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Cristian
26th September 2016, 17:00
wiki: (https://en.wikipedia.org/wiki/Le_Sage%27s_theory_of_gravitation)


Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. 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. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together. This mechanical explanation for gravity never gained widespread acceptance, although it continued to be studied occasionally by physicists until the beginning of the 20th century, by which time it was generally considered to be conclusively discredited.



"It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities." - Richard P. Feynman, Character of Physical Law, Penguin, 1992, pp 57-8.



The theory posits that the force of gravity is the result of tiny particles (corpuscles) 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.

https://upload.wikimedia.org/wikipedia/commons/7/76/Pushing2.png
P2: Two bodies "attract" each other

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 Pierre Prévost, Charles Bonnet, Jean-André Deluc, Charles Mahon, 3rd Earl Stanhope and Simon Lhuilier. 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) .

Euler, Bernoulli, and Boscovich

Leonhard Euler once remarked that Le Sage's model was "infinitely better" than that of all other authors, and that all objections are balanced out in this model, but later he said the analogy to light had no weight for him, because he believed in the wave nature of light. After further consideration, Euler came to disapprove of the model, and he wrote to Le Sage:[12]
“ You must excuse me Sir, if I have a great repugnance for your ultramundane corpuscles, and I shall always prefer to confess my ignorance of the cause of gravity than to have recourse to such strange hypotheses. ”

Daniel Bernoulli was pleased by the similarity of Le Sage's model and his own thoughts on the nature of gases. However, Bernoulli himself was the opinion that his own kinetic theory of gases was only a speculation, and likewise he regarded Le Sage's theory as highly speculative.[13]

Roger Joseph Boscovich pointed out, that Le Sage's theory is the first one, which actually can explain gravity by mechanical means. However, he rejected the model because of the enormous and unused quantity of ultramundane matter. 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. 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?[14] ”

A very similar argument was later given by Maxwell (see the sections below). Additionally, Boscovich denied the existence of all contact and immediate impulse at all, but proposed repulsive and attractive actions at a distance.

Lichtenberg, Kant, and Schelling

Georg Christoph Lichtenberg's[15] knowledge of Le Sage's theory was based on "Lucrece Newtonien" and a summary by Prévost. 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. In 1790 he expressed in one of his papers his enthusiasm for the theory, believing that Le Sage's theory embraces all of our knowledge and makes any further dreaming on that topic useless. He went on by saying: "If it is a dream, it is the greatest and the most magnificent which was ever dreamed..." and that we can fill with it a gap in our books, which can only be filled by a dream.[16]

He often referred to Le Sage's theory in his lectures on physics at the University of Göttingen. However, around 1796 Lichtenberg changed his views after being persuaded by the arguments of Immanuel Kant, who criticized any kind of theory that attempted to replace attraction with impulsion.[17] Kant pointed out that the very existence of spatially extended configurations of matter, such as particles of non-zero radius, implies the existence of some sort of binding force to hold the extended parts of the particle together. Now, that force cannot be explained by the push from the gravitational particles, because those particles too must hold together in the same way. To avoid this circular reasoning, Kant asserted that there must exist a fundamental attractive force. This was precisely the same objection that had always been raised against the impulse doctrine of Descartes in the previous century, and had led even the followers of Descartes to abandon that aspect of his philosophy.

Another German philosopher, Friedrich Wilhelm Joseph Schelling, rejected Le Sage's model because its mechanistic materialism was incompatible with Schelling's very idealistic and anti-materialistic philosophy.[18]

Laplace

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.[19] This was taken by most researchers, including Laplace, as support for the Newtonian concept of instantaneous action at a distance, and to indicate the implausibility of any model such as Le Sage's. Laplace also argued that to maintain mass-proportionality the upper limit for earth's molecular surface area is at the most the ten-millionth of earth surface. To Le Sage's disappointment, Laplace never directly mentioned Le Sage's theory in his works.

