“Newton, forgive me,” Einstein wrote in an autobiographical essay. “You found the only way which, in your age, was just about possible for a man of highest thought and creative power.” What was Einstein asking forgiveness for? That is the subject of this splendid book by Clifford Will, a physicist at Washington University, in St. Louis.
The subject is general relativity, or Einstein’s theory of gravity, and how it has repeatedly been confirmed since 1960 by major experiments. But first some background.
The simplest kind of relative motion was fully understood by the ancients. If you are on a large ship that moves at a steady rate through calm waters, you can toss a ball back and forth as easily as on shore, even though the ball follows complicated paths relative to the stationary land. Of course the land is not really stationary. The earth rotates and goes around the sun. The sun moves relative to the stars of our Milky Way galaxy. The galaxy in turn rotates and moves relative to other galaxies. Is there some sort of fixed reference frame against which a final, absolute motion can be defined?
Yes, said Newton. Motion is absolute with respect to space. Before Einstein, physicists trying to explain how light can go through a vacuum—waves seem to require a medium to transmit them—postulated a fixed substance called the ether. Experiments had shown that the speed of light through this imagined ether was independent of the speed of its source. It should be possible, therefore, to determine the absolute motion of the earth with respect to a “stagnant” ether by measuring the speed of light in different directions on the earth’s surface. The famous Michelson-Morley experiment of 1881 proved this could not be done. There was no trace of an “ether wind” generated by the earth’s motion.
In 1905, apparently unaware of the Michelson-Morley results, Einstein published his special theory of relativity. Essentially, it discarded the notion of an ether, and asserted that light (or any other portion of the electromagnetic spectrum) has a constant relative velocity regardless of the motion of an observer. If you travel alongside a light beam at half the speed of light, or even go the opposite way, the beam will always go past you at about 186,000 miles per second. Granting this absolute value for the speed of light relative to “the observer”—an observer moving in any direction at any speed—all sorts of strange effects involving space, time, mass, and energy, including the famous formula E = mcu2, inexorably follow.
The special theory concerned only motions in one direction at a constant speed. What about accelerated motions, such as the violent inertial effects astronauts undergo when their ship blasts off, or the inertia that caused a young earth to bulge at its equator? Inertia is the tendency of bodies to stay at rest or continue moving in a straight line unless an external force acts on them. It is hard to walk on a merry-go-round because inertia acts as a centrifugal force that propels you outward. When the rotating earth was forming, the stronger centrifugal force near its equator, where matter moved faster than near the poles, gave the earth its present oblate shape. Do not these effects establish absolute motion? If you rotate a bucket of water, said Newton, inertia causes the water’s surface to become concave. Is this not proof that the bucket, not the world, is rotating?
No, said Einstein in his general theory of relativity, published in 1915. There is no way to distinguish between a rotating bucket and a motionless bucket with a universe whirling around it. Only the relative motion of bucket and universe is “real.” We say the bucket rotates because it is much simpler to take the universe as fixed, just as it is simpler to say I stand on the earth instead of saying the earth rests on the bottom of my shoes. We choose the Copernican system over the Ptolemaic, not because it is true and the other false, but because it is enormously simpler.
Generalizing the special theory to all motion was a far greater creative leap than the special theory. Had Einstein not published his paper on the special theory, others would soon have reached the same conclusions. Indeed, Henri Poincaré in France and H.A. Lorentz in the Netherlands almost got there ahead of Einstein. But the general theory was such an amazing jump of the imagination, into totally unexplored territory, that physicists are still in awe over how Einstein managed it.
At the heart of the general theory is what Einstein called the principle of equivalence. It asserts that gravity and inertia are one and the same. If we take the universe as fixed, we say inertia caused the earth to bulge. If we take the earth as fixed, the rotating universe generates a gravity field that caused the bulge. The relative rotation of earth and universe creates a single force field that can be called gravitational or inertial depending on our choice of a reference frame. Had someone suggested to Newton that inertia and gravity were two names for the same force he would have thought that person crazy.
The principle of equivalence made it necessary, as Professor Will adroitly explains, to replace Newton’s “flat” three-dimensional Euclidian space with a non-Euclidian space of four dimensions. The fourth coordinate is time, and the curvature of space-time varies from place to place. Gravity ceases to be a “force” in the Newtonian sense. The earth goes around the sun not because the sun tugs it but because the sun warps space-time in such a way that the earth finds an elliptical orbit the simplest, “straightest” path it can take in space as it hurtles ahead in time. As John Wheeler likes to say, the stars tell space-time how to bend, and the bends tell the stars and other objects where to go.
In general relativity this distortion of space-time propagates like a wave, traveling at the speed of light. Quantum mechanics requires that gravity waves have their associated particles called gravitons. A variety of weird events occurring outside our galaxy, all carefully covered by Professor Will, strongly imply the existence of gravity waves. However, gravity is such a weak interaction that no one has yet detected its waves in a laboratory. Claims to have done so remain unreplicated. More sensitive tests are now under way, and it would be hard to find a physicist who doubts that gravity waves and gravitons eventually will be detected.
