User:MRE/LeSage gravity

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When Sir Isaac Newton published his Theory of Universal Gravitation, he noted that he could not propose a mechanism by which it worked. In 1784 Georges-Louis Le Sage (1724-1803) of Geneva proposed a simple kinetic theory of gravitation.[1] Le Sage’s theory reached its zenith of popularity in the late nineteenth century, when it was shown by Lord Kelvin to be compatible with the then newly discovered kinetic theory of gases.[2] It had in fact influenced John Herapath's thinking in developing the kinetic theory. The strength of Le Sage’s theory was that it could reproduce Newton’s law exactly. By the turn of the century, however, the theory had been discredited, most notably by James Clerk Maxwell.[3] In the twentieth century, it was still studied by a few researchers, such as the Russian astrophysicist V. V. Radzievskii.[4] Today it is still studied by a small minority of researchers working outside the current mainstream theory of gravity.

Contents

[edit] Le Sage's Basic Theory

Le Sage's theory is not based on the concept of a universal attraction of matter. Instead it posits that gravity is the result of a medium of tiny particles, similar to a gas), which fills the entire universe. According to the theory, the vast majority of these particles pass through normal objects (like the Earth or Sun) virtually unhindered, much like the neutrinos of modern physics. A very small fraction, however, will either be absorbed, scattered or both (depending on the specific model) and these interactions cause an inward pressure to be exerted on the object. If an isolated object is struck equally from all sides it will experience only this inward directed pressure and thus no net directional force(s). If a second object is present, however, both objects experience a force acting to move each towards the other. This occurs because the gas pressure that would normally be present from the direction of the second object is partially blocked when passing through that object. For this reason the theory is often referred to as push gravity or shadow gravity, although within the physics community it is more widely referred to as particle gravity or Lesage garvity.

The main attraction of LeSage gravity is that can reproduce Newton's law exactly. Let A and B be two masses separated by a distance R. Consider the force which B by virtue of its shading effect exerts on A. The particles impinging on A may be viewed as originating from a spherical surface with radius R centred about A. The number of particles ordinarily striking A, if B were absent, is proportional to the cross-sectional area of A and hence, by the LeSage assumption of a highly porous structure for A, to its mass. With B present, however, a fraction of the particles is intercepted which varies directly with the cross-sectional area of B, and hence B’s mass, and indirectly with the surface area of the sphere, which is proportional to R2. The attractive force is thus proportional to the product of the masses over the square of the separation. A exerts an equal and opposite force on B.

[edit] Early Development of the Theory

Long before Le Sage conceptualized his theory, a very similar theory had been suggested in 1690 by Nicolas Fatio de Duillier, a friend of Newton's. While suggesting many mechanisms of gravity, Newton himself preferred not to adopt any particular one. Le Sage had formulated his own theory independently. Nonetheless, after learning of Fatio's work, Le Sage gave credit to Fatio in all his writings and scrupulously collected and preserved Fatio's papers. For historical accounts of Fatio's and Le Sage's theories, see references [5][6][7].

Le Sage proposed that gravity is caused by the continuous bombardment of ordinary matter by what he termed “ultramundane corpuscles”, tiny particles originating from the depths of space. Like the neutrinos of modern science, he supposed that most of these particles would pass through even massive bodies such as the Earth unhindered. Le Sage proposed separately that the corpuscles were miniscule relative to their separation; that their motions were rectilinear; that they rarely if ever interacted; that their motions could be regarded as equally dense streams moving in all directions; and that their velocities were extremely high. The latter postulate allowed the frictional resistance of the corpuscular sea to bodies in motion through it to be kept very small relative to the attractive force. In order that the gravitational force be proportional to the mass of a body, rather than its cross-sectional area, Le Sage postulated moreover that the basic units of ordinary matter were highly porous to the corpuscles. In some of his writings he referred to them as cage-like structures, in which the diameters of the “bars” were small relative to the dimensions of the “cages”. An isolated body in this medium would be shelled uniformly from all directions and would thus experience no net force upon it. In a system of two or more bodies, however, the mutual shading of corpuscles would result in an apparent force of attraction between the two bodies.

