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# Physics: Newtonian Physics

## Introduction

Newtonian physics, also called Newtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist Sir Isaac Newton (1642–1727). Several ideas developed by later scientists, especially the concept of energy (which was not defined scientifically until the late 1700s), are also part of the physics now termed Newtonian.

Newtonian physics can explain the structure of much of the visible universe with high accuracy. Although scientists have known since the early twentieth century that it is a less accurate description of the physical world than relativity theory and quantum physics, corrections required for objects larger than atoms that move significantly slower than light are negligible. Since Newtonian physics is also mathematically simple, it remains the standard for calculating the motions of almost all objects from machine parts, fluids, and bullets to spacecraft, planets, and galaxies.

## Historical Background and Scientific Foundations

Although Newton redefined the basic concepts of mechanics and devised his laws of motion and universal gravitation in the late 1600s, he based his work on important scientific discoveries about matter and motion that had already been established. Without these earlier achievements, he could not have produced the four laws that are the foundation of Newtonian physics: his three laws of motion and his law of universal gravitation.

From the at least the fourth century BC until Newton's time, European scientific thought was modeled largely on the theories of ancient Greek thinkers such as Plato (c.428–348 BC) and Aristotle (384–322 BC). So great was Aristotle's influence, in fact, that the world-view held by most European scholars until the seventeenth century is termed Aristotelian. This did not rule out the investigation of events using experiment and mathematics, which are now the heart of the scientific method, but it did not particularly encourage them either. This is because Aristotelians saw the universe and everything in it primarily in terms of their meaning, rather than cause and effect.

Aristotelians also inherited flawed assumptions about specific physical questions. For example, if an object were in motion, they assumed something must keep it in motion, whether a mysterious quality in the object called impetus, the surrounding air, or something else. For many centuries this mindset confounded efforts to unravel the physics of motion.

Despite many preconceptions, the Middle Ages and the Renaissance did produce some significant scientific developments. Manual workers such as joiners, builders, navigators, and shipbuilders accumulated knowledge about practical methods and materials. Scholars advanced knowledge in several branches of mathematics, recovering the long-forgotten or poorly copied works of the Greek mathematicians Euclid (born c.300 BC) and Archimedes (287–212) and making new discoveries of their own. In the 1500s, stimulated by existing Arab work, algebra was developed by Italian mathematicians such as Niccolò Fontana Tartaglia (1499–1557). The word “algebra” itself is from the Arabic al-jabr, meaning “reunion.” Many tools, physical and intellectual, had to be in place before Galileo Galilei (1564–1642), Newton, and the other founders of modern physical science could achieve their triumphs in the sixteenth and seventeenth centuries.

The way was partly prepared for the new way of thinking that Newton and others called “experimental philosophy” or “mechanical philosophy” by French philosopher and mathematician René Descartes (1596–1650). Descartes assumed, like most earlier thinkers, that the universe can be explained by top-down reasoning from general first principles, with little or no need for particular experiments; famously, he thought that all knowledge could proceed from the logical statement “I think, therefore I am” (Cogito ergo sum in the original Latin).

Descartes reasoned wrongly that neither atoms nor a vacuum could exist. Yet he prefigured the modern scientific approach by seeking a comprehensive, mechanical, rational interpretation of nature. In particular, he proposed that the motions of the planets could be accounted for by a vortex or swirl of “subtle matter”—matter not perceptible to the senses—stirred throughout the solar system by the rotation of the sun on its axis. The sun, he theorized, like a spinning whisk at the center of a large bowl of cream, set the subtle matter twirling around it; since the twirling would naturally diminish with distance, this, according to Descartes, explained why planets more distant from the sun move more slowly than those that are closer.

Descarte's vortex theory of planetary motion was popular in Europe at the time Newton published his own theory of the solar system in Philosophiae Natu-ralis Principia Mathematica (Mathematical Principles of Natural Philosophy), usually referred to simply as the Principia (1687). Newton's mechanics explained both earthly and planetary motion, signaling the downfall of Descartes's vortex theory and his entire approach to knowledge. Experiment combined with mathematics, rather than top-down philosophical speculations, would define all serious attempts to understand the physical world from that time onward.

It was no accident that the motions of the planets concerned both Descartes and Newton. Before the advent of Newtonian physics, observational astronomy was the only science with mathematically precise knowledge or predictive power. Chemistry consisted mostly of unconnected bits of practical knowledge accumulated by trial and error. Modern concepts of the elements did not begin to develop until English scientist Robert Boyle's (1627–1691) experiments disproved Plato's theory that all matter is composed of four elements—earth, air, fire, and water—in 1660.