When a relativist says it is permissible to deem Newton’s bucket stationary and the universe spinning, what does he mean by “universe”? Does he mean no more than the totality of stars and other celestial objects, or does he include a space-time structure, a metric field, that would be there even if the material universe disappeared? If the universe contained nothing but Newton’s bucket, could the bucket rotate? If so, would its water experience inertia?
Mach’s principle, named by Einstein for the nineteenth-century Austrian physicist and philospher Ernst Mach, maintains that if the bucket were all there is, it would be meaningless to say it rotates. From this point of view inertia arises because there is accelerated motion (rotation is a form of acceleration) relative to the galaxies and other forms of matter and energy in the universe. (In Newton’s day both Leibniz and Bishop George Berkeley had similarly argued against Newton that space is no more than a relation between bodies, with no reality by itself.) Although Mach lived to reject both special relativity and the existence of atoms, Einstein was greatly influenced by him, and in his younger years was strongly attracted to the simplicity of Mach’s principle. Later he became doubtful.
General relativity, Will makes clear, is compatible both with Mach’s principle and the view that inertia arises wholly or in part from accelerated motion with respect to a metric field of space-time that is independent of the matter and energy it contains. Recent tests have tended to go against Mach’s principle. Many pages of the book under review are devoted to a fantastic experiment designed by three Stanford physicists for an earth-orbiting laboratory. Based on the precessions of sophisticated gyroscopes, it could give a conclusive answer to the profound questions raised by Leibniz, Berkeley, and Mach. Planning for this test has been going on for more than two decades.
In 1962 when my Relativity for the Million was published—it was written for high school students—I said that although the special theory was so completely vindicated it had become part of classical physics, evidence for the general theory remained feeble. Professor Will recalls an occasion that same year when a famous astronomer at the California Institute of Technology advised a graduate student to avoid relativity because it “had so little connection with the rest of physics and astronomy.” Kip Thorne, the student, wisely ignored this advice. He is now at the forefront of research in the fast-expanding field called relativistic astronomy.
When I revised my book in 1976 for an edition retitled The Relativity Explosion, new tests of general relativity had been proliferating for fifteen years. Since 1976 more and better tests have been made. If you want to know details about these ingenious experiments, and how the general theory has passed them all with what the author calls “flying colors,” there is no better book available, none more clearly written for laymen or more up-to-date, than Was Einstein Right?
Einstein himself was supremely confident about his general theory because of its elegance and simplicity. Simplicity? Its complicated mathematics gave rise to endless cartoons, jokes, and anecdotes. The book recalls a story often told about Sir Arthur Stanley Eddington, among the first of eminent British astronomers to accept general relativity. A colleague said to Eddington, “You must be one of three persons in the world who understands general relativity.” Eddington was silent. “Don’t be modest,” said the colleague. “On the contrary,” Eddington is said to have replied, “I am trying to think who the third person is.”
In the light of observational and experimental results, and the unification of gravity and inertia, the general theory is amazingly and beautifully simple. Professor Will recalls Einstein’s joking remark that if tests ever decided against the theory it would only prove God made a mistake when he designed the universe. Of course Einstein knew that elegance is not enough to make a theory fertile. Early in the game he himself had proposed three ways of testing the basic ideas of general relativity. How much does light from distant stars bend when it passes close to the sun? Does the elliptical orbit of Mercury rotate on the plane at a rate which agrees with relativity? And is the wavelength of light shifted toward the red side of the spectrum when influenced by gravity?
Before 1960 all three tests gave only weak confirmations. Repeated attempts to measure the bending of starlight, as it grazed the sun during a total eclipse, were marred by huge margins of error. Measurements did confirm bending, but the degree of bend was impossible to pin down. Even Newtonian physics, Will reminds us, predicts the bending of light by gravity, though only half the amount required by relativity. Mercury’s orbit seemed to support Einstein, but again other explanations could not be ruled out. The gravitational red shift of light had almost no empirical support.
In the 1960s, Will writes, physicists suddenly found themselves in possession of fantastically powerful new tools. “Atomic clocks” of various kinds made possible incredibly accurate measurements of time. Laser instruments were perfected. Larger radio and X-ray telescopes were built. Faster computers made it easier to analyze complex data. Radar and laser light could be bounced off mirrors on the moon, and off planets and satellites. What Will calls a renaissance of interest in general relativity soon emerged. At first the solar system was the new testing “laboratory.” In the 1970s the laboratory enlarged to regions far beyond our galaxy.
Professor Will makes an important distinction between the basic ideas of general relativity, which physicists now take for granted, and the ten tensor equations Einstein finally provided as a way of measuring the curvature of space-time. If by “general relativity” we mean those equations, then in the 1960s many rival theories, with slightly different equations, were proposed. The most important was a theory devised by Princeton’s Robert Dicke and his former graduate student Carl Brans. The Brans-Dicke theory, as it was later called, accepted all the central ideas of general relativity, but modified Einstein’s field equations by adding a second field. As a consequence, it made predictions that differed slightly from Einstein’s.
Measurements of the sun’s shape seemed to show that the sun was fatter at its equator than had been suspected, perhaps because its core rotated faster than its surface. When this oblateness was taken into account, the Brans-Dicke theory predicted the rotation of Mercury’s orbit better