Gravity

"Hooke... followed Bacon in his attempt to demonstrate that the effects of gravity on a body must diminish as the body was sunk into the bowels of the earth. He sought to discover how far the effects were altered at great heights or in the region of the equator; and he threw light on the problem by observations and experiments on the pendulum. From the globular shapes of the heavenly bodies and the stable conformations of the ridges on the moon he deduced that the moon and the planets had gravity; and by 1666 he saw the motion of a comet (for example) as incurvated by the pull of the sun... and suggested that the motion of the planets might be explicable on the kind of principles that account for the motion of a pendulum. In 1674 he was suggesting that by this route one could arrive at a mechanical system of the planets which would be "the true perfection of astronomy." He pointed out that... account must be taken of the force which all heavenly bodies must be presumed to be exerting on one another. ...By 1678 he had formulated the idea of gravitation as a universal principle; and by 1679 he, too, had discovered that the diminution of the force of gravity is proportional to the square of the distance. ...But ...Hooke did not produce the mathematical demonstrations of his system."

"Frank Wilczek, 26:01 of 40:44"

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory."

"Even though it is, properly speaking, a postprediction, in the sense that the experiment was made before the theory, the fact that gravity is a consequence of string theory, to me, is one of the greatest theoretical insights ever."

"If supersymmetry plays the role in physics that we suspect it does, then it is very likely to be discovered by the next generation of particle accelerators, either at Fermilab... or at CERN... Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of "string theory," which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost."

"It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory."

"Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered."

"It is observed by Bacon, in his essay on the opinions of Parmenides, that the most ancient philosophers, Empedocles, Anaxagoras, Anaximenes, Heraclitus, and Democritus, submitted their minds to things as they found them; but that Plato made the world subject to ideas, and Aristotle made even ideas, as well as all other things, subservient to words; the minds of men beginning to be occupied, in those times, with idle discussions and verbal disputations, and the correct investigation of nature being wholly neglected. Plato entertained, however, some correct notions respecting the distinction of denser from rarer matter by its greater inertia; and it would be extremely unjust to deny a very high degree of merit to Aristotle's experimental researches, in various parts of natural philosophy, and in particular to the vast collection of real information contained in his works on natural history. Aristotle attributed absolute levity to fire, and gravity to the earth, considering air and water as of an intermediate nature. By gravity the ancients appear in general to have understood a tendency towards the centre of the earth, which they considered as identical with that of the universe; and as long as they entertained this opinion, it was almost impossible that they should suspect the operation of a mutual attraction in all matter, as a cause of gravitation. The first traces of this more correct opinion respecting it are found in the works of Plutarch."

"William Gilbert published a famous book on the magnet in 1600 and laid himself open to the gibes of Sir Francis Bacon for being one of those people so taken by their pet subject of research that they could only see the whole universe transposed into terms of it. Having made a spherical magnet called a ', and having found that it revolved when placed in a magnetic field, he decided that the whole earth was a magnet, that gravity was a form of magnetic attraction, and that the principles of the magnet accounted for the workings of the Copernican system as a whole. Kepler and Galileo were both influenced by this view, and with Kepler, it became an integral part of his system, a basis for the doctrine of almost universal gravitation."

"Descartes was liable to be misled by too easy an acceptance of data that had been handed down by scholastic writers. ...two grand Aristotelian principles helped to condition the form of the universe as he reconstructed it—first, the view that a vacuum is impossible, and secondly, the view that objects could only influence one another if they actually touched—there could be no such thing as attraction, no such thing as . ...Descartes insisted that every fraction of space should be fully occupied all the time by continuous matter... infinitely divisible. The particles were... packed so tightly that one of them could not move without communicating the commotion to the rest. The matter formed whirlpools in the skies, and it was because the planets were caught each in its own whirlpool that they were carried around... all similarly caught in a larger whirlpool, which had the sun as its centre... Gravity itself was the result of these whirlpools of invisible matter which had the effect of sucking things down towards their centre. ...In the time of Newton the system of Descartes and the theory of vortices or whirlpools proved to be vulnerable to both mathematical and experimental attack."

