Gregory chap 9

Gregory chap 9 - I76 CHAPTER 8 ISAAC NEWTON A HIGHPOINT OF...

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Unformatted text preview: I76 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE CHAPTER 9 March 2, 1727. As he lay dying later that same month, Newton affirmed the ribil— lious religious stance he had so long embraced by refusmg the slacrfimeitso .te e church. Three days after his death on March 20, the“ records of tie. on ocr gy marked his passing with the terse announcement: The Cha’ir being acant y the Death of Sir Isaac Newton there was no Meeting this Day. f When Isaac Newton set off for Cambridge University in the early summer 0 1661 there was not yet a consensus about the viability of the new Copernican View of the cosmos. Galileo had offered a reason why planets would continue to move forever around the sun in circular orbits, but Kepler had shown that the orbitsgvege not circular. Why did the planets continue to. move in elliptical orbit; :rmin t ef sun? Not only did Newton give the answer in the Priznegozn throug ais Haws 10 motion and universal gravitation, but his answer prov1ded a means of an yzucilg t 1e motions of all matter, whether in the heavens or here on Earth. Newton funitl: nat- ural philosophy into one comprehensive system that would dominate or t e next two centuries. ——————©—————— Newtonianism, the Earth, and the Universe During the Eighteenth Century © Suggestions for Reading Gale E. Christianson, In the Presence of the Creator: [sane Newton and His Times (New Y 1: Free Press, 1984). . I ’ . I Bettjjr]; Teeter Dobbs, T/aefzznm Faces of Genius (Cambridge: Cambridge Unrversrty P s, 2002). I .- Richrafrsd Westfall, Never at Rest: A Biography of [sane Newton (Cambridge: Cambridge University Press, 1983). The novel ideas that came into science in the seventeenth century were incompat— ible in many. ways with the more comfortable cosmos of former times. Copernicus had already moved the Earth off to the side, away from the center of the system of spheres that had always provided humans a home. But even in the early versions of the Copernican system, including that defended by Galileo, the cosmos at least remained finite in extent. After Descartes and especially after Newton, it was no longer possible to insist that space did not extend infinitely in all directions. It took some time to build a consensus about the meaning of Newton’s achieve— ment. After all, there was much more about it to disagree with than just the question , of whether the universe had a center or not. The linchpin on which all depended in Newton’s system was his notion of an attractive force that acted at a distance. For mechanical philosophers who continued in the heritage of Descartes, this was a major stumbling block. The transmission of Newton’s force appeared to make use of an intervening medium that was occult, and that was simply unacceptable to them. © The Rise ofNewtonianism (Q In spite of the fame Newton enjoyed among his fellow British citizens, his system initially found few followers abroad. After 1730 Newton’s system began to attract followers—particularly in France—who defended a worldview that has been called 'Newtonianism. But prior to 1730, the continuing influence of Rene Descartes in France and Gottfried Leibniz in the German states was sufficient to assure that the Cartesian and Leibnizian worldviews provided strong competition for Newton’s I77 178 CHAPTER 9: NEWTONlAleM, THE EARTH, AND THE UNIVERSE thought. Only in Holland did Newton’s system find avid defenders across the English Channel. Competing Systems of Natural Philosophy The basic assumptions individual natural philosophers made. about how nature worked determined differences among them that carried implications throughout their systems. In the early eighteenth century these differences produced an important debate about force and action in nature and also involved the issue of Gods relation— ship to the natural world. Cartesians, Leibnizians, Newtonians. The most important issue separating Newton’s system from those of Descartes and Leibniz remained an understanding of the nature of force. The Cartesian position was clear: force was a push or pull that acted on material objects by means of material contact. All natural effects were due to mechanical motions of matter, making the appeal of the CarteSian philosophy its intu— itive clarity. Cartesians in the first half of the eighteenth century did not feel obligate:l to accept the specific mechanical motions Descartes had used to explain indiv1 u phenomena, but they did not doubt that things like magnetism resulted from some combination of such motions. Descartes exerted a strong hold on the french mind because his readers understood him to have clarified the basis for intelligibility itself in physics. ‘ Because followers of Descartes insisted that force was transmitted only through collisions of matter, they refused to associate force with nonmaterial agenCies in nature. Nature was a realm of the material. It