A critical aspect of the model, which was recognized by Le Sage and would later lead to grave difficulties, related to the nature of the collisions between the corpuscles and the units of ordinary matter. The collisions could not be entirely elastic, for in this case the shading effect would be exactly nullified by corpuscles rebounding from the shading mass to strike the shaded one. To counter this, Le Sage proposed that the particles were either carried away at reduced velocities or else stuck to the bars of the cage-like units of matter.

Due to their ad hoc and somewhat unusual formulation, Le Sage’s ideas were not well-received during his day. Le Sage, however, was completely undeterred by his critics and spent the greater part of his life developing epistemological arguments to defend his theory.

[edit] The Revival by Kelvin

Le Sage's theory enjoyed a resurgence of interest in the 1870’s, when Kelvin demonstrated a close analogy with the kinetic theory of gases. All of the various postulates introduced by Le Sage concerning the gravitational corpuscles (rectilinear motion, rare interactions, etc.) could be collected under the single notion that they behaved as a gas. The range of the gravitational force would be proportional to the mean free path of the Le Sage corpuscles, which in turn would be governed by their diameters and numerical densities. A finite range of gravitation would allow for a gravitationally stable universe. Kelvin also noted that the potentially observable deviations from Newton’s law due to ‘self-shading’ of corpuscles in large planets, for example, could be minimized by extending their porosity to as great proportions as necessary, by imagining that the cage bars of Le Sage’s atoms were sufficiently small. Kelvin also adopted Le Sage’s explanation of high corpuscular velocities for the imperceptible resistance experienced by bodies in motion through the corpuscular medium.

Kelvin’s major contribution to the debate lay in the thorny problem of the nature of collisions between Le Sage corpuscles and ordinary bodies. Le Sage had realized that the interactions between the gravitational particles and ordinary matter must be inelastic, that is, the particles must lose energy in the process. Without this, the net force on the object would be zero. Kelvin, however, suggested that elastic collisions might be feasible if, following Clausius’ notion of vibrational and rotational energies in gas molecules, the translational energies of Le Sage corpuscles after collision were converted to these other modes. In this way, the total energy of the system would be conserved. Moreover, the translational energies of the corpuscles could be restored in later collisions between corpuscles, as Clausius had shown that the translational component of kinetic energy in a gas remains in a constant ratio to the total kinetic energy. There would thus be no need for a ‘gravitational death’ of the Universe owing to the progressive loss of translational kinetic energy of corpuscles.

A devastating critique of the Kelvin-Le Sage theory was published by Maxwell in the Ninth Edition of the Encyclopaedia Britannica under the title ‘Atom’ in 1875. Maxwell condemned the theory on thermodynamic grounds, stating 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 ultramundane corpuscle. Maxwell assumed that the latter quantity was much greater than the former and thus concluded that ordinary matter should be incinerated within seconds under the Le Sage bombardment. Preston soon showed, however, that the number density of the Le Sage corpuscles could be made so high and their masses so low that the Le Sage pressure could be maintained despite the low kinetic energies of the individual corpuscles.[8] Nonetheless, many historians came to the view that Maxwell had the last word on the subject.

George Darwin later drew an analogy between Le Sage’s mechanism and the newly appreciated phenomenon, discovered by Poynting, whereby two radiating spheres would repulse one another.[9] Darwin 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, or in the case that Kelvin’s compensatory mechanism were operating and all translational kinetic energy was given up by corpuscles after collision with bodies, would Newton’s law stand up.

It can thus be seen that several closely interconnected problems frustrated the development of Le Sage’s theory, problems which have also plagued Le Sage-type models ever since. These relate to the thermodynamic question and the likelihood of a frictional drag and gravitational aberration effect. The combined influence of the many negative assessments, perhaps in conjunction with a general shift away from mechanical ether theories, appear to have led to a progressive loss of interest in the Le Sage’s theory after the end of the nineteenth century.

[edit] Electromagnetic Variants of the Theory

In the twentieth century Le Sage’s theory was more or less entirely eclipsed by Einstein’s theory of General Relativity. Just as in the previous centuries, isolated efforts to improve the theory have nonetheless been made. If there is a common thread amongst the newer theories, it is that the main obstacles that faced Kelvin in his day are still in need of resolution today.