"In the middle of the 1660s, Borelli, Newton, Huygens and Hooke were wrestling with various parts of the same planetary problems, some of them treading on one another's heels in the study of the nature of light... in England, experiments with the pendulum clock had started independently, and Christopher Wren, , William Balle and Laurence Rooke appear to have unaugurated the enquiry into laws of motion, Robert Hooke performing most of the experiments. The 1670s must represent one of the greatest decades in the scientific revolution, if not the climax... and in both London and Paris... achievements... were of a remarkable nature. So far as the gravitational theory... our attention ought to be directed not merely to Newton... but to the combined operations of the English group. The Royal Society... following Baconian principles, sought to collect... the data necessary for the establishment of the Copernican hypothesis... ideally... "freely communicating their methods and pooling their gains." Here the names... in the forefront are... Isaac Newton, Robert Hooke, Edmond Halley and Christopher Wren."

"The globe of the Earth stands supportless in space... Just as the [spherical] bulb of a Kadamba flower is covered all around by blossoms, just so is the globe of the Earth surrounded by all creatures, terrestrial as well as aquatic."

"There are some oddities in the perspective with which we see the world. The fact that we live at the bottom of a deep gravity well, on the surface of a gas covered planet going around a nuclear fireball 90 million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be, but we have done various things over intellectual history to slowly correct some of our misapprehensions."

"Anaxagoras... speaks absurdly concerning the permanency of the infinite: for he says that the infinite itself supports itself; and this because it is in itself: for nothing else contains it. As if where any thing is it is naturally there. But this is not true: for a thing may be situated in a certain place by force, and not where it is naturally adapted to be. If, therefore, the whole is by no means moved; for that which is established in itself, and is in itself, is necessarily immoveable; yet it should be said why it is not naturally adapted to be moved: for it is not just that he who thus speaks should be dismissed; since there may be any thing else which is not moved; but nothing hinders it from being naturally adapted to be moved: for earth also is not borne along; nor if it were infinite could it be locally moved, in consequence of being restrained by the middle. It would not, however, remain in the middle, because there is not any other place into which it could be moved, but because it is not natural to it so to be moved. Though, indeed, it might be said, that the earth supports itself. If, therefore, this is not the cause of the permanency of the earth if it were infinite, but its gravity is the cause; and that which is heavy abides in the middle, and the earth is in the middle: in like manner also, the infinite will abide in itself, through some other cause, and not because it is infinite, and will itself support itself. At the same time likewise, it is manifest, that it is necessary every part of it should abide: for as the infinite abides supported in itself; so likewise whatever part of it is assumed, will abide in itself: for the places of the whole and the part are of the same species; as of the whole earth and a clod, the place is downward; and of the whole of fire, and a spark, the place is upward. So that if the place of the infinite is in itself, there will be the same place also of a part of the infinite. It will abide therefore, in itself. And, in short, it is evident that it is impossible to say that there is an infinite body, and at the same time that there is a certain place for bodies, if every sensible body either possesses gravity or levity. And if it is heavy, it has a natural tendency to the middle; but if light, it naturally tends upward: for it is necessary that an infinite body should be such. But it is impossible that the whole should be passive in either way, or the half in both ways: for how will you divide? Or how will one part of the infinite be above, and another below? Or how will it have extremes or a middle? Further still; every sensible body is in place; but the species and differences of place are upward and downward, before and behind, to the right hand and to the left: and these things not only thus subsist with relation to us, and by position, but have a definite subsistence in the universe itself. But it is impossible that these things should be in the infinite: and in short it is impossible that there should be an infinite place."

"Moreover, force, gravity, and words of that kind, are often, and not unwisely, used in the concrete; in such a way that they know the movement of the body, the difficulty of resistance, etc. But when they are used by philosophers to signify certain natures, precise and abstract from all these, which are neither subject to the senses, nor can be understood by any power of the mind, nor can they be shaped by the imagination, they in turn give rise to errors and confusion."

