Warped Passages - Lisa Randall [42]
At the beginning of the last century the British physicist Lord Kelvin said, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.”* Lord Kelvin was famously incorrect: very soon after he uttered those words, relativity and quantum mechanics revolutionized physics and blossomed into the different areas of physics that people work on today. Lord Kelvin’s more profound statement, that “scientific wealth tends to accumulate according to the law of compound interest,”† is certainly true, however, and is especially appropriate to these revolutionary developments.
This chapter explores the science of gravity, and how it evolved from the impressive achievement of Newton’s laws to the revolutionary advances of Einstein’s theory of relativity. Newton’s laws of motion are the classical physics laws that scientists used for centuries to compute mechanical motion, including motion caused by gravity. Newton’s laws are magnificent, and they allow us to make predictions of motion that work spectacularly well—well enough to send men to the Moon and satellites into orbit, well enough to keep the superfast trains in Europe on the tracks when rounding corners, well enough to prompt the search for the eighth planet, Neptune, based on peculiarities in Uranus’s orbit. But alas, not well enough for an accurate GPS system.
Incredibly, the GPS system now in use requires Einstein’s theory of general relativity to achieve its one-meter accuracy. Determinations of the variation in snow depth on Mars using laser ranging data from orbiting spacecraft also incorporate general relativity, and yield values with an unbelievable precision of 10 cm. Certainly, at the time it was developed, no one—not even Einstein—anticipated such practical applications of a theory as abstract as general relativity.
This chapter will explore Einstein’s theory of gravity, a spectacularly accurate theory that applies to a wide range of systems. We’ll begin by briefly reviewing Newton’s gravitational theory, which works fine for the energies and speeds we encounter in daily life. We’ll then move on to the extreme limits in which it fails: namely, very high speed (close to the speed of light) and very large mass or energy. In these limits, Newtonian gravity is superseded by Einstein’s theory of relativity. With Einstein’s general relativity, space (and spacetime) evolved from a static stage to a dynamical entity that can move and curve and have a rich life of its own. We’ll consider this theory, the clues that led to its development, and some of the experimental tests that convince physicists that it’s right.
Newtonian Gravity
Gravity is the force that keeps your feet on the ground and is the source of the acceleration that returns a tossed ball to Earth. In the late sixteenth century, Galileo showed that this acceleration is the same for all objects on the surface of the Earth, no matter what their mass.
However, this acceleration does depend on how far the object is from the Earth’s center. More generally, the strength of gravity depends on the distance between the two masses—gravity’s pull is weaker when objects are farther apart. And when what creates the gravitational attraction is not the Earth, but some other object, gravity’s strength will depend on the mass of that object.
Isaac Newton developed the gravitational force law that summarizes how gravity depends on mass and distance. Newton’s law says that the force of gravity