The existence of microorganisms was not known until 1676, when Dutchman Antoni van Leeuwenhoek (1632–1723) built the first microscope. Medicine, too, was rudimentary in Newton's day; the fact that the heart pumps blood through the body, for example, only became widely accepted after 1616, when this theory was published in works by English doctor William Harvey (1578–1657).

Social Milieu

The 1600s were a time of upheaval in all aspects of European society, including religion, science, politics, commerce, and the arts. The Protestant Reformation, starting in the early 1500s, had split the centuries-old religious consensus of Europe along approximately geographic lines, with Protestant countries to the North and Roman Catholic countries to the South. The Reformation called ancient patterns of thought into question and triggered wars that plagued the continent for decades.

The Commercial Revolution, which ran from the early 1500s to about 1650, also helped break up old patterns of thought and motivate new discoveries in science and technology. Techniques for long-distance ocean navigation were needed, stimulating new precision work in astronomy and clock making.

England, Newton's native country, suffered especially brutal upheavals. From 1642 to 1651, a bloody

civil war pitted the Puritans (Calvinist Protestants) against the Anglicans (members of the English state church). After the Puritans beheaded King Charles I (1600–1649) in 1649, Oliver Cromwell (1599–1658) became first chairman of the Council of State, then Lord Protector from 1653 until his death in 1658. The British monarchy was restored under Charles II in 1660.

A few years later, during an outbreak of plague, young Isaac Newton—a Puritan who was also fascinated not only by science but alchemy and the biblical book of Revelation—took refuge from pestilence in his mother's country house. There, in a space of 18 months (1665–1666), he conceived the basic elements of a new physics: the three laws of motion, the law of universal gravitation, and calculus. He also did extensive work in optics, though he did not have the revolutionary effect there that he did in mechanics.

The Science

Medieval astronomy was based on Claudius Ptolemy's (AD c.90–c.168) Mathematike syntaxis (Mathematical collection), better known in the West by a shortened form of its Arabic title, the Almagest. According to Ptolemy, the planets were embedded in vast crystal spheres centered around Earth and moving in changeless, perfect circles. Their motion was imparted by supernatural means from the outermost sphere of all, that of the fixed stars. This model was challenged by Nicolaus Copernicus (1473–1543) in the 1500s. In 1543 he published De revolutionibus orbium coelestium (Six books concerning the revolutions of the heavenly orbs), in which he proposed that the sun, not Earth, is at the center of the universe.

Copernicus's revision of the universe prompted a wave of new astronomical work. Tycho Brahe (1546–1601) made naked-eye observations of the motions of the sun, moon, and planets that were the most accurate to that date. After Brahe's death, his assistant Johannes Kepler (1571–1630), an advocate of the Copernican system, tried to fit Brahe's precise new observational data to equations describing planetary orbits, beginning with the planet Mars. At first he assumed a circular

## IN CONTEXT: GALILEO AND THE CHURCH

Galileo Galilei (1564–1642) was an Italian physicist who perfected the modern scientific method. His work on accelerated motion was essential groundwork for Newtonian physics. Unfortunately, Galileo's defense of Copernican (or heliocen-tric) astronomy—the view that Earth rotates around the sun, not the other way around—ran afoul of established religious doctrine. The Catholic Church, which taught that Earth is stationary, declared in 1616 that heliocentrism was “false and altogether contrary to Scripture.”

In 1633 the elderly Galileo was brought before the Inquisition and found guilty of heresy (preaching incorrect belief) and shown the instruments of torture that would be used on him if he did not retract his statements. Under duress, Galileo publicly retracted his belief in heliocentrism and spent the rest of his life under house arrest. Blind and disappointed, he died in 1642, the same year Isaac Newton was born. Because of Galileo's conviction, scientists were fearful of speaking truthfully in Southern Europe for decades afterward, and most of the work in the Scientific Revolution was thereafter done in England and Northern Europe.

