Creating classical physics by accounting for the phenomena of the physical world through mathematics
Isaac Newton
(1642–1727)
The two bombshells dropped by Albert Einstein—the Special Theory of Relativity in 1905 and the General Theory of Relativity in 1915—disrupted classical physics by showing that Newton’s Three Laws of Motion, which had been accepted as absolute truth since 1687, when they were published in his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), were only approximately correct. According to Einstein, Newton’s Laws of Motion broke down when the velocities in question approached the speed of light. Later in the twentieth century, the emergence of quantum mechanics showed that the laws also broke down at the micro level.
Why, then, do we still study Newton if modern physics has effectively repealed his “laws”? The answer is very simple. While the mechanics of Newton do not apply near or at the speed of light or in the unimaginably small spaces of atomic-particle physics, none of us lives near or at the speed of light or within the spaces defined by particle physics. Light speed is real, and the behavior of atomic particles is real. But, day to day, neither of these much matters to us. We live in a reality that is both much slower than the speed of light and much bigger than the dimensions of atomic particles. In our reality, everything Newton revealed to us remains of great use and is absolutely fundamental.
No theorist of physics is more important or more original—and therefore more disruptive of all that went before him—than Newton. His laws of motion and his law of universal gravitation explained all that moves on earth or in heaven. He invented the calculus, giving human beings a method for calculating continuous change, which, until calculus, was essentially incalculable. He explained the nature both of light and of color. He both enabled and triggered the great scientific revolution of the seventeenth century. Since we cannot travel at light speed or live within an atom, we cannot get away from Isaac Newton.
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According to the Julian calendar then in use, Isaac Newton was born on Christmas Day 1642, in Woolsthorpe, near Grantham, Lincolnshire. It was an auspicious day on which to be born—unless, like Newton, you were premature, tiny, frail, and fatherless—the illiterate yeoman farmer who sired him having died before his son entered the world. Newton’s widowed and impoverished mother entrusted his care to his grandmother by the time he was three. She remarried a wealthy rector who would take Hannah Newton as his wife only if she were free to raise his family, not hers. As fate would have it, he was not long-lived, and Hannah returned to Woolsthorpe in 1653 after his death.
She returned to an unhappy, lonely boy, whom she took out of school so that he could work the farm. To the immeasurable benefit of science, he was a miserable farmer, and he resumed his schooling in Grantham, preparing to enter Trinity College, Cambridge. When he left Woolsthorpe in June 1661, it was without regret. At Cambridge, he found the home he had never really had.
Cambridge was highly respected in the seventeenth century; but, like other universities of the era, it was still largely dedicated to an early Renaissance curriculum. Aristotle and a handful of other classical authors were the basis of education. Though he reveled in his books, Newton was by no means a standout undergraduate—at least not in class. Much of his education during his Cambridge years was self-administered. He read contemporary thinkers, such as Descartes and Hobbes. In preference to Euclid’s Elements, cornerstone of the Cambridge mathematics curriculum, he embraced Descartes’s Géométrie, which was far more advanced and complex. Although he was awarded his degree in 1665, it was without honors or distinction of any kind.
Newton would have nevertheless preferred to stay on at Cambridge for graduate study, but 1665 was the first of two straight plague years, and the university was forced to shut its doors. For the next two years, Newton was compelled to wait out the plague in Woolsthorpe.
He did not idle there. He later commented that in those days of plague, he was in his “prime of age for invention, and minded mathematics and philosophy more than at any time since.” It was in the solitude of Woolsthorpe that he began the invention of what he called his mathematical “method of fluxions,” the calculus, a method that the German polymath Gottfried Wilhelm Leibniz (1646–1716) would independently invent a decade later. Calculus gave Newton and physics a mathematical procedure for calculating continuous change—rates of change and slopes of curves in the case of differential calculus, and the accumulation of quantities and the areas under or between curves in the case of integral calculus. Calculus would become the language through which the physics of a dynamic universe could be created and communicated. As if this were not sufficient achievement, during his eighteen months of enforced exile from Cambridge Newton also outlined his breakthrough theory of light and color and began to work out the mechanics of planetary motion—the problem that would result in his mature masterpiece, Philosophiae Naturalis Principia Mathematica (1687).
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In April 1667, Cambridge reopened and Newton returned. Despite his lack of official academic distinction, he gained election as a minor fellow at Trinity College. In 1668 he was awarded a master’s degree and made a Trinity senior fellow. Stunningly, in 1669, though he was yet to reach his twenty-seventh birthday, Newton was named to succeed the distinguished Isaac Barrow (1630–1677) as Lucasian Professor of Mathematics. From this new office, he set about ordering and analyzing his research into optics.
Elected to the Royal Society in 1672, he presented his first public paper, on the nature of color, demonstrating by experiment that “the colours of all natural bodies have no other origin than this, that they are variously qualified to reflect one sort of light in greater plenty than another.” In other words, white light is composed of the colors of the spectrum and color is a property of light. Objects interact with the colors of light rather than generating color themselves.
