drafted a particle theory in 1869, in which he assumes that the absorbed energy is used by bodies partly to generate heat and partly to generate magnetism . He speculated that this was a possible answer to the question of where the energy of the stars comes from.

Kelvin, Tait

Lord Kelvin

Le Sage's own model was modernized mainly through the work of Lord Kelvin in 1872 within the framework of the kinetic gas theory. After summarizing the theory, Kelvin realized that absorbed energy was a much bigger problem than Leray believed. The heat generated would cause any body to burn up in a fraction of a second. That is why Kelvin described a mechanism that had already been developed in a modified form by Fatio in 1690. Kelvin believed that the particles suffer a loss of their translational energy components after the collision, i.e. that they become slower, but vibrate and rotate more strongly . The bodies hit would not heat up, but the particles themselves would carry the energy away with them after the impact in the form of increased vibration and rotation. This is to be understood in connection with Kelvin's theory of a vortex nature of matter. Based on his interpretation of the principles of Clausius , according to which the ratio between the 3 energy modes in a gas remains constant, he assumed that the particles would regain their original energy configuration over cosmic distances through collisions with other particles and thus the gravitational effect would not with the Time decreases. Kelvin believed that because of this it was possible to use the particles as a practically inexhaustible source of energy and thus to construct a kind of perpetual motion machine . For thermodynamic reasons, however, such a construction is not possible and Kelvin's interpretation of Clausius' theory had to be rejected.

Following Kelvin, Peter Guthrie Tait called the Le Sage theory in 1876 the only plausible explanation of gravity that had been found up to that point. He further said:

"The most singular thing about it is that, if it be true, it will probably lead us to regard all kinds of energy as ultimately Kinetic."

"The most remarkable thing about it [about Le Sage's theory] is that if it is correct, it will possibly lead us to ultimately view all forms of energy as kinetic."

- Peter Guthrie Tait

Preston

Samuel Tolver Preston showed that many of the postulates introduced by Le Sage for the particles, such as linear motion, sparse interaction, etc., can be summarized under the assumption that they behave - on a cosmic level - like a gas, the particles of which are a have extremely large mean free path. Preston also accepted Kelvin's suggestion of the internal modes of motion of the particles. He illustrated Kelvin's model by comparing it to the collision of a steel ring and an anvil . This would not be particularly affected, but the steel ring would be subject to very strong vibrations and therefore lose speed. He argued that the mean free path of the particles is at least the distance between the planets. At greater distances, the particles (in the Kelvin sense) could regain their original translational motion size through collisions with other particles. Therefore he was of the opinion that from a certain distance the gravitational effect between two bodies would no longer occur, regardless of their size. Paul Drude suggested in 1897 that this would be a possibility to give a physical basis to the theories of Carl Gottfried Neumann and Hugo von Seeliger , which suggested an absorption of gravity in empty space.

Maxwell

James Clerk Maxwell

A review of the Le-Sage-Kelvin theory was published by James Clerk Maxwell in the Encyclopaedia Britannica in 1875 . After describing the basic mechanism, he wrote:

“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 . ”

“Here seems to be a path leading towards an explanation of gravity, which - if it can be shown to be consistent with the facts in other respects as well - can prove to be the royal path into the very mystery of science. "

- James Clerk Maxwell

Nevertheless, he rejected the model because, according to the laws of thermodynamics, the kinetic energy of the body must match that of the particles, whereby the energy of the latter is much greater than that of the molecules of the body. As a result of this process, the bodies should burn up in no time. Kelvin's solution would maintain the mechanical equilibrium between the systems, but not the thermodynamic one. He concluded:

"We have devoted more space to this theory than it seems to deserve, because it is ingenious, and because it is the only theory of the cause of gravitation which has been so far developed as to be capable of being attacked and defended."

"We have devoted more space to this theory than it seems deserves because it is ingenious and because it is the only theory about the cause of gravity that is so far developed to be suitable for attack and defense."

- James Clerk Maxwell

Maxwell went on to explain that the theory thus requires an enormous amount of external energy and therefore violates energy conservation as a fundamental principle of nature. Preston responded to Maxwell's criticism with the argument that the kinetic energy of the individual particles can be made as small as desired by increasing their number and therefore the difference in energy is not as great as Maxwell assumed. However, this question was later dealt with in more detail by Poincaré, who showed that the thermodynamic problem remained unsolved.