Cristian
26th September 2016, 17:33
Historical Assessments of the Fatio-Lesage Theory (http://www.mathpages.com/home/kmath209/kmath209.htm)



It’s an interesting historical fact that the attitudes of scientists toward the Fatio-Lesage “explanation” of gravity have varied widely, not just from one scientist to another, but for individual scientists at different moments. This is exemplified by Newton’s ambivalence. On one hand, he told Fatio that if gravity had a mechanical cause, then the mechanism must be the one Fatio had described. On the other hand, Newton usually inclined toward the view that gravity does not have a mechanical (material) cause. It’s true that he explicitly denied (in a famous letter to Bentley) the intelligibility of bare action at a distance, but he just as explicitly rejected (in a letter to Leibniz) the notion that space is filled with some material substance (a la Descartes) that communicates the force of gravity. His alternative was to say that gravity is caused by the will and spirit of God, not by any material cause. Of course, he gave consideration to various possible material mechanisms, and even included some Queries in the latter editions of Opticks, speculating on the possibility of an ether that is least dense near matter, and whose density increases the further we recede from matter. This could be interpreted as a somewhat obscure reference to Fatio’s theory, since the flux of gravific corpuscles is reduced in the vicinity of matter, due to the shadowing effect. And yet David Gregory reported that, behind Fatio’s back, Newton laughed at his method of explaining gravity, and Newton scrupulously avoided mentioning any such explanations in his cherished Principia – aside from making it clear that his conception of gravity did not assume any particular mechanism, nor even whether gravity was due to an inherent pull between matter or was caused by some kind of impulsion. Indeed Fatio was unhappy that Newton never publicly acknowledged, let alone endorsed, his theory. He wrote to Conduitt in 1730



I have often wondered how the second and third Edition of Sir Isaac Newton’s Principles do touch so lightly upon this matter. For if there be a mechanical cause of gravity – as it is most probable – there is also a demonstration that there can be no cause of it than that which I give, and Dr. I. knew it very well.



Apparently Fatio didn’t appreciate how anathema his “explanation of gravity” was to Newton’s fundamental doctrine, which was to eschew occult (i.e., hidden) causes for manifest phenomena. Even setting outside the outlandishness of the explanation, Newton was never able to extract from Fatio’s idea any testable consequence that could support it, so the idea remained an occult mechanism which, according to Newton, is not the proper purview of science.



Subsequent scientists have had similarly ambivalent reactions to the theory of Fatio and Lesage. For example, Euler originally expressed interest in Le Sage’s theory, stating (in the same conditional manner employed by Newton) that if gravity is due solely to impulse forces, then something like Lesage’s theory must be true. However, Euler ultimately rejected Lesage’s theory, and when Lesage persisted in trying to persuade him, Euler finally replied



So you must excuse me Sir, if I have a great repugnance for your corpuscles ultramundane, and I shall always prefer to confess my ignorance of the cause of gravity than to have recourse to such strange hypotheses.



This striking ambivalence regarding the Fatio-Lesage theory has many other examples. Herschel spoke for many scientists when he said it was “too grotesque to need serious consideration”, whereas Thomson and Tait gave it serious consideration, the latter even asserting that it was “the only plausible answer which has yet been propounded”. Darwin too gave the idea “serious consideration”, but he also said “no man of science is disposed to accept it as affording the true road”.



Several of the founders of modern kinetic theory, including both John Herapath in 1820 and John James Waterston in 1845, began their investigations by trying to devise mechanical explanations of gravity. Herapath seems to have been influenced explicitly by Lesage’s writings, whereas Waterston was apparently one of the many independent discoverers of the concept. However, it must also be said that, as the principles of kinetic theory emerged, the plausibility of a Lesagean explanation of gravity was diminished rather than increased. Subsequently, Thomson and Tait (who dubbed themselves T and T’) were intrigued by the Fatio/Lesage concept, although Thomson pointed out that the theory was untenable if the ultra-mundane corpuscles are regarded as elementary entities with no internal structure. This is because the corpuscles must give up momentum to ordinary matter, and if they have no internal energy modes, they must also impart energy to ordinary matter, and this energy will be enormous (considering the high speed of the corpuscles necessary to avoid drag and aberration), sufficient to vaporize all ordinary matter in a fraction of a second.



In an effort to remedy this problem, Kelvin considered (as Fatio had done nearly 200 years before) that perhaps the corpuscles are not elementary entities, but are actually compound systems with internal energy modes of enormous capacity. This idea is problematic for several reasons. First, and most fundamentally, internal energy modes (such as vibration or rotation) require an extremely strong force of attraction to hold the various parts of the corpuscle together, and therefore each distinct part of a corpuscle must act as a center of force, attracting it to the other parts of the corpuscle. Maxwell remarked on this with his characteristically dry wit



Such centres of force are no doubt in their own nature indivisible, but then they are also singly incapable of vibration. To obtain vibrations we must imagine molecules consisting of many such centres, but in doing so the possibility of these centres being separated altogether is again introduced… it is in questionable scientific taste, after using atoms so freely to get rid of forces acting at sensible distances, to make the whole function of the atoms an action at insensible distances.