was unacceptable to. offer explana— tions of natural phenomena that depended on spiritual or nonmaterial occult agen— cies. To Cartesians, the assertion that force acted at a distance was equivalent to an eal to a nonmaterial a enc . . aplLeibniz’s system was fgeprelsented after his death by the natural philosopher Christian von Wolff, whose work was available to German readers Wltl'lln- a year of Leibniz’s death in 1715. Wolff regarded Descartes’s explanations of the physical world as helpful but limited. The Cartesian approach applied to what we see, but it did it: relate to the deeper reality Wolff believed lay beneath appearances. For the superficr level of appearances, Wolff was content to embrace Descartes s mechanical lnFEl‘aCthfiS to make the appearances intelligible. To explain how force acted, he too rejected t e occult agencies of medieval Scholastic thought (and therefore also action at a'distance) in favor of forces transmitted only through contact between masses. Like his mentor Leibniz, he described the physical world as a clock designed by God to work perfectly. Wolff emphasized Leibniz’s appeal to the principle of suffic1ent reason, according to which we understand the existence of something when we find the reason for it. Because everything has a sufficient reason, we can use our reason to show that the world has been made perfectly. ' The difference between the Leibnizians and the CarteSians emerged at the deeper level of reality’s basic components. Leibniz had held that matter was not equivalent to extended space, as Descartes taught, but was made up of unextended pomts he called ' mmamwmmiaw»an:wmWiWXéamassawWmmmsawuwmiamawmwmmmémmwmmmammmmammgwmkwwawmm THE RISE OF NEWTONIANISM monads. Monads were nonmaterial metaphysical entities that resembled souls. They were the source of the force; indeed, they were the source of all the activity that accom- panied matter. By making a distinction between the source of force and the means by which it was transmitted, Leibnizians were both critical of Newton’s action at a dis- tance and of Descartes’s banishing of spirit from the natural world. Newton’s cause was taken up abroad by the Dutchman W J. ’sGravesande (1688—1742), who published an introduction to the philosophy of Newton in 1720. ’sGravesande answered those critics of Newton who asserted that his action at a dis— tance amounted to a return to occult causes by declaring that gravity was not the cause of anything. It was an effect. Gravity was the name we give to the movement of bod— ies toward one another when left to themselves. According to ’sGravesande, physics should focus its attention on the results of experiments rather than try to devise grand causal explanations. Like other Nevvtonians in England, he ignored Newton’s own attempt to find a cause for gravitational force in the special kind of ethereal substance that Newton made public in the 1717 edition of the Optic/es. When Newton died in 1727, many who defended his system shunned the question of the cause of gravity, understanding the system to rest simply on Newton’s laws of motion and a gravita— tional force that acted at a distance according to the inverse square law. The vis viva controversy. Over the course of the eighteenth century Cartesians, Leibnizians, and Nevvtonians became embroiled in a disagreement known as the 212's oil/a controversy. It centered on the question of whether force in the universe could be lost—that is, whether the total amount of force in the cosmos could become dimin— ished, in which case the cosmos, left to itself, would run down and eventually come to a standstill. To many this prospect was inconsistent with their understanding of God’s creative abilities. But if force was conserved and could not be lost, how was force to be measured? In his Princzples of Philosophy, Descartes had asserted that because God was unchangeable, he “conserves the world in the same action with which he created it.” Descartes envisioned the universe as he imagined God saw it from the outside—a realm filled with material objects in motion. All this motion, which involved many collisions of matter, constituted the world’s action or activity. Descartes felt that God had invested this activity in the world at the Creation and that he held it constant. The constant exchange of motion over time among portions of matter constituted the history of nature itself. Descartes felt that the universe was a machine that would not run down because, in spite of the exchanges, God made sure that no motion was lost. The sum total of all the activity always remained the same because God had given to individual motions of matter the property, as Descartes put it, “of passing from one to the other, according to their different encounters.” But how was one to measure this “action”? Discussion of this problem continued into the eighteenth century and beyond, pitting those who preferred Descartes’s measure—something he called the “quantity of motiOii”—agaiiist others who opted for something Leibniz called 