Isenkrahe

Caspar Isenkrahe first published his model in 1879, with many other writings following by 1915. In contrast to his predecessors, he worked out a more detailed application of the kinetic gas theory in the Le Sage model. Like Le Sage, he argued that the particles are absolutely hard and therefore the collisions are elastic tangential, and inelastic perpendicular to the surface of the body and received the same factor of 2/3. However, he was of the opinion that there was a real loss of energy during the collisions and that therefore the law of conservation of energy was no longer applicable in this area, which was and is incompatible with the thermodynamic principles. Isenkrahe explained that the energy losses are negligible due to the low number of collisions. He criticized the Kelvin-Preston model because he saw no reason why the reflected particles should vibrate and rotate more, because the opposite is just as possible. From the fact that the proportionality of gravity to mass can only be maintained with enormous porosity of matter, he drew the conclusion that the effect of thermal expansion must make the body heavier. This happens because with a lower density, mutual shielding of the body molecules is less common.

Rysanek

In another model, Adalbert Rysanek developed a very careful analysis of the phenomena in 1887, taking Maxwell's law of particle speeds in a gas into account. He distinguished between a light ether and a gravitation ether, since according to his calculations the absence of a resistance of the medium in the orbit of Neptune requires a lower speed of the gravitational particles of 5 · 10 ¹⁹ cm / s. Similar arguments were made by Bock. Like Leray, Rysanek argued that the absorbed energy could explain the origin of the solar energy, and that the absorbed energy could also be passed on to the light ether. However, this information was too imprecise to invalidate Maxwell's objection.

you Bois-Reymond

In 1888 Paul du Bois-Reymond argued against the Le Sage theory that in order to achieve exact mass proportionality as in Newton's model (which presupposes an infinitely large penetrability), the pressure of the particles must also be infinitely large. Although he took into account the argument that the mass proportionality for very large masses was by no means experimentally confirmed, he saw no reason to give up the proven Newtonian action at a distance based on a mere hypothesis. He stated (like others before him) that immediate impact effects themselves are completely inexplicable and are basically also based on effects at a distance. The main aim of such a theory, to exclude all effects at a distance, is thus not realizable.

waves

In addition to the kinetic gas theory, the concepts of waves in the ether used in the 19th century were also used to construct similar models. Then an attempt was made to replace Le Sage's particles with electromagnetic waves . This was done in conjunction with the electron theory of the time in which the electrical nature of all matter was assumed.

Basement, Boisbaudran

In 1863 F. and E. Keller published a theory of gravity in which they developed a Le Sage mechanism in connection with longitudinal waves of the ether. They assumed that these waves spread in all directions and would lose some momentum after the impact on the bodies, so that the pressure between the bodies is a little less than from the outside. In 1869 Lecoq de Boisbaudran created practically the same model as Leray (heat, magnetism), but like Keller he replaced the particles with longitudinal waves.

Lorentz

Hendrik Antoon Lorentz

In 1900 Hendrik Antoon Lorentz tried to reconcile gravitation with his Lorentz ether theory . He noted that Le Sage's particle theory was not compatible with it. However, the discovery that electromagnetic waves generate a kind of radiation pressure and that they can penetrate matter relatively easily in the form of X-rays led Lorentz to the idea of ​​replacing the particles with extremely high-frequency EM rays. He was actually able to show that shadowing creates an attractive force between charged particles (which were understood as the basic building blocks of matter). However, this only happens on condition that the entire radiation energy is absorbed. That was the same fundamental problem as in the particle models. He therefore rejected the model and, as he continued, orbit instabilities would also be expected due to the finite propagation speed of the waves.

Returning to the topic, Lorentz discussed Martin Knudsen's findings in 1922 about the behavior of gases with very long free paths, which was followed by a summary of both Le Sage's particle theory and his own electromagnetic variant. However, he repeated his conclusion from 1900: Without absorption there is no gravitation in this theory.