The church eventually admitted its mistake, but not until many years later. In 1822 the church lifted its ban on books teaching the view that Earth goes around the sun; in 1981 Pope John Paul II (1920–2005) convened a new commission to study the Galileo case. In 1992 the commission declared that the case had been marked by “tragic mutual incomprehension.” This has not been enough for some, including a former director of the Vatican observatory (from 1978–2006), priest George Coyne (1933–), who would have liked a more thorough admission of responsibility for Galileo's persecution and a true apology.

orbit for Mars, as all had done before him, but he could not make the observational data fit. Eventually he found that the best fit was given not by a circle but by an ellipse (a curve like the outline of an egg).

Kepler was the first to describe the motions of the planets in terms of mathematical laws. He stated three, two of which involved time as a variable. Using time to describe the world mathematically was a significant advance for physics; the European scientific tradition inherited from the Greeks was primarily static (motion-less) and geometrical. Its attention went primarily to the shapes of curves and rarely used mathematics to describe dynamic (time-dependent) processes.

Kepler published two of his laws in 1609 and the third in 1619. They were purely descriptive, that is, they offered no explanation of why the planets acted as speci-fied, nor did they describe how any other objects (such as falling apples) might move.

After Brahe and Kepler, Galileo laid crucial groundwork for Newtonian physics. He mistakenly rejected Kepler's proof that the planets moved in elliptical orbits, but conducted precise experiments in the laboratory to characterize the movements of accelerating bodies—objects that are changing the direction or rapidity of their motion. Like Kepler, he searched for mathematical laws to describe the way physical systems change over time.

Galileo concluded that the distance covered by a steadily accelerating object is proportional to the square of the time it has been accelerating. He also discovered that objects accelerate steadily under the influence of gravity, which he treated as a constant force unaffected by distance (which it is, approximately, near Earth's surface). He found that objects accelerate with equal speed regardless of their weight—that is, a heavier ball does not fall faster than a light ball of the same size. Perhaps most fundamentally, he found that objects tend to maintain their straight-line motion unless acted upon by a force. This overthrew the Aristotelian view that a force is needed to maintain an object's state of motion.

With Galileo's physics and Kepler's astronomy in place, the stage was set for Newton's triumph.

Newton's Physics

Newton's influence is due mostly to his major work, Philosophiae Naturalis Principia Mathematica, published in 1687 and best known by the shortened form of its Latin title, Principia. This work was produced partly at the urging of Newton's friend, English astronomer Edmond Halley (1656–1742), who also financed the project, helping to produce one of the most important works in the history of science.

Of all the scientists working in his day, only Newton conceived that there could be a single universal system of mechanics—that is, a physics that would describe both earthly and celestial motions at the same time. In the Principia, Newton established such a physics with his three laws of motion and his law of gravitation. Elaborating these laws and unifying them with a rigorous idea of “energy” in the late eighteenth century produced a system, Newtonian (or mechanical) physics, that is still used today for everything from engineering design to the analysis of galactic motion.

Newton's three laws of motion are as follows:

1. An object remains at rest or moves in a straight line at a constant speed unless acted upon by a nonzero total force.
2. A force acting on a body causes it to accelerate (change its state of motion) to a degree that is proportional to the body's mass. Stated as an equation, writing F for force, m for mass, and a for acceleration, we have F = ma. In

other words, an object's velocity and momentum changes with time in proportion to the force acting on it.

3. Forces occur in pairs pointing in opposite directions.

This law is most often stated as: For every action there is an equal and opposite reaction. For example, when a gun fires, the force acting on the bullet as it accelerates through the barrel is equal to the recoil of the gun acting on the shooter's hand or shoulder.

The fourth basic law of Newtonian physics is the law of universal gravity: F = Gm 1 / r 2 m 2. Here F is gravitational pull, G is the universal gravitational constant (a fixed number, G = 6.6742 × 10 -11 m 3 kg -1 s -2), m 1 is the mass of one object, m 2 is the mass of the other object, and r is the distance between the centers of the two objects. Larger masses mean larger gravitational force,

## IN CONTEXT: SURPRISE: NEWTON WAS RIGHT!

Even though three centuries have passed since Isaac Newton published his theory of gravitation in 1687, scientists are still testing it. Newton's law says that the gravitational attraction between any two objects decreases with the square of the distance between them; doubling the distance means one fourth the force. This type of relationship, called an inverse-square law, is accurate at the scale of baseballs, planets, or galaxies, but, according to quantum physics, should fail when objects are close together. Masses separated by as little as the width of a human hair (56 millionths of a meter or micrometers, µm) should, according to some theories, experience measurably less gravitational attraction than Newtonian law predicts.