For ages before Newton, the proposition that color is intrinsic to light was subject to debate. Newton ended the dispute—almost. The prickly natural philosopher and early microscopist Robert Hooke (1635–1703), curator of experiments at the Royal Society, persisted in attacking this explanation, and so the argument over various aspects of Newton’s experimental methods roiled until 1675, when Newton published another paper, which Hooke did not disagree with but attacked as a plagiarism of his own work. Deeply wounded, Newton withdrew from public and, in 1678, suffered a nervous collapse. This was intensified the next year by the death of his mother, which caused him to withdraw even deeper.
Newton began secretively studying alchemy, accumulating and devouring books on the subject, and conducting many elaborate experiments. Until recently, modern scholars believed that Newton’s clandestine approach to alchemy was the futile pursuit of an irrational superstition. They lamented the waste of a genius’s time. This interpretation, however, reveals more about modern scholarly prejudices than it does about Newton.
Close study of Newton’s alchemical notes reveals that his experiments were quite serious and meticulously executed. He hoped to find in alchemy an insight into nature that could not be found through mathematics, mechanics, and optics. Newton saw in alchemy an assertion that hidden forces of attraction and repulsion were critical at the infinitesimal particulate level. In a sense, Newton’s alchemical insights anticipated, however vaguely, the much later insights of atomic and particle physics. More immediately, however, alchemy shaped his view of celestial mechanics, including the mysterious force he would call gravity.
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Everyone knows the story of what happened when Newton observed the fall of an apple in his Woolsthorpe garden one day in 1666. Some versions of the story portray him as dozing under an apple tree and being rudely awakened when an apple hit him on the head. In fact, his own recollection makes no mention of being apple-struck, but he did remark that in this year he “began to think of gravity extending to the orb of the Moon.”
Newton scholars today believe he had a slip of memory. The concept of gravity did not come to him suddenly with the fall of an apple, but worked its way through his mind over some twenty years. Surprisingly, it was the disputatious Hooke who spurred his thought. Hooke began corresponding with Newton in November 1679 on the subject of planetary motion. Newton replied, only to soon break off the exchange. But he did not stop thinking. Early in 1680, he began formulating the relationship between central attraction and a force, gravity, that fell off with the square of distance. He did not participate directly in the London conversations among Hooke, the astronomer Edmund Halley (1656–1742), and the architect Christopher Wren (1632–1723) concerning the problem of planetary motion—that is, what drives the planets to move, and why is that movement orbital? It was Halley who, in August 1684, left London to visit Newton in Cambridge and pose to him the question: What type of curve does a planet describe in its orbit around the sun, assuming an inverse square law of attraction?
Newton was prepared with an answer: It was an ellipse. Surprised, Halley asked him how he knew.
Newton responded that he had calculated it—but, having mislaid the calculation, he promised to do the mathematical work again and send the result to Halley.
What he sent to Halley in November 1684 was a manuscript titled De motu corporum in gyrum (On the Motion of Bodies in an Orbit). Over the next three years, his calculations explaining the motion of orbiting bodies grew into Philosophiae Naturalis Principia Mathematica. Published in 1687, this may be the single most important book in the history of science. The book is best known for its three laws of motion and the law of universal gravity. These alone explained not only planetary orbits, but the physical nature of all things that moved anywhere in the universe. The fact that someone had finally explained something so basic as why a thing fell and why a thing had weight was disruptive. But the very title of the book got to the heart of the disruption: Mathematical Principles of Natural Philosophy. Newton proved that mathematics could account for the phenomena of nature. In this, he connected the human intellect directly to the world outside the mind.
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Principia revealed something else—the basic emotional fragility of Isaac Newton. Ever the troublemaker, Hooke wanted a share of the credit for Newton’s book, and, as his dispute with Newton dragged on, Newton threatened to withhold Book III of the Principia from publication—just to spite him. When others persuaded him to proceed, Newton did so, but not before removing every mention of his enemy’s name. (Indeed, when he finally assembled and distilled all his work on light in his Opticks, he delayed publication and stopped attending meetings of the Royal Society until Hooke, ailing, finally died in 1703.
Principia made Newton famous. In 1689 he was even elected to Parliament. In 1693 he suffered another nervous collapse. After some three years, he recovered and, in need of financial support, was appointed Warden of the Mint in 1696. Ensconced in London, he basked in fame and accolades. The self-imposed delay in the publication of Opticks turned out to be fortunate, because it added to his glory at a time when he had largely ended his scientific and mathematical work. In 1705, the year after the publication of Opticks, this impoverished half-orphan from Woolsthorpe was knighted. He lorded over the Royal Society as its president and used his position to outmaneuver Leibniz to gain for himself the lion’s share of credit for calculus. He died, in London, on March 20, 1727.