JJ Thomson

In 1904 Joseph John Thomson considered an EM-based Le Sage model in which the radiation is far more penetrating than ordinary X-rays. He argued that the warming cited by Maxwell can be avoided if it is assumed that the absorbed radiation is not converted into heat, but is re-emitted as secondary radiation of much greater penetration. He noted that this process could explain where the energy of the radioactive substances comes from. However, he said an internal cause for the radioactivity was much more likely. In 1911 Thomson came back to this topic and explained that this secondary radiation is very similar to the effect that electrically charged particles cause when penetrating normal matter, the secondary process being X-rays. He wrote:

“It is a very interesting result of recent discoveries that the machinery which Le Sage introduced for the purpose of his theory has a very close analogy with things for which we have now direct experimental evidence […] Röntgen rays, however, when absorbed do not , as far as we know, give rise to more penetrating Rontgen rays as they should to explain attraction, but either to less penetrating rays or to rays of the same kind. "

“It is a very interesting result of recent discoveries that the machinery introduced by Le Sage in the service of his theory has a very close analogy with things for which we now have direct experimental certainty [...] X-rays, however, do not produce more penetrating X-rays as they are necessary to generate the attraction, but the same or less penetrating rays arise. "

- Joseph John Thomson

Tommasina, Brush

In contrast to Lorentz and Thomson, Thomas Tommasina used waves with very long wavelengths around 1903, he used small wavelengths to explain chemical effects. In 1911 Charles Francis Brush also proposed a model with long waves, but later changed his mind and preferred waves with extremely high frequencies.

Further assessments

GH Darwin

In 1905, George Howard Darwin calculated the gravitational force between two bodies at extremely small distances to see whether a Le Sage model deviated from the law of gravitation. He came to the same conclusion as Lorentz that the collisions must be completely inelastic and, contrary to the assumption of Le Sage, not only with perpendicular radiation, but also with radiation tangential to the surface of the matter. This goes hand in hand with an exacerbation of the thermal problem. In addition, it must be assumed that all elementary components of matter are of the same size. He went on to say that the emission of light and the associated radiation pressure represent an exact equivalent of the Le Sage model. A body with a different surface temperature will move towards the colder part. Finally, he later said that he had seriously considered the theory, but that he himself would not study it further. He didn't think any scientist would accept it as the correct way to explain gravity.

Poincaré

Henri Poincaré

Based in part on Darwin's calculations, Henri Poincaré published an extensive review in 1908. He concluded that the attraction in such a model is proportional to where S is the surface area of ​​all molecules on earth, v is the velocity of the particles and ρ is the density of the medium. Following Laplace, he said that in order to maintain mass proportionality , the upper limit for S is a maximum of ten millionth part of the earth's surface. He explained that the resistance is proportional to Sρv and thus the ratio of resistance and attraction is inversely proportional to Sv . In order to keep the resistance in relation to the attraction as low as possible, Poincaré calculated the enormous value of v = 24 · 10 ¹⁷ · c as the lower limit for the speed of the particles , where c is the speed of light. Since lower limits for Sv and v are now known and an upper limit for S is also fixed, the density and thus the heat can be calculated from this, which is proportional to Sρv ³ . This is sufficient  to heat the earth by 10 ²⁶ ° C every second . Poincaré noted dryly that “the earth would obviously not endure such a state for long” . Poincaré also analyzed some wave models (Tommasina and Lorentz) and noted that these have the same problems as the particle models (enormous wave speed, warming). After describing the model of the re-emission of secondary waves proposed by Thomson, Poincaré said: "One is forced to such complicated hypotheses if one wants to make Le Sage's theory practicable." ${\displaystyle S{\sqrt {\rho }}v}$

He added that if fully absorbed under the Lorentz model, the Earth's temperature  would rise by 10 ¹³ ° C per second. Poincaré also examined Le Sage's model in connection with the principle of relativity , where the speed of light represents an impassable limit speed. In the case of particle theory, he therefore noted that it was difficult to establish a law of collision compatible with the new principle of relativity.

David Hilbert

In 1913, David Hilbert examined both Le Sage's and especially Lorentz's theory in his physics lectures. He stated that his theory does not work because z. B. the law of distance is no longer valid if the distance between the atoms is large enough compared to their wavelength. However, Erwin Madelung , a colleague of Hilbert at the University of Göttingen, used the Lorentz schema to explain the molecular forces. Hilbert rated Madelung's mathematical model as very interesting, although some statements could not be verified experimentally.

Richard Feynman

In 1964, Richard Feynman also investigated such a model, primarily to find out whether it was possible to find a mechanism for gravity without the use of complex mathematics. However, after calculating the resistance that the bodies had to experience in this sea of ​​particles, he gave up his efforts for the same reasons (unacceptable speed) as they were described before. He concluded:

'Well', you say, 'it was a good one, and I got rid of the mathematics for awhile. Maybe I could invent a better one '. Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravitation today, other than the mathematical form.