Soon after the revival by Kelvin, many authors, including Hendrik Lorentz and Charles Brush, attempted to substitute electromagnetic waves for Le Sage’s corpuscles.[10][11] Assuming that space is filled with radiation of a very high frequency, 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. This situation thus merely reinforced the previous difficulties noted above in Le Sage’s own theory and served to discourage further research along this line.

One possible difficulty of electromagnetic Le Sage models is connected to the problem of gravitational aberration. As pointed out initially by Pierre-Simon Laplace and later many others, it would appear that the gravitational force would need to be propagated at a velocity >> c to avoid introducing forces into astrophysics that are known not to exist. At the same time, other authors, such as Henri Poincaré, supposed that within the Galaxy and Solar System such forces may be compensated for by others and that aberration effects in these settings may thus not arise.[12]

[edit] Predictions of Le Sage's Theory

Perhaps the main prediction of Le Sage gravity is that deviations in Newton's law will arise when the gravitational force between two bodies is screened by a third body. In this context, the reported erratic behaviour of pendulums during eclipses, often referred to as the Allais effect, has sometimes been ascribed to Le Sage-type gravitational shielding. In general, observational evidence for gravitational absorption during solar and lunar eclipses is inconclusive.[13]

In the same connection, Le Sage’s theory in the twentieth century became intertwined with an alternative theory of gravitation, also involving shading effects, proposed by Quirino Majorana .[14] Majorana took as a starting assumption that a material screen set between two other bodies would diminish the force of attraction between the latter due to gravitational absorption by the screen. This state of affairs might be most readily envisioned if the gravitational force was caused by “a kind of energical flux, continually emanating from ponderable matter”. The situation might then be analogous to the absorption of light in passage through a semi-transparent medium. His view thus differed sharply from Le Sage’s, in that matter itself, rather than the remote regions of space, is the source of the gravitational fluxes. In a series of elaborate laborotory experiments, Majorana found evidence for a small but definite amount of gravitational absorption.

The phenomenon uncovered by Majorana initially attracted considerable interest, especially from A. A. Michelson. Upon publication of an article by the astronomer H. N. Russell,[15] however, Michelson apparently lost interest and Majorana’s work was largely neglected by physicists. Russell first demonstrated that, in order that large deviations from Kepler’s laws not occur under Majorana’s theory, the inertial masses of bodies must remain at all times proportional to the gravitational masses. Russell then went on, however, to show that even granted this proportionality, a major problem arose in the case of the tides, the solar tides in particular being some 370 times greater on the side of the Earth facing away from the Sun compared to the side facing the Sun. A possible solution to this criticism was later given by Vladimir Radzievskii, who showed that the same degree of shielding of the force between two bodies results whether the screening mass is placed between the two bodies or exterior to both of the bodies. Since the time of Majorana’s experiments, a number of laboratory investigations have been conducted in an effort to duplicate Majorana’s findings.[16] In general, these studies have failed to detect an effect of the same magnitude as Majorana’s.

A related prediction of LeSage gravity is a deviation from the inverse-square law for very large masses. As a body approaches a certain critical size, all of the Le Sage particles incident upon it are absorbed and/or scattered by the body. Beyond this size no greater screening can thus occur. Although the effect would be small, certain astronomical events, like planetary occultations, could result in measurable differences in orbits. While Kurt Bottlinger found some evidence for such an effect in the Moon’s orbit around the Earth, the variations in the Moon’s motion were later ascribed to other causes.

In Le Sage's corpuscular model, as Kelvin had observed, gravity has only a finite range. This range is effectively determined by the mean free path of the gravitational particles. The observed large-scale structure of the cosmos requires that the mean free path be large enough to allow for the gravitational aggregation of structures of immense size.

Another crucial aspect of this model requires that moving bodies experience drag or friction, just as one experiences when moving their hand through water. Without any mitgating factors, this friction must cause any moving object to slowly come to rest relative to the underlying rest frame of the field. As emphasized by Le Sage and Kelvin, this friction is eliminated if the Le Sage particles move at or near infinite speeds (much greater than the speed of light). However, to do so would be in direct contradiction to the notion that the speed of light is a universal limiting velocity, which forms the basis for the Special Theory of Relativity.