In 2006, a group of physicists led by D.J. Kapner tested Newton's law of gravitation by measuring the gravitational pull between a pair of small, spinning metal disks as little as 56 µm apart. They found that Newton's law was still valid even at this distance.

This simple result—derived from an experimental setup that could fit inside a soda can—may have consequences for our understanding of the whole universe. In the 1990s astronomers discovered that 70% of all the energy and mass in the universe consists of a mysterious “dark energy” of a still unknown nature. Some theories attempting to explain dark energy, such as string theory, make predictions about the force of gravity. At least one such theory—the fat-graviton theory—was ruled out by the recent spinning-disk experiment. In coming years, even more sensitive tests of Newton's law will be made to further constrain physicists' attempts to explain the nature of universe.

bigger F; more distance between the masses, bigger r, means less.

Newton showed that these four laws could account simultaneously for Galileo's laboratory results—the behavior of everyday objects in the vicinity of Earth's surface—and for the motions of the planets. A single set of laws, compact enough to jot down on a card, could describe the motions of all the stars, planets, and moons in the universe. Moreover, to achieve this astonishing result Newton had had to invent a new branch of mathematics to handle quantities that change with time in an unsteady way. He called it the method of fluxions, but today it is known as calculus, the basic mathematical language of all physical science.

Impacts and Issues

Most branches of science were in a disorderly state when Newton published his Principia in 1687. Newtonian A feather and an apple falling at the same rate in a vacuum chamber. This experiment demonstrates the validity of Isaac Newton's (1642–1727) ideas on gravity and inertia. © Jim Sugar/Corbis. mechanics was the first scientific discipline to achieve apparent perfection: Newton's laws passed every experimental test, explained the tides and other vexing problems of astronomy, and defeated the Cartesian theory of vortices.

But it was also controversial. Critics, such as German scientist Gottfried Leibniz (1646–1716), who invented calculus independently of Newton, attacked Newton's theory of gravitation as mystical or useless: how could one mass act on another instantaneously across a distance, without being in direct or at least indirect contact with it? The new theory did not explain anything. Newton was disturbed by this problem too, saying that he found what was called “action at a distance” implausible. Yet he defended his method, writing in 1715: “His [Leibniz's] arguments against me are founded upon metaphysical & precarious hypotheses & therefore do not affect me: for I meddle only with experimental Philosophy.” It did not matter, Newton maintained, whether he had explained gravity or not: an

explanation was desirable, but could not be had until an accurate description of what gravity does was available.

Leibniz also criticized Newton's assumptions about absolute space, which, the latter stated, if it existed, would be flat everywhere (i.e., obey the laws of Euclidean geometry) and infinite in all directions. Leibniz's philosophical objection was vindicated over 200 years later when German physicist Albert Einstein (1879–1955) showed that the idea of absolute Newtonian space had to be abandoned and replaced by curved, relative space.

Despite its defects, Newtonian physics revolutionized science. Mathematically stated theories tested against physical observations became the standard in almost all fields of scientific thought. Banished forever was medieval reliance on authoritative books and the Cartesian reliance on reason unchecked by observations.

Impact on Society

The Principia, written in Latin and intensely mathematical, was not read widely. Its intellectual impact on society was mediated by authors who took up the cause of Newton's “experimental Philosophy” and wrote for the general public. The most influential of these was French thinker Voltaire, born François-Marie Arouet (1694–1778), who explained Newton's science accurately in nontechnical terms in his book Eléments de la philosophie de Newton (Elements of Newton's philosophy, 1738).

For Voltaire and similar thinkers, Newton's triumph in mechanics proved that science would eventually explain everything, including human actions, in terms of rigid cause-and-effect (deterministic) laws: “It would be very singular,” Voltaire wrote, “that all nature, all the planets, should obey eternal laws, and that there should be a little animal, five feet high, who in contempt of these laws, could act as he pleased, solely according to his caprice.”

Armed with the ironclad credibility of the new science, these writers began to attack traditional religion. Their skepticism contributed to a decline in religious belief in industrial societies that has continued steadily to the present day and is especially true in Europe. In the United States, the general populace remains almost universally religious, but scientists express lower rates of religious belief in polls, with physicists—Newton's intellectual heirs—being the most nonreligious group (only about 20% of physicists believed in God as of 1998). This is ironic, given that Newton himself was a devout Christian.

Some of Newton's contemporaries, such as Irish philosopher Bishop Berkeley (1685–1753), attacked the new materialism. However, such holdouts fought a losing battle, and, during the eighteenth century, the intellectual climate in England and northern Europe became predominantly pro-scientific and deterministic.