To put it more bluntly, it is an intellectual sham to pretend to eliminate elementary forces of attraction between distinct entities by invoking a model that relies crucially on elementary forces of attraction between distinct entities. In other words, even if Kelvin’s suggestion was viable (which it isn’t, as discussed below), it wouldn’t accomplish what he intended, which was to explain the apparent force of attraction purely in terms of repulsive contact forces (vis a tergo) without the need for any elementary force of attraction, in accord with the Cartesian notion that all action can be reduced to instances of contact forces. Lesage himself sought to distinguish between attraction and cohesion, the latter being a force tending to hold the contiguous parts of a single entity together. This may have motivated Lesage to envisage ordinary matter as a contiguous lattice structure (“cages”), to avoid the need for attraction between spatially separate matter. However, to endow spatially extended matter with cohesiveness as well as internal dynamics is to embed a field theory within a particle theory. We must then postulate a set of physical laws governing the cohesion (and repulsion) of the elements of a continuous medium, and the forces involved in these laws must be produced by a process that is totally dis-similar to the particle-based mechanism of gravity.



The only other alternative is to opt for the “turtles all the way down” strategy. Suppose that, in order to explain the forces of attraction (or cohesion) holding each compound gravitational corpuscle together, we postulate another radiation field of even finer corpuscles with even greater penetrating power and even greater speeds, producing a “meta-gravity”, thereby accounting for the cohesion of the gravitational corpuscles (and presumably another parallel flux to account for the cohesion of ordinary matter). Of course, we then face the same heat problem for the gravitational corpuscles that we previously faced for ordinary matter, so we must now appeal to a meta-meta-gravity, and so on, ad infinitum. There is some evidence in De Rerum Natura that Lucretius had something like this in mind when he wrote (as translated by William Ellery Leonard)



For thou wilt mark here many a speck, impelled

By viewless blows, to change its little course,

And beaten backwards to return again,

Hither and thither in all directions round.

Lo, all their shifting movement is of old,

From the primeval atoms; for the same

Primordial seeds of things first move of self,

And then those bodies built of unions small

And nearest, as it were, unto the powers

Of the primeval atoms, are stirred up

By impulse of those atoms' unseen blows,

And these thereafter goad the next in size;

Thus motion ascends from the primevals on,

And stage by stage emerges to our sense,

Until those objects also move which we

Can mark in sunbeams, though it not appears

What blows do urge them.



We might also compare this with the modern theory of Brownian motion. However, even if we were prepared to contemplate this infinite hierarchy of radiation fields, with energies increasing to infinity as we rise in the hierarchy, it would not work, because the effective interaction cross-section between two particles is the sum of their radii, so it can never be less than the larger of the two radii, which is that of the particles of ordinary matter. The original ultra-mundane corpuscles are already of negligible size compared with these, so none of the meta-corpuscles can have a lesser interaction cross-section. The only alternative is to postulate zero cross-sections for all particles, and let their interactions be governed by fields with differing coupling strengths. But this again involves force at a distance, the very thing we are supposedly trying to eliminate.



Setting aside the fact that the Fatio-Lesage model, even if it were viable, would not accomplish its intent, we might still wonder whether the Lesagean model is viable on its own terms. As already mentioned, in order to convey a given amount of momentum, a simple particle moving at speed v must lose a specific amount of translational speed, which corresponds to a specific amount of translational kinetic energy. There are several possibilities as to what might become of this enormous quantity of energy, but to even enumerate these possibilities we must agree on a theoretical basis, because the kinetics and dynamics of particles depend on this basis. For example, in Newtonian terms the momentum of a massive particle is mv and the kinetic energy is mv2/2, whereas in special relativity (and any other empirically viable theory of mechanics) the momentum and total mass-energy are mv/[1-(v/c)2]1/2 and mc2/[1-(v/c)2]1/2. Furthermore, for an entity moving at the speed c (like an electromagnetic wave) the rest mass is necessarily zero, and the momentum and energy are related by p = E/c. Therefore, according to the empirically viable theories of mechanics and electrodynamics, any conveyance of momentum at the speed of light must be accompanied by a proportional transference of energy. In addition, the drag and aberration associated with a Lesagean flux of speed c would be unacceptably great, so the idea of a light-speed Lesage model is ruled out on three counts (or four, if we include the fact that it wouldn’t dispense with the need for elementary attractive forces even if it did work.).