“'Good,' you will say, 'it was a good model and I got rid of the math for a while. Maybe I could find a better model. Maybe you can because nobody knows everything. But from Newton's time until now, none has given any other theoretical description of the mathematical machinery behind this law that has not either repeated the same thing over and over, made mathematics harder, or predicted some false phenomena. So until today there is no other model of the theory of gravity than in the mathematical form. "

Predictions and Criticism

Matter and particles

Porosity of matter

A fundamental prediction of the theory is the extreme porosity of matter. As already described, matter must largely consist of empty space, so that the particles can penetrate almost unhindered and so all components of the body participate equally in the gravitational interaction. This prediction has been confirmed (in some ways) over time. In fact, matter consists largely of empty space (apart from the fields) and certain particles such as neutrinos can penetrate almost unhindered. However, the idea of ​​the elementary components of matter as classical entities, whose interactions take place through direct contact and are dependent on their shape and size (at least as that was presented by Fatio to Poincaré), does not correspond to the representation of elementary particles in modern quantum field theories .

Background radiation

Every Fatio / Le Sage model postulates the existence of a space-filling, isotropic fluid or radiation of enormous intensity and penetration. This is somewhat similar to the background radiation , especially in the form of the microwave background (CMBR). The CMBR is actually a space-filling, isotropic radiation, but its intensity is far too low, as is its penetration ability. On the other hand, neutrinos have the necessary penetration ability, but this radiation is not isotropic (since individual stars are the main sources of neutrinos) and its intensity is even lower than that of the CMBR. In addition, both types of radiation do not spread faster than light , which is a further prerequisite, at least according to the above calculations. From a modern point of view, and not in the context of Fatio's model, the possibility of neutrinos as carrier particles in a quantum gravity was considered and refuted by Feynman.

shielding

B10: Shielding from gravity

This effect is closely related to the assumed porosity and permeability of the matter, which is necessary to maintain the proportionality to the mass. To explain this more precisely: Those atoms which are no longer hit by the particles would no longer have any part in the shielding and thus the heavy mass of the body (B10, above). However, this effect can be increased by increasing the porosity of the material, i.e. H. by downsizing their components, can be minimized at will. This reduces the probability that these components are exactly in line and shield each other (B10, bottom). However, this effect cannot be completely switched off, because in order to achieve complete penetrability, the components of the matter should no longer interact with the particles at all, which would also result in the disappearance of any gravitation. This means that above a certain limit, a difference between inert and heavy mass, i.e. a deviation from the equivalence principle , should be observed.

Any shielding of gravitation is therefore a violation of the equivalence principle and consequently incompatible with Newton's law of gravitation and Einstein's general theory of relativity (GTR) . So far, however, no gravitation shielding has been observed. For more information on the relationship between Le Sage and the shielding of gravity, see Martins.

Regarding Isenkrahe's proposal for a connection between density , temperature and weight : Since his argumentation is based on the change in density, and the temperature can be lowered and raised at constant density, Isenkrahe's theory does not imply a fundamental relationship between temperature and weight. (There is indeed such a connection, but not in the sense of Isenkrahe. See section Interaction with energy ). The prediction of a relationship between density and weight could not be confirmed experimentally either.

speed

resistance

One of the main problems of the theory is that a body moving relative to the reference system in which the speed of the particles is the same in all directions , would have to feel a resistance in the direction of movement. This is because the speed of the particles hitting the body is greater in the direction of movement. Analogous to this, the Doppler effect must be observed in wave models. This resistance leads to a steady reduction in the orbit around the sun and is (according to Fatio, Le Sage and Poincaré) proportional to uv , where u is the speed of the body and v that of the particles. On the other hand, the gravitational force is proportional to v² , which means that the ratio of drag to gravitational force is proportional to u / v . At a certain speed u the effective resistance can be made arbitrarily small by increasing v . As calculated by Poincaré, v must be at least 24 · 10 ¹⁷ · c, i.e. much greater than the speed of light . This makes the theory incompatible with the mechanics of the special theory of relativity , in which no particles (or waves) can propagate faster than light, because due to the relativity of simultaneity , depending on the reference system, causality violations would occur. Even if superluminal speeds were possible, that would again lead to enormous heat production - see below.