The new science also transformed the world in economic, military, and other matters. Newtonian physics did not make these changes alone: chemistry, medicine, mathematics, electromagnetics, and other scientific fields were also crucial. Other forms of science took up the Galilean and Newtonian methods of mathematical law-testing. Together, the new science unleashed a flood of new technologies that drove the Industrial Revolution starting in the late 1700s and has continued to the present.

## Modern Cultural Connections

Newtonian physics continues to be applied in every area of science and technology where force, motion, and gravitation must be reckoned with. However, today's physicists, unlike Newton, know that his laws do not work in all circumstances. The behaviors of objects traveling near the speed of light, or interacting on the size scale of subatomic particles, are not described accurately by Newtonian physics. Relativity theory and quantum physics are required in such non-Newtonian realms, and even these theories have limits.

Despite the advent of later, more complete theories, scientists continue to study Newtonian physics. As

## IN CONTEXT: THE ULTIMATE NEWTONIAN MACHINE

A spacecraft is the ultimate Newtonian machine because it relies for propulsion on rockets, which are the most straightforward possible application of Newton's second law of motion, the principle that every force acting on some object is paired with an equal and opposite force acting on some other object. Gases exiting a rocket push against the rocket's combustion chamber, and the combustion chamber pushes with equal and opposite force against the gases. The gases fly off in one direction, the chamber (with rocket attached) in the opposite direction.

A spacecraft that has left the atmosphere is governed only by the forces exerted by its rockets—Newton's second law—and the force of gravity, described by Newton's law of universal gravitation. Newton's laws therefore account for almost everything that affects the path of a spacecraft in flight. During the 1968 journey of Apollo 8, which circled the moon, a child on Earth wondered aloud who was driving the spaceship. When the question was relayed to him by radio, astronaut Bill Anders replied, “I think Isaac Newton is doing most of the driving right now.”

Spacecraft and rocketry have had a profound impact on modern society. Space probes have greatly multiplied our knowledge of the planets and more distant universes, satellites have transformed communications, and ballistic missile's—equipped with a non-Newtonian invention, the nuclear bomb—have made it physically possible to destroy most of the human race in a few minutes.

described in the sidebars, scientists have measured the force of gravity at distances as small as the width of a human hair to see if Newton's law holds for objects so close together. Their results, published in 2007, showed that Newtonian physics still held, even at such small distances. This ruled out of some of the most promising theories put forward to explain the mysterious fact (discovered in the late 1990s) that the universe is not only expanding, but expanding more quickly all the time.

In the early 1980s research began to focus on the possibility that Newtonian physics may not be correct even in non-quantum, non-relativistic realms—situations in which it has always been believed to be essentially perfect. A new type of physics, called modified Newtonian dynamics (MOND), first proposed by Israeli physicist Moti Milgrom in 1983, suggests that Newton's second law should be modified for small accelerations. Since small accelerations are common in astronomical settings, MOND would account for a number of observations that other theories describe as the result of an unknown, invisible form of matter called dark matter. MOND is controversial; some physicists support it, but most are convinced that some form of dark matter accounts for those observations. In the scientific style established by Newton and Galileo, the question will eventually be settled by comparing the predictions of rival theories to actual observations.

bibliography

Books

Bell, Arthur. Newtonian Science. London: Edward Arnold Publishers, Ltd., 1961.

Cohen, I. Bernard. The Newtonian Revolution: With Illustrations of the Transformation of Scientific Ideas. New York: Cambridge University Press, 1980.

Crombie, A.C. Medieval and Early Modern Science, Vol. II: Science in the Later Middle Ages and Early Modern Time's: XIII–XVII Centuries. New York: Doubleday, 1959.

Laue, Max von. History of Physics. Translated by Ralph Oesper. New York: Academic Press Inc., 1950.

Periodicals

Ball, Philip. “A Jump That Would Prove Newton Wrong.” Nature. 446 (2007): 357.

Ignatiev, A. Yu. “Is Violation of Newton's Second Law Possible?” Physical Review Letters 98 (2007):101101.

Kapner, D.J., et al. “Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale.” Physical Review Letters 98, no. 2 (2007).

Speake, Clive. “Gravity Passes a Little Test.” Nature 446 (March 1, 2007): 31–32.

Larry Gilman

Paul Davies

K. Lee Lerner