Physics

The period of the scientific revolution can be taken to extend, simplistically but handily, from 1543, with the publication of Nicolaus Copernicus's De revolutionibus orbium coelestium, to 1687, with the publication of Isaac Newton's Philosophiae naturalis principia mathematica, often referred to simply as the Principia. The term "revolution" remains useful, despite the fact that scholars have suggested that the period shows significant continuities with what came before and after. Copernicus (1473–1543) was attracted to a heliocentric, or Sun-centered, model of the universe (already considered over one thousand years before by Aristarchus of Samos) because it eliminated a number of complexities from Ptolemy's model (including the equant), provided a simple explanation for the diurnal motion of the stars, and agreed with certain theological ideas of his own regarding the Sun as a kind of mystical motive force of the heavens. Among the problems posed by Copernicus's model of the heavens, the most serious was that it contradicted Aristotelian physics.

Heliocentrism was pursued again by the German mathematician Johannes Kepler (1571–1630). Motivated by a deep religious conviction that a mathematical interpretation of nature reflected the grand plan of the Creator and an equally deep commitment to Copernicanism, Kepler worked with the Danish astronomer Tycho Brahe (1546–1601) with the intention of calculating the orbits of the planets around the Sun. After Brahe's death, Kepler gained control of his former associate's data and worked long and hard on the orbit of Mars, eventually to conclude that it was elliptical. Kepler's so-called "three laws" were identified later by other scholars (including Newton) from different parts of his work, with the elliptical orbits of the planets becoming the first law. The second and third laws were his findings that the area swept out by a line connecting the Sun and a particular planet is the same for any given period of time; and that the square of a planet's period of revolution around the Sun is proportional to the cube of its distance from the Sun.

The career of Galileo Galilei (1564–1642) began in earnest with his work on improved telescopes and using them to make observations that lent strength to Copernicanism, including the imperfections of the Moon's surface and the satellites of Jupiter. His public support of Copernicanism led to a struggle with the church, but his greater importance lies with his study of statics and kinematics, in his effort to formulate a new physics that would not conflict with the hypothesis of a moving Earth.

His work in statics was influenced by the Dutch engineer Simon Stevin (1548–1620), who made contributions to the analysis of the lever, to hydrostatics, and to arguments on the impossibility of perpetual motion. Galileo also repeated Stevin's experiments on free fall, which disproved Aristotle's contention that heavy bodies fall faster than light bodies, and wrote about them in On Motion (1590), which remained unpublished during his lifetime. There, he made use of a version of Buridan's impetus theory (see sidebar, "Causes of Motion: Medieval Understandings"), but shifted attention from the total weight of the object to the weight per unit volume. By the time of Two New Sciences (1638), he generalized this idea by claiming that all bodies—of whatever size and composition—fell with equal speed through a vacuum.

Two New Sciences summarized most of Galileo's work in statics and kinematics (the "two sciences" of the title). In order to better study the motion of bodies undergoing constant acceleration, Galileo used inclined planes pitched at very small angles in order to slow down the motion of a rolling ball. By taking careful distance and time measurements, and using the results of medieval scholars (including the mean speed theorem), he was able to show that the ball's instantaneous velocity increased linearly with time and that its distance increased according to the square of the time. Furthermore, Galileo proposed a notion of inertial motion as a limiting case of a ball rolling along a perfectly horizontal plane. Because, in this limiting case, the motion of the ball would ultimately follow the circular shape of the earth, his idea is sometimes referred to as a "circular inertia." Finally, Galileo presented his analysis of parabolic trajectories as a compound motion, made up of inertial motion in the horizontal direction and constant acceleration in the vertical.

The French philosopher René Descartes (1596–1650) and his contemporary Pierre Gassendi (1592–1655) independently came up with an improved conception of inertial motion. Both suggested that an object moving at constant speed and in a straight line (not Galileo's circle) was conceptually equivalent to the object being at rest. Gassendi tested this idea by observing the path of falling weights on a moving carriage. In his Principia philosophiae (1644), Descartes presented a number of other influential ideas, including his view that the physical world was a kind of clockwork mechanism. In order to communicate cause and effect in his "mechanical philosophy," all space was filled with matter, making a vacuum impossible. Descartes suggested, for example, that the planets moved in their orbits via a plenum of fine matter that communicated the influence of the Sun through the action of vortices.

Building on work in optics by Kepler, Descartes used the mechanical philosophy to derive the laws of reflection and refraction. In his Dioptrics (1631), he proposed that if light travels at different velocities in two different media, then the sine of the angle of incidence divided by the sine of the angle of refraction is a constant that is characteristic of a particular pair of media. This law of refraction had been discovered earlier, in 1621, by the Dutch scientist Willibrord Snel, though Descartes was probably unaware of this work. In 1662, the French mathematician Pierre de Fermat recast the law of refraction by showing that it follows from the principle that light follows the path of least time (not necessarily the least distance) between two points.

The study of kinematics yielded various conservation laws for collisions and falling bodies. Descartes defined the "quantity of motion" as the mass times the velocity (what is now called "momentum") and claimed that any closed system had a fixed total quantity of motion. In disagreement with Descartes, Gottfried Wilhelm von Leibniz (1646–1716) suggested instead the "living force" or vis viva as a measure of motion, equal to the mass times the square of the velocity (similar to what is now called "kinetic energy"). For a falling body, Leibniz asserted that the living force plus the "dead force," the weight of the object times its distance off the ground (similar to "potential energy"), was a constant.

The culmination of the scientific revolution is the work of Isaac Newton. In the Principia (1687), Newton presented a new mechanics that encompassed not only terrestrial physics but also the motion of the planets. A short way into the first book ("Of the Motion of Bodies"), Newton listed his axioms or laws of motion:

1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed …
2. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed …
3. To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction … (1999, pp. 416–417)

The first law restates Descartes's concept of rectilinear, inertial motion. The second law introduces Newton's concept of force, as an entity that causes an object to depart from inertial motion. Following Descartes, Newton defined motion as the mass times the velocity. Assuming that the mass is constant, the "change of motion" is the mass (m) times the acceleration (a); thus the net force (F) acting on an object is given by the equation F ma. Analyzing the motion of the Moon Figure 2. Optics: Newton's crucial prism experiment led Newton to the inverse-square law of universal gravitation. Partly as a result of a debate with the scientist Robert Hooke (1635–1703), Newton came to see the Moon as undergoing a compound motion, made up of a tangential, inertial motion and a motion toward the Sun due to the Sun's gravitational attraction. The Dutch physicist Christiaan Huygens (1629–1695) had suggested that there was a centrifugal force acting away from the center of rotation, which was proportional to v²/r, where v is the velocity and r is the distance from the center of rotation. Newton had derived this result before Huygens but later renamed it the centripetal force, the force that is required to keep the body in orbit and that points toward the center of rotation. Using this relation and Kepler's finding that the square of the period was proportional to the cube of the distance (Kepler's "third law"), Newton concluded that the gravitational force on the Moon was proportional to the inverse square of its distance from Earth.

Newton presented his law of universal gravitation in the third book of the Principia ("The System of the World"), and showed that it was consistent with Kepler's findings and the orbits of the planets. Although he derived many of these results using a technique that he invented called the method of fluxions—differential calculus—Newton presented them in the Principia with the geometrical formalism familiar to readers of the time. He did not publish anything of his work on the calculus until De Analysi (1711; On analysis) during a priority dispute with Leibniz, who invented it independently.