"The earth attracts inert bodies in space towards itself. The attracted body appears to fall down on the earth. Since the space is homogeneous, where will the earth fall?"

"GRAVITATION, n. The tendency of all bodies to approach one another with a strength proportion to the quantity of matter they contain -- the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A."

"Our two greatest problems are gravity and paper work. We can lick gravity, but sometimes the paperwork is overwhelming."

"In order that a pendulum may continue to make the same number of oscillations in a given time, it must be shortened as it is carried towards the equator; and the variation of its length in different latitudes affords an accurate measurement of the force of gravity. But the force of gravity has known relation to the figure of the earth, which, therefore, may be determined, by observing the length of the seconds pendulum at different points on its surface."

"Cotes's Preface [to the 2nd edition of Principia] is of historical importance... It is interpreted as advocating the theory of "action at a distance", and the theory that gravity is an innate property of matter. Phrases in Newton's Principia appear to carry a similar implication. ...In these expressions, the "bodies" or the "corpuscles" are represented as active, as "attracting." They are not passive like a chip of wood carried about by a eddy in a pool, or like a planet passively swept through space by a Cartesian vortex. It was easy, therefore, to jump to an inference that in the Newtonian theory, gravity was an innate, inherent property of matter. ...such an interpretation was made by writers on the European continent, for example by Huygens, Lalande, [Jean Baptiste] Bordas-Demoulin, and others. Thus, after the publication of the Principia in 1687, Huygens... abandoned the explanation of the planetary motion by Descartes' theory of vortices, and published his adherence to Newton's celestial mechanics. But Huygens did not accept the view that gravitation was an innate property of matter, a view which he attributed to Newtonian philosophy. On this point Huygens rejected what interpreted to be the tenet of Newton, and continued his adhesion to the tenet of Descartes. While the reader of the first edition of Principia had some justification in attributing to Newton the view that gravity was an innate property of matter, they were nevertheless mistaken. In the first edition Newton had made no explicit declaration on this point. ...Newton was no more a believer in gravity as an innate property of bodies than was Descartes. But the readers of the first edition of Principia had no means of knowing this."

"Newtonian action at a distance is spoken of as "immediate action." Newton, on the other hand, postulates an agent and gives it time to act. To be sure, in his calculations of gravitational attractions, he assumes, as a necessary approximation (having no experimental data on the speed of propagation of gravitational action), that the action is instantaneous, but not so in his talks on gravity. In a letter to Boyle he considers the cause of gravitation between two approaching bodies. They "make the ether between them begin to rarify"; and again, in his hypothesis on light, he says, "So may the gravitating attraction of the earth be caused by the continual condensation of some other such like ethereal spirit... in such a way... as to cause it [this spirit] from above to descend with great celerity for a supply; in which descent it may bear down with it the bodies it pervades, with force proportional to the superficies of all their parts it acts upon.""

"Laplace made the assumption that the transmission of gravity is not instantaneous, and he found that in order to produce the known effects in the secular acceleration of the moon, gravity must travel seven million times faster than the speed of light. ...Laplace's calculation has been found to be incomplete, and his velocity of gravity illusory."

"For the better part of my last semester at Garden City High, I constructed a physical pendulum and used it to make a “precision” measurement of gravity. The years of experience building things taught me skills that were directly applicable to the construction of the pendulum. Twenty-five years later, I was to develop a refined version of this measurement using laser-cooled atoms in an atomic fountain interferometer."

