General relativity is still considered by many to be the most ingenious physical theory ever articulated. The famous physicist Richard Feynman confessed once, “I still can’t see how he thought of it.” The theory was based largely on two profound insights: (1) the equivalence between gravity and acceleration, and (2) the transformation of the role of space-time from that of a passive spectator to that of a major player in the drama of universal dynamics. First, by contemplating the experience of a person who is free-falling in the gravitational field of the Earth, Einstein realized that acceleration and gravity are essentially indistinguishable. A person living inside a closed elevator on Earth, with the elevator accelerating upward continuously, may think that she lives in a place that has a stronger gravity—a bathroom scale will certainly record a weight that is higher than her normal weight. Similarly, astronauts in the space shuttle were experiencing “weightlessness” because both they and the shuttle were undergoing the same acceleration relative to the Earth. In his Kyoto Lecture in 1922, an impromptu speech to students and faculty members, Einstein described how the idea came to him: “I was sitting in a chair in the patent office in Bern when all of a sudden a thought occurred to me: ‘If a person falls freely he will not feel his own weight.’ I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.”

Einstein’s second idea turned Newton’s gravity on its ear. Gravity is not some mysterious force that acts across space, Einstein contended. Rather, mass and energy warp space-time in the same way that a person standing on a trampoline causes it to sag. Einstein defined gravity as the curvature of space-time. That is, planets move along the shortest paths in the curved space-time created by the Sun, just as a golf ball follows the undulation of the green, or a Jeep negotiates the dunes of the Sahara Desert. Light does not travel in straight lines, either, but curves in the warped neighborhood of large masses. Figure 32 shows a letter written by Einstein in 1913, as he was developing the theory. In the letter, addressed to the American astronomer George Ellery Hale, Einstein explained the bending of light in a gravitational field and the Sun’s deflection of light from a distant star. This crucial prediction was first tested in 1919 during an eclipse of the Sun. The person who organized the observations (in Brazil and on Principe Island in the Gulf of Guinea) was Arthur Eddington, and the deviations recorded by his team and by the expedition headed by the Irish astronomer Andrew Crommelin (of about 1.98 and 1.61 seconds of arc) were consistent, within the estimated observational errors, with Einstein’s prediction of 1.74 seconds of arc. (Newtonian gravity predicted half that.) Time is “curved” as well in general relativity: Clocks that are near massive bodies tick more slowly than clocks that are far away from them. Experiments have confirmed this effect, which is also taken into account routinely by GPS satellites.

Figure 32

Einstein’s pivotal premise in general relativity was a truly revolutionary idea: What we perceive as the force of gravity is merely a manifestation of the fact that mass and energy cause space-time to warp. In this sense, Einstein was closer, at least in spirit, to the geometrical (rather than dynamical) views of the astronomers of ancient Greece than to Newton and his emphasis on forces. Instead of being a rigid and fixed background, space-time can flex, curve, and stretch in response to the presence of matter and energy, and those warps, in turn, cause matter to move the way it does. As the influential physicist John Archibald Wheeler once put it, “Matter tells space-time how to curve, and space-time tells matter how to move.” Matter and energy become eternal partners to space and time.