Another possible Le Sage effect is orbital aberration. Unless the Le Sage corpuscles are moving at speeds much greater than the speed of light, as Le Sage and Kelvin supposed, there is a time delay in the interactions between bodies (the transit time). In the case of orbital motion this results in each body reacting to a retarded position of the other, which creates a leading force component. This component will act to accelerate both objects away from each other. This is a classical dilemma known as retarded potential.

[edit] Connections to Geology

It has long been noted that the thermodynamic problem in Le Sage’s model could potentially be avoided if the energy of the absorbed particles or waves were converted to new mass. While such a conversion is difficult to visualize in conventional terms, the possibility of mass creation has been linked in geology to the theory of the expanding Earth. The latter theory posits that the bimodal distribution of continental crust and ocean basins on the Earth is due not to plate tectonics on a globe of constant size, but rather to the formation of new oceanic crust on an expanding globe. Among the early theorists to link LeSage gravity to Earth expansion were I.O. Yarkovsky [17] and Ott Hilgenberg (2003). Shneiderov, on the other hand, attempted to link earth expansion to internal heating caused by the collisions of LeSage particles.[18]

The expanding Earth theory had a resurgence in the 1960s and 1970s with the discovery of the formation of new ocean crust at mid-ocean ridges. Since the evidence for subduction at that time was sketchy, Bruce Heezen and other workers were led back to the postulate of Earth expansion. Subsequent evidence for subduction pushed the expanding Earth theory to the side once more. A small minority of geologists continue however to explore the hypothesis, occasionally invoking Le Sage-type notions (2003).

[edit] Current Status of the Theory

Le Sage gravity has never had mainstream support and that lack of support continues to this day. Today, most work on gravitational theory is done in the contexts of general relativity and quantum gravity. Although this model has resurfaced several times in recent decades, it still is not taken seriously by the vast majority of physicists.

The current attempts to revitalize Le Sage's theory include both particle and electromagnetic wave variants. Similarly to Le Sage and Kelvin, Tom Van Flandern has argued that the lack of apparent aberration in the Sun's gravitational force on the Earth implies corpuscular speeds much greater than c. [19][20]. In an effort to link Le Sage gravity to general relativity, Van Flandern employs a separate medium as carrier of light. The finite gravitational range of Le Sage particle models was invoked to explain the rotation curves of galaxies without resorting to dark matter.

In the case of slower moving Le Sage particles, Mingst and Stowe have suggested that the long predicted drag effect in Le Sage's theory is actually seen in the measurable slowing of the Pioneer and Ulysses spacecraft, the so-called Pioneer Anomaly. In the case of orbital motion, they suggest that push back of the drag on that fraction of the field which is causing the drag could give rise to orbital stability. In a similar vein, the interactions of a Le Sage medium with a rotating material body were suggested as an alternative explanation for the frame-dragging effect of general relativity.[21][22]

Other workers have linked Lesage gravity to cosmology. Similarly to some expanding Earth theorists, Halton Arp has suggested that all objects increase in mass at a rate close to the Hubble rate. In Arp's non-standard cosmology, mass increase in quasars and galaxies affords an alternative explanation for the cosmological redshift without universal expansion.[23] On the other hand, in Toivo Jaakkola's Equilibrium Cosmology, Lesage gravity underlies a universe in which all energy conversion processes are in a state of continual equilibrium.[24] A similar model is suggested by Matthew Edwards, in which gravity is caused by a relativistic interaction of an electromagnetic background, seen as a preferred reference frame, with bodies that are in motion within this frame.[25]

Other recent models adopting Le Sage's mechanism include those of Buonomano and Engels [26] and Iosif Adamut.[27]