"The essence of Riemann's discoveries consists in having shown that there exist a vast number of possible types of spaces, all of them perfectly self-consistent. When, therefore, it comes to deciding which one of these possible spaces real space will turn out to be, we cannot prejudge... Experiment and observation alone can yield us a clue. To a first approximation, experiment and observation prove space to be Euclidean, and this accounts for our natural belief... merely by force of habit. But experiment is necessarily innacurate, and we cannot foretell whether our opinions will not have to be modified when our experiments are conducted with greater accuracy. Riemann's views thus place the problem of space on an empirical basis excluding all a priori assertions on the subject. ...the relativity theory is very intimately connected with this empirical philosophy; for... Einstein is compelled to appeal to a varying non-Euclideanism of four-dimensional space-time in order to account with extreme simplicity for gravitation. ...had the extension of the universe been restricted on a priori grounds... to three dimensional Euclidean space, Einstein's theory would have been rejected on first principles. ...as soon as we recognise that the fundamental continuum of the universe and its geometry cannot be posited a priori... a vast number of possibilities are thrown open. Among these the four-dimensional space-time of relativity, with its varying degrees of non-Euclideanism, finds a ready place."

"With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain....the theory of relativity is the theory of the space-time metrical field."

"Let us revert to the metrical field, as defining the space-time structure. Although Riemann had attributed the existence of the structure, or metrical field, of space to the binding forces of matter, there is not the slightest indication in Einstein's special theory that any such view is going to be developed later on; in fact, it does not appear that Einstein was influenced in the slightest degree by Riemann's ideas. ...in the special theory, the problem of determining whence the structure, or field, arises, what it is, what causes it, is not even discussed in a tentative manner. Space-time, with its flat structure, is assumed to be given or posited by the Creator. But in the general theory the entire situation changes when Einstein accounts for gravitation, hence for a varying lay of the metrical field, in terms of a varying non-Euclidean structure of space-time around matter. We are then compelled to recognise not only that the metrical field regulates the behaviour of material bodies and clocks, as was also the case in the special theory, but, furthermore, that a reciprocal action takes place and that matter and energy in turn must affect the lay of the metrical field. But we are still a long way from Riemann's view that the field is not alone affected but brought into existence by matter; and it is only when we consider the cosmological part of Einstein's theory that this idea of Riemann's may possibly be vindicated. And here we come to a parting of the ways with de Sitter and Eddington on one side, Einstein and Thirring on the other, and Weyl somewhere in between the two extremes."

"In the year 1900 Max Planck wrote... E = hv, where E is the energy of a light wave, v is its , and h is... . It said that energy and frequency are the same thing measured in different units. Plank's constant gives you a rate of exchange for for converting frequency into energy... But in the year 1900 this made no physical sense. Even Plank himself did not understand it. ...Now Hawking has written down an equation which looks rather like Plank's equation... S = kA, where S is the entropy of a black hole, A is the area of its surface, and k is... Hawking's constant. Entropy means roughly the same thing as the of an object. ...Hawking's equation says that entropy is really the same thing as area. The exchange rate... is given by Hawking's constant... But what does it really mean to say that entropy and area are the same thing? We are as far away from understanding that now as Planck was of understanding quantum mechanics in 1900. ...[T]his equation will emerge as a central feature of the still unborn theory which will tie together gravitation and quantum mechanics and thermodynamics."

"Light-waves in passing a massive body such as the sun are deflected through a small angle. This is additional evidence that the Newtonian picture of gravitation as a tug is inadequate. You cannot deflect waves by tugging at them, and clearly another representation of the agency which deflects them must be found."

"The Newtonian scheme says that the planet tends to move in a straight line, but the sun's gravity pulls it away. Einstein says that the planet tends to take the shortest route and does take it."

"Einstein's law of gravitation controls a geometrical quantity curvature in contrast to Newton's law which controls a mechanical quantity of force."

"Enter superstring theory. The concept that particles are really tiny strings dates from the 1960s, but it took on wings in 1974, when John Schwarz... and Joel Scherk... came to terms with what had been an ugly blemish in their calculations. String theory kept predicting the existence of a particle with zero mass and a spin of two. Schwarz and Scherk realized that this unwelcome particle was nothing other than the graviton, the quantum carrier of gravitational force (Although there is no quantum theory of gravity yet, it is possible to specify some of the characteristics of the quantum particle thought to convey it.) This was liberating: The calculations were saying not only that string theory might be the way to a fully unified account of all particles and forces but that one could not write a string theory without incorporating gravity. Ed Witten... recalled that this news constituted "the greatest intellectual thrill of my life."