222': viva. \X/hen Descartes asked himself what might be a measure of the quantity of motion, he thought about the force that a piece of matter exerted when it encountered another 179 180 CHAPTER 9: NEWTONIANISM, THE EARTH, AND THE UNIVERSE piece of matter. That, he reasoned, obviously depended on two factors: how big the mass was and how fast it was moving. He concluded that the force of motion could be expressed as the product of mass (m) and velocity (v), and he determined that this was a measure of the quantity of motion. If we consider just two pieces of matter moving toward each other, we can calculate the force of motion of the first piece (m, 2/1) and also that of the second (7722112 ). Adding these two amounts, we have the total force of motion of the two (ml 711 + 7713U2). Descartes held that, after the collision, this total amount remained the same, although the individual velocities of the two pieces of matter might change. Whatever velocity was given up by one piece of matter was given to the other, so that the total sum of the masses times their velocities remained the same. What happened in the case of just two pieces of matter also happened in every other collision in the universe. The sum total of what Descartes identified as the force of motion remained the same, while the changes in the velocities of individual pieces of matter due to collisions constituted the activity of the universe. For Descartes, God’s immutability meant that the total force of motion in the universe was conserved and the universe would run forever. There are problems with Descartes’s claim, the most obvious of which is that it does not work for what are called inelastic collisions. If two equal blobs of clay move directly toward each other at equal velocities, when they collide they do not rebound at the same velocity but stick together, and the motion stops. What hap- pened to the total force of motion in this case? It would appear that it has not been conserved but destroyed. To incorporate situations like this into Descartes’s analy— sis, his follower, Christian Huygens, asserted that it was necessary to specify the direction in which the masses were moving. In other words, the forces of motion of masses moving directly toward each other must be considered opposite in sign. If in the above case the masses are equal, and if the first mass of clay is assigned a positive force of motion (+ my), then the second would have an equal negative force of motion (—— 7722/). Adding up the total before and after the collision would give zero in both cases. Had the masses not been clay, but some perfectly elastic substance, then the total force of motion would still have been zero before and after the collision, except that the velocities of the two equal masses would have changed sign as they rebounded from each other. The contrary motions God had put into the universe at its beginning balanced each other in the end. This improvement made by Huygens, however, still left a major problem. With every inelastic collision there would be less motion in the universe. That would mean that the actual motion in the universe was running down, a result unacceptable to Descartes. He had proposed his idea in order to guarantee that the machinery of the universe would continue to run. In an article in 1686 entitled “A Brief Demonstration of a Notable Error in Descartes,” Leibniz pointed out that Descartes’s measure of the force of motion would not, in fact, prevent the universe from running down. He proposed a differ- ent measure of the force of motion, something he called 111': vim, or “living force.” The problem of the running down of the universe was an issue as long as the force of motion was regarded as a signed quantity—one that could be positive or negative. As such one force could destroy another, diminishing the total God had originally mwwmeMMmWWMW/nWMW/ww . MmmmmmwmmmWmmwxmmsmwmzw THE RISE OF NEWTONIANISM invested in his creation. Leibniz proposed that a better measure of the force of motion was proportional to the mass times the square of the velocity (771112), which was always a positive quantity. He claimed that in inelastic collisions, like the one involving blobs of clay, the vi: aim: was not destroyed when the pieces of clay stopped moving after collision; rather, the motion was transferred to the particles that made up the clay. So the total motion continued at another level, the amount of 111': vz'wz in the universe remained the same, and the universe did not run down. Many people did not accept 212': vim, if for no other reason than it was too abstract a notion. Nor was Leibniz persuasive with his explanation of why 212's viva was not lost during inelastic collisions. Among those who came out in favor of 111': viwz as a meas- ure of the force of motion was the Dutch Newtonian, ’sGravesande. His major con— tribution to the discussion—which resulted from his wish to base conclusions as much as possible on experiments——was to think of measuring the efiéct a moving mass might