[edit] References

  1. ^ Le Sage, G.-L., 1784 (for the year 1782), “Lucrèce Newtonien”, Memoires de l’Academie Royale des Sciences et Belles Lettres de Berlin, 1-28.
  2. ^ Thomson, W. (Lord Kelvin), 1873. “On the ultramundane corpuscles of LeSage”, Phil. Mag., 4th ser., 45, 321-332.
  3. ^ Maxwell, J.C., 1875. “Atom”, Encyclopedia Britannica, Ninth Ed., pp. 38-47.
  4. ^ Radzievskii, V.V. and Kagalnikova, I.I., 1960. “The nature of gravitation”, Vsesoyuz. Astronom.-Geodezich. Obsch. Byull., 26 (33), 3-14. A rough English translation appeared in a U.S. government technical report: FTD TT64 323; TT 64 11801 (1964), Foreign Tech. Div., Air Force Systems Command, Wright-Patterson AFB, Ohio (reprinted in Pushing Gravity).
  5. ^ Aronson, S., 1964. “The gravitational theory of Georges-Louis LeSage”, The Natural Philosopher, 3, 51.
  6. ^ Evans, J.C. (2002). "Gravity in the century of light: sources, construction and reception of Le Sage's theory of gravitation", Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 9-40
  7. ^ van Lunteren, F. (2002). "Fatio on the cause of universal gravitation", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 41-59,
  8. ^ Preston, S.T., 1877. “On some dynamical conditions applicable to LeSage’s theory of gravitation”, Phil. Mag., fifth ser., vol. 4., 206-213 (pt. 1) and 364-375 (pt. 2).
  9. ^ Darwin, G.H., 1905. “The analogy between Lesage’s theory of gravitation and the repulsion of light”, Proc. Roy. Soc. 76, 387-410.
  10. ^ Lorentz, H.A., 1900. Proc. Acad. Amsterdam, ii, 559. A brief treatment in English appears in Lectures on theoretical physics, Vol. 1(1927), MacMillan and Co., Ltd., 151-155 (an edited volume of translations of a lecture series by Lorentz).
  11. ^ Brush, C.F., 1911. “A kinetic theory of gravitation”, Nature, 86, 130-132.
  12. ^ Poincaré, H., 1906. “Sur le dynamique de l’électron”, Rend. Circ. mat Palermo 21, 494-550.
  13. ^ Gillies, G.T., 1997. “The Newtonian gravitational constant: recent measurements and related studies”, Rep. Prog. Phys. 60, 151-225.
  14. ^ Majorana, Q., (1920). “On gravitation. Theoretical and experimental researches”, Phil. Mag. [ser. 6] 39, 488-504.
  15. ^ Russell, H.N., 1921. “On Majorana’s theory of gravitation”, Astrophys. J. 54, 334-346.
  16. ^ Martins, de Andrade, R., 1999. “The search for gravitational absorption in the early 20th century”, in: The Expanding Worlds of General Relativity (Einstein Studies, vol. 7) (eds., Goemmer, H., Renn, J., and Ritter, J.), Birkhäuser, Boston, pp. 3-44.
  17. ^ Beekman, G., I. O. Yarkovsky and the Discovery of 'his' Effect, J. Hist. Astron., 37, 71-86, 2006
  18. ^ Shneiderov, A.J., 1961. “On the internal temperature of the earth”, Bollettino di Geofisica Teorica ed Applicata 3, 137-159.
  19. ^ Van Flandern, T., 1999. Dark Matter, Missing Planets and New Comets, 2nd ed., North Atlantic Books, Berkeley, Chapters 2-4.
  20. ^ Van Flandern, T. (2002)"Gravity", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 93-122
  21. ^ Mingst B. and Stowe, P. (2002) "Deriving Newton's gravitational law from a Le Sage Mechanism", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 183-194
  22. ^ Stowe, P. (2002): "Dynamic effects in Le Sage models", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 195-200
  23. ^ Arp, H.C., 1998. Seeing Red:Redshifts Cosmology and Academic Science, Montreal: C. Roy Keys, Inc.
  24. ^ Jaakkola, T., 1996. “Action-at-a-distance and local action in gravitation: discussion and possible solution of the dilemma”, Apeiron 3, 61-75.
  25. ^ Edwards, M.R.(2002). "Induction of gravitation in moving bodies", in Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation, M. R. Edwards (ed.), Montreal: C. Roy Keys Inc., pp. 137-154
  26. ^ Buonomano, V. and Engel, E., 1976. “Some speculations on a causal unification of relativity, gravitation, and quantum mechanics”, Int. J. Theor. Phys. 15, 231-246.
  27. ^ Adamut, I.A., 1982. “The screen effect of the earth in the TETG. Theory of a screening experiment of a sample body at the equator using the earth as a screen”, Nuovo Cimento C 5, 189-208.


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