"We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!"

"One other test of gravity... is the question of whether the pull is exactly proportional to the mass... and changes in velocity are inversely proportional to the mass... That means that two objects of different mass will change their velocity in the same manner in a gravitational field. ...That is Galileo's old experiment from the Leaning Tower of Pisa. ...How accurate is it? It was measured in an experiment by ...Eötvös in 1909 and ...by Dicke, and is known to one part in 10,000,000,000. ...[S]uppose you wanted to know whether the pull is exactly proportional to the inertia. The earth is going around the sun, so the things are thrown out by inertia. But they are attracted by the sun to the extent that they have ... So if they are attracted to the sun in a different proportion from that thrown out by inertia, one will be pulled towards the sun, and the other away from it, and so, hanging them on opposite ends of a rod on another Cavendish quartz fiber, the thing will twist towards the sun. It does not twist at this accuracy, so we know that the sun's attraction to two objects is exactly proportional to its coefficient of inertia; in other words, its mass."

"Poetry had a much more serious beginning than is usually imagin'd, and... the Muses have of late days mightily deviated from their original Gravity."

"Edward Witten is fond of declaring that string theory had already made a dramatic and experimentally confirmed prediction: "String theory had the remarkable property of predicting gravity." What Witten means by this is that both Newton and Einstein developed theories of gravity because their observations of the world clearly showed them that gravity exists, and that, therefore, it required an accurate and consistent explanation. On the contrary, a physicist studying string theory—even if he or she was completely unaware of general relativity—would be inexorably led to it by the string framework."

"Much as Kaluza found that a universe with five spacetime dimensions provided a framework for unifying electromagnetism and gravity, and much as string theorists found that a universe with ten spacetime dimensions provided a framework for unifying quantum mechanics and general relativity, Witten found that a universe with eleven spacetime dimensions provided a framework for unifying all string theories."

"He used to say the left-hand side of his equation is beautiful and the right-hand side is ugly. Much of what he was doing in the latter part of his career was trying to move the right-hand side to the left... and understand matter as a geometrical structure. To build matter itself from geometry—that in a sense is what string theory does. ...especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. ...He would have liked the fact that there is an underlying geometrical principle — which, unfortunately, we don’t really yet understand."

"It turns out that the energy of a gravitational field—any gravitational field—is negative. During inflation, as the universe gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy of gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started—presumably something very small. ...This capability for producing matter in the universe is one crucial difference between the inflationary model and the previous model."

"The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916... in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. ...The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover.."

"Inflation takes advantage of this possibility... to let gravity be the repulsive force that drove the universe into the period of expansion that we call the Big Bang. In fact, when one combines general relativity with conventional ideas, now, in particle physics there really is a pretty clear indication, I should say, not quite a prediction... that at very high energy densities one expects to find states of matter which literally turn gravity on its head and cause gravity to become repulsive."

"What it takes to produce a gravitational repulsion is a negative pressure. According to general relativity, it turns out... both pressures and energy densities can produce gravitational fields, unlike Newtonian physics, where it's only mass densities that produce gravitational fields."

"A positive pressure produces an attractive gravitational field... Positive pressures are just sort of normal pressures and attractive gravity is normal gravity, so normal pressures produce normal gravity, but it is possible to have negative pressures, and negative pressures produce repulsive gravity, and that's the secret of what makes inflation possible."

"The gravitational repulsion created by this small patch of repulsive gravity material would be, then, the driving force of the Big Bang and it would cause the region to undergo exponential expansion... there is a certain doubling time, and if you wait the same amount of time it doubles again, and if you wait the same amount of time it doubles again... and it's because these doublings build up so dramatically, it doesn't take very much time to build the whole universe. In about 100 doublings this tiny patch of 10-28 cm can become large enough, not to be the universe, but to be a small marble-sized region which will then ultimately become the observed universe, as it continues to coast outward after inflation ends."

"Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement."

"Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic. A geodesic is the shortest (or longest) path between two nearby points."