At this point, a determined Lesagean is faced with a few possible alternatives. He might attempt to proceed based on the premise of corpuscles moving many orders of magnitude faster than light, but then he must also propose an entirely new system of dynamics, including new definitions of momentum and kinetic energy, because the existing definitions are not applicable to particles moving faster than light. (This is true regardless of whether one adopts the Einsteinian or the Lorentzian interpretation of relativity.) But if we are prepared to entertain completely new laws of physics, then the program is self-defeating, because the original intent was to account for gravitational attraction in terms of the ordinary mechanical behavior of material objects. It isn’t clear whether any alternative system of physical laws can be formulated, but even if it could, this would represent the abandonment, not the accomplishment, of the original intent.



The dedicated Lesagean might also try to imagine some way of modifying the Lesage mechanism so that it yields a non-central force to avoid the aberration and drag problems without requiring super-luminal speeds. However, this again would entail completely new physical laws, because the aberration and drag problems correspond directly to basic conservation of momentum for kinetic corpuscles, which supposedly are the basis of the theory. Needless to say, any suggestion that the Lesagean flux undergoes vortex motion, ala Descartes, is completely untenable, not only for all the reasons (e.g., retrograde orbits) that led to the abandonment of the Cartesian system in the first place, but also because it is grossly inconsistent with the Lesagean mechanism itself, which relies on purely rectilinear paths and non-interacting corpuscles, at least on the scale over which the force of gravity varies inversely as the square of the distance.



Many other considerations undermine the viability of the Fatio-Lesage model of gravity. For example, from the absence of any appreciable shielding effect for gravity, we know that the difference between the upward and downward flux at the earth’s surface can be no greater than 1 part in 107, and therefore the apparent force of 1 pound on a small mass near the Earth’s surface is actually just the difference between two gigantic opposing forces, as indicated in the figure below.

http://www.mathpages.com/home/kmath209/kmath209_files/image001.gif

http://www.mathpages.com/home/kmath209/kmath209_files/image001.gif


This has several important implications. First, it implies that the ultra-mundane flux arriving from opposite regions of the universe must be incredibly isotropic. Suppose for example that the ultra-mundane flux had the same degree of isotropy as the cosmic microwave background radiation, which is about 1 part in 105. This is extremely isotropic by most standards (in fact, it’s so isotropic that some process like cosmic inflation seems necessary to account for it), and yet this degree of isotropy would cause fluctuations in the “weight” of a 1 pound object (in the shape of a slender rod, to make it sensitive to the directional flux) on the order of 100 pounds. This conflicts grossly with the empirical uniformity in the weight of objects at different locations and orientations near the Earth’s surface. Hence the ultra-mundane flux must not only travel many orders of magnitude faster than the speed of light, it must also be many orders of magnitude more isotropic than any known field. (This entails an incredible uniformity not only of the speed and intensity of the particle rays, but also of the directions.) Since the particles arriving here at any given moment have come from distant regions of space in opposite directions at speeds far in excess of the speed of light, it’s clear that they have had no chance to interact with each other prior to their arrival, so we cannot explain the phenomenal uniformity other than by calling it a perpetual miracle.



Another implication concerns the expenditure of work. According to the usual way of thinking, when a 1 lb object falls through a distance of 1 foot, the “force of gravity” has performed 1 ft-lb of work on the object, converting potential energy into kinetic energy. However, according to the Fatio-Lesage model, the downward flux has performed 10000001 ft-lbs of work on the object, which in turn has performed 10000000 ft-lbs of work on the upward flux. The net work on the object is still just 1 ft-lb, but this has been accomplished only by the fantastically precise balance of two enormous expenditures of work, and nearly all of this excess effort must be degraded into non-translational forms of energy. As a result, there is a gigantic production of entropy, and it should be noted that this applies just as much to Kelvin’s model (with corpuscles able to absorb energy) as it does to the basic Fatio-Lesage model. In either case, the energy must be absorbed in non-coherent vibration or rotation, with the corresponding increase in entropy. In fact, this applies even if the macroscopic object is stationary. The mere production of 1 pound of force, in the Fatio-Lesage model, involves an almost unimaginable rate of entropy production in the ultra-mundane flux. Hence, processes that we are used to regarding as isentropic, such as the motions of planets in their orbits, are actually (according to Fatio-Lesage) tremendously non-isentropic. The concept of entropy as distinct from energy was still being developed and clarified in Maxwell’s day, but these were clearly the considerations that Maxwell had in mind when he wrote (in an encyclopedia article on the Atom)