Aberration

An effect that also depends on the particle speed is the aberration of gravitation . Due to the finite speed of gravity, there are time delays in the interaction of the celestial bodies, which, in contrast to resistance, lead to a constant increase in orbits. Here, too, a greater speed than that of light must be assumed. While Laplace gave a lower limit of 10 ⁷ · c, more recent observations gave a lower limit of 10 ¹⁰ · c. It is not known whether the Le Sage model also has effects like those in GTR , which compensate for this form of aberration.

Range

The shadow effect only applies exactly to 1 / r² if there is no interaction between the particles - i.e. That is, the law of distance depends on the mean free path of the particles. However, if they collide with each other, the shadow "blurs" at a greater distance. This effect depends on the model represented and the assumed internal energy modes of the particles or waves. In order to avoid this problem in general, Kelvin and others postulated that the particles could be defined as small as desired at any time, which means that they would only meet very rarely despite the large number - this would minimize this effect. The presence of large-scale structures in the universe such as galaxy clusters speaks in any case for a range of gravity over at least several million light years.

energy

absorption

As explained in the historical section, another problem with this model is the absorption of energy and thus the production of heat . Aronson gave a simple example of this:

• If the kinetic energy of the particles is smaller than that of the bodies, the particles will move with greater speed after the collisions and the bodies will repel each other .
• If the body and the particles are in thermal equilibrium, there is no force.
• If the kinetic energy of the body is smaller than that of the particles, an attractive force arises . But as shown by Maxwell and Poincaré, these inelastic collisions would have to bring the bodies to white heat in fractions of a second, especially if a particle speed greater than c is assumed.

Isenkrahe's deliberate violation of the law of conservation of energy as a possible solution was just as unacceptable as Kelvin's application of Clausius' theorem, which, as Kelvin himself noted, leads to a perpetual motion mechanism. The suggestion of a secondary re-emission mechanism for wave models (analogous to Kelvin's change in energy modes) aroused the interest of J. J. Thomson, but was not taken very seriously by Maxwell and Poincaré. This is because large amounts of energy would spontaneously be converted from a cold to a warmer form, which is a gross violation of the second law of thermodynamics .

The energy problem was also discussed in connection with the idea of ​​an increase in mass and the theory of expansion . Iwan Ossipowitsch Jarkowski 1888 and Ott Christoph Hilgenberg 1933 combined their expansion models with the absorption of an ether. However, this theory is largely no longer viewed as a valid alternative to plate tectonics . In addition, due to the equivalence of mass and energy and the application of the energy absorption values ​​calculated by Poincaré, the earth's radius would increase considerably in a very short time.

interaction

As predicted in the GTR and based on experimental confirmations, gravity interacts with all forms of energy and not just normal matter. The electrostatic binding energy of the nucleons , the energy of the weak interaction of the nucleons and the kinetic energy of the electrons all contribute to the heavy mass of an atom, as has been demonstrated in high-precision measurements of the Eötvös type . This means that faster movement of the gas particles increases the gravitational effect of the gas. Le Sage's theory does not predict such a phenomenon, nor do the other known variations of the theory.

Non-gravitational applications and analogies

Mock gravity

In 1941, Lyman Spitzer calculated that the absorption of radiation between two dust particles leads to an apparent attraction which is proportional to 1 / r² (although he was obviously not familiar with the analogous theories of Le Sage and, in particular, Lorentz's investigations on radiation pressure). George Gamow , who called this effect mock gravity , suggested in 1949 that after the Big Bang the temperature of the electrons fell faster than the temperature of the background radiation. Absorption of the radiation leads to the Le Sage mechanism between the electrons calculated by Spitzer, which is said to have played an important role in the formation of galaxies after the Big Bang. However, this proposal was refuted in 1971 by Field, who showed that this effect was far too small, since the electrons and the radiation were almost in thermal equilibrium. In 1986, Hogan and White suggested that a form of mock gravity influenced galaxy formation through the absorption of pre-galactic starlight. But in 1989 Wang and Field showed that any form of mock gravity is incapable of producing a sufficiently large effect to affect the galaxy formation.

plasma

The Le Sage mechanism has been identified as a significant factor in the behavior of complex plasmas . Ignatov showed that inelastic collisions create an attractive force between two grains of dust suspended in a collision-free, non-thermal plasma . This attraction is inversely proportional to the square of the distance between the dust grains and can compensate for the Coulomb repulsion between them.