"The universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe."

"'I should here have described some Clocks and Time-keepers of great use, nay absolute necessity in these and many other Astronomical observations, but that I reserve them for some attempts that are hereafter to follow, about the various wayes I have tryed, not without good success of improving Clocks and Watches and adapting them for various uses, as for accurating Astronomy, completing the Tables of the fixt stars to Seconds, discovery of Longitude, regulating Navigation and Geography, detecting the properties and effects of motions for promoting secret and swift conveyance and correspondence, and many other considerable scrutinies of nature: And shall only for the present hint that I have in some of my foregoing observations discovered some new Motions even in the Earth it self, which perhaps were not dreamt of before, which I shall hereafter more at large describe, when further tryalls have more fully confirmed and compleated these beginnings. At which time also I shall explaine a Systeme of the World, differing in many particulars from any yet known, answering in all things to the common Rules of Mechanicall Motions: This depends upon three Suppositions. First, that all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them, from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and the Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that Mercury also, Venus, Mars, Saturne, and Jupiter by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodys whatsoever that are put into direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified;'—But these degrees and proportions of the power of attraction in the celestiall bodys and motions, were communicated to Mr. Newton by R. Hooke in the yeare 1678, by letters, as will plainely appear both by the coppys of the said letters, and the letters of Mr. Newton in answer to them, which are both in the custody of the said R. H., both which also were read before the Royall Society at their publique meeting, as appears by the Journall book of the said Society.—'but it is a notion which if fully prosecuted as it ought to be, will mightily assist the astronomer to reduce all the Cœlestiall motions to a certaine rule, which I doubt will never be done true without it. He that understands the natures of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having my self many other things in hand which I would first compleat, and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.'"

"Having enumerated some of the most remarkable Proprieties of Gravity, we come in the next place to consider what may be the Cause thereof. And first, I believe I shall not need to say much against the Opinion of Intelligent Matter, which supposes every part of Matter to act understandingly, for that being supposed, all Philosophy is vain, and there needs no farther Inquiry into Nature. And secondly, I have as little to say to its Cousin-german Opinion, viz. the Regimen of an Hylarchick Spirit. And 3ly, The Epicurean Atoms seem to me to give as little of Explanation almost as either of the former. And 4ly, For the Peripatetick Doctrine of tendency to the Center of the Universe, besides that the Foundation is false, the Earth being proved not to be in the Center, 'tis not yet understood what the tendency is. 5ly, The Cartesian Doctrine and that of Mr. Hobbs are both insufficient, because they do not give any reason why Bodies should descend towards the Center under or near the Poles. 6ly, Nor will the Magnetism of Gilbert or Kepler serve; for, as I shall afterwards shew, that is a Propriety distinct from Gravity, and of quite another nature."

"I could... largely explain, and plainly evince, that the Motions of several Bodies at a distance, are caused by the internal motion of the founding Body; and that this Power of moving is every way propagated by the ambient Medium, which excites in solid Bodies at a distance, a similar Motion. I could farther also prove, that every one of these distinct internal Motions of Bodies, as that of Light, and that of Sound, have distinct and differing Mediums, by which those Motions are communicated from the affecting to the affected Body: And so I conceive also that the Medium of Gravity may be distinct and differing both from that of Light, and from that of Sound. I conceive then, that the Gravity of the Earth may be caused by some internal Motion of the internal or central Parts of the Earth; which internal and central Motion may be caused, generated and maintained by the Motion of the external and all the intermediate parts of its Body: So that the whole Globe of the Earth may contribute to this Motion, as it will happen to a Globe of Glass or solid Mettal, to any part of which no internal Motion can be communicated, without at the same time affecting the whole with the same Motion. And I shall most plainly and evidently prove, when I come to the Explication of Magnetism, that this is undeniably performed and effected by this means."

"If light takes the path with the least time between two points, and light beams bend under the influence of gravity, then the shortest distance between two points is a curved line. Einstein was shocked by this conclusion: If light could be observed traveling in a curved line, it would mean that space itself is curved."