We may also observe that according to this theory the habitable universe, which we are accustomed to regard as the scene of a magnificent illustration of the conservation of energy as the fundamental principle of all nature, is in reality maintained in working order only by an enormous expenditure of external power, which would be nothing less than ruinous if the supply were drawn from anywhere else than from the infinitude of space, and which, if the contrivances of the most eminent mathematicians should be found in any respect defective, might at any moment tear the whole universe atom from atom.



Still another implication concerns Kelvin’s suggestion that the “spent” corpuscles, after interacting with ordinary matter and acquiring an enormous amount of internal energy (with corresponding loss of translational energy), could be restored to their former condition by mingling with fresh corpuscles in the far reaches of space. (As Maxwell dryly put it, Kelvin “has also suggested the possibility of the vortex corpuscle regaining its swiftness and losing part of its vibratory agitation by communion with its kindred corpuscles in the infinitude of space”.) Clearly this suggestion is untenable, because it entails a reduction in the overall entropy of the universe, countering the production of entropy resulting from the creation of gravitational force. Of course, if we posit an infinite universe with only a finite amount of mass, then the spent corpuscles might asymptotically approach their original condition, but in that case it’s irrelevant, because the matter in the habitable universe would forever be bombarded with fresh corpuscles of low entropy from the infinite ultra-mundane regions. But in any universe where there is a finite ratio of ordinary matter to ultra-mundane corpuscles, the entropy must continually increase.



Maxwell actually repeated this criticism of the Fatio-Lesage concept many times, so he apparently regarded it as the most damning (speaking at a time prior to the recognition of the relativistic aspects of dynamics). For example, in his review of Challis’ Essay on the Mathematical Principles of Physics he wrote



…in whatever way we regard Lesage’s theory [including Kelvin’s variant], the cause of gravitation in the universe can be represented only as depending on an ever fresh supply of something from without… the universe is not even temporarily automatic, but must be fed from moment to moment by an agency external to itself… if the corpuscles were from any cause to be supplied at a different rate, the value of every force in the universe would suffer change… the preservation of the universe is effected only by the unceasing expenditure of enormous quantities of work, so that the conservation of energy in physical operations, which has been the subject of so many measurements, and study of which has led to so many discoveries, is apparent only, and is merely a kind of “moveable equilibrium” between supply and destruction.



Likewise in his encyclopedia article on Attraction he wrote in regard to Lesage’s theory



It is remarkable that of the… hypotheses which go some way towards a physical explanation of gravitation, every one involves a constant expenditure of work… According to such hypotheses we must regard the processes of nature not as illustrations of the great principle of the conservation of energy, but as instances in which, by a nice adjustment of powerful agencies not subject to this principle, an apparent conservation of energy is maintained. Hence we are forced to conclude that the explanation of the cause of gravitation is not to be found in any of these hypotheses.



In 1905 G. H. Darwin published a paper entitled “The Analogy between Lesage’s Theory of Gravitation and the Repulsion of Light”, in which he derived expressions for the forces of attraction and drag and for the energy transfer in Lesage’s theory, based on the assumption of spherical particles as the elementary opaque entities from which macroscopic bodies are composed. He allowed for differing amounts of elasticity in the normal and tangential directions, but he neglected the effects of secondary impacts of reflected particles. His main conclusions were that the mutual forces of attraction between bodies would be equal and opposite only if all the elementary particles are of exactly the same size, and that the force is perfectly proportional to the inverse square of the distance only if the gravific corpuscles are perfectly inelastic (i.e., are totally absorbed when they strike ordinary matter). He points out that, on this basis, the theory “demands a continual creation of energy at infinity to supply the gravific machinery”, which like Maxwell he regards as “a fundamental objection to the physical truth of Lesage’s hypothesis”.

Foxie Loxie
27th September 2016, 12:53
Just wondering if you have checked out The Electric Universe theory. You can find it under Thunder Bolts.org, I believe.