have, rather than merely the force it might exert. Thinking of the force of a mass in motion as the afict (or damage) the mass produced in a collision, as opposed to the pus/7 exerted during a collision, proved to make a difference. ’sGravesande did a series of experiments in which he dropped masses onto clay and then measured the dents that were made. He varied the heights and the weights of the masses, measuring the various dents produced. He found that the impressions in the clay were the same if, when he used a mass with half the weight of another (although of the same size and shape), he dropped it from twice the height. Descartes, of course, would conclude that, if the dents were the same in the two cases, then the measure of the motion should be mu in both cases. But ’sGravesande showed that because the lesser mass was dropped from a greater height, it hit the clay at a greater speed (Viv). He demonstrated that the product of the lesser mass (Vzm) and the greater velocity (Viv) was not 7720, but $77211. He concluded therefore that Descartes’s measure of the force of motion, mass times velocity, had to be in error. ’sGravesande said the correct measure of the force of motion was %mv2. This meas— ure covered both of the preceding cases. In the first case, when the mass was 772 and the velocity was 1/, his formula gave Van/2212. In the second case, when the masswas 1/2772 and the velocity was Viv, the product of one—half the mass times the velocity squared also gave Vzmvz. So for ’sGravesande the measure of the force of motion caus— ing the dent made in the first case did equal that causing the dent made in the second. ’sGravesande had shown to his own satisfaction that Leibniz’s 112's viwz was a better measure of the force of motion than Descartes’s quantity of motion. By siding with Leibniz here, ’sGravesande not only opposed the Cartesians. In this instance he also went against Newton, who did not regard vi: vim as anything real. Just as Leibniz had found, ’sGravesande discovered that not everyone immediately agreed with him; in fact, the debate about conservation of quantity of motion and of vi: viwz continued throughout the eighteenth century. The discussion, recall, had been initiated in a theological context having to do with God’s preservation of action in the world. With the exception of those who agreed with Newton (who felt that God would step in to correct the universe if it ran down sufficiently), it was impor- tant to the participants in the discussion to find an explanation that would prevent the universe from slowly degrading. 181 182 Voltaire CHAPTER 9: NEWTONIANISM, THE EARTH, AND THE UNIVERSE The Growth ofNewton’s Reputation Newton’s work finally came to the attention of a wider public in France through a popular account of its basic conclusions that appeared in 1733. In addition, a pum- ber of issues came to the surface after 1730 whose outcomes promoted Newtons rep- utation as a man ahead of his time. Not only had he seen farther than those who came before him, but in some cases he appeared to have anticipated solutions to problems that arose only after he had departed. The accumulated effect of these developments contributed to the emergence by the latter part of the century of a prominent group of French Newtonian natural philosophers. The popularization of Newton in France. The introduction of Newton’s ideas to many in France occurred in 1733, when Francois Marie Arouet, who had taken the pen name Voltaire, published his Philosophical Letters. The French authorities had imprisoned Voltaire earlier in his career because of satirical things he had written about the French government. When he insulted a powerful nobleman in 1726, he was given the choice of another stint in prison or a period in exile. He chose the latter, living in England for the next three years. While in England he studied the customs of the English, their form of government, and the ideas of their philosophers, and he was especially drawn to the work of Newton. In his Letters he praised Newton, whom he called “this destroyer of the Cartesian sys— tem,” and went on to present a comparison ofNewton’s system to that of his countryman Descartes. After declaring that Newton had proven by experiments that Descartes was wrong about the universe being filled everywhere with matter, Voltaire proclaimed that Newton “brings back the vacuum, which Aristotle and Descartes had banished from the world.” In the Letters Voltaire carefully explained the role played by gravitational force, “the great spring by which all Nature is moved,” reproducing a summary of Newton’s proof that the moon and planets are held in their orbit by this force. The reader quickly realized that in Voltaire’s view Newton’s system was far superior to any other. Along with his preference for Newton, it was clear that Voltaire also preferred English customs, laws, and society to their French counterparts. The message of the book got Voltaire into trouble once mor...
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