Vacuum energy

In quantum field theory, the existence of virtual particles is assumed, which lead to the so-called Casimir effect . Hendrik Casimir found out that when calculating the vacuum energy between two plates, only particles of certain wavelengths appear. Because of this, the energy density between the plates is lower than outside, which leads to an apparent attractive force between the plates. However, this effect has a very different theoretical basis from Fatio's theory.

Recent developments

Examination of Le Sage's theory in the 19th century identified several closely related problems. These include the enormous warming, unstable orbits due to resistance and aberration as well as the unobserved shielding of gravity. The recognition of these problems together with a general departure from kinetic gravitational models resulted in an increasing loss of interest. Eventually Le Sages and other theories were supplanted by Einstein's general theory of relativity .

Although the model is no longer seen as a valid alternative, outside of the mainstream attempts at revitalization are being made, such as the models by Radzievskii and Kagalnikova (1960), Shneiderov (1961), Buonomano and Engels (1976), Adamut (1982), Jaakkola (1996), Van Flandern (1999) and Edwards (2007). Various Le Sage models and related topics are discussed in Edwards et al. discussed.

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Individual references to historical primary literature

1. ↑ Fatio (1690)
2. ↑ Fatio (1701)
3. ↑ Fatio (1743)
4. ↑ Cramer (1731)
5. ↑ Redeker (1736)
6. ↑ Le Sage (1756)
7. ↑ Le Sage (1761)
8. ↑ Le Sage (1782)
9. ↑ Le Sage (1818)
10. ↑ Lichtenberg (2003)
11. ↑ Kant (1786)
12. ↑ Schelling (1797)
13. ↑ Laplace (1805)
14. ↑ Leray (1869)
15. ↑ Thomson (1873)
16. ↑ ^{a b} Tait (1876)
17. ^ Preston (1877)
18. ↑ ^{a b c} Maxwell (1875)
19. ↑ Isenkrahe (1879)
20. ↑ Bock (1891)
21. ↑ Rysanek (1887)
22. ↑ Bois-Reymond (1888)
23. ↑ Keller (1863)
24. ↑ Boisbaudran (1869)
25. ↑ Lorentz (1900)
26. ↑ Lorentz (1922)
27. ↑ Thomson (1911)
28. ↑ ^{a b} Thomson (1911)
29. ↑ Tommasina (1928)
30. ↑ Brush (1911)
31. ↑ Darwin (1905)
32. ↑ Darwin (1916)
33. ↑ Poincaré (1908)

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Individual references to primary literature

1. ↑ Feynman (1964)
2. ^ Feynman (1995)
3. ↑ Carlip (1999)
4. ↑ Carlip (1997)
5. ↑ Spitzer (1941)
6. ↑ Gamow (1949)
7. ↑ Field (1971)
8. ↑ Hogan (1989)
9. ↑ Field (1989)
10. ↑ See Carsten Killer: Dusty Plasmas - An Introduction. August 2016, accessed February 21, 2018 . 
11. ↑ Ignatov (1996)
12. ↑ Radzievskii (1960)
13. ↑ Shneiderov (1961)
14. ↑ Buonomano (1976)
15. ↑ Adamut (1982)
16. ↑ Jaakkola (1996)
17. ↑ Van Flandern (1999)
18. ^ Edwards (2007)
19. ^ Edwards (2002)

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Individual references to secondary literature

1. ↑ ^{a b} Prevost (1805)
2. ↑ ^{a b c d e} toe (1980)
3. ↑ Wolf (1862)
4. ↑ Evans (2002)
5. ↑ ^{a b} Playfair (1807)
6. ↑ Drude (1897)
7. ^ Corry (1999)
8. ↑ Bertolami (2006)
9. ↑ Martins (1999)
10. ↑ Martins (2002)
11. ↑ Aronson (1964)
12. ↑ Scalera (2003)

Web links

• LeSage's Shadows
• Omni-Directional Flux
• Kinetic Pressure and Tetrode's Star
• Nicolas Fatio and the Cause of Gravity
• Fatio, Le Sage and the camisards
• Historical Assessments of the Fatio-Lesage Theory

This article was added to the list of excellent articles on October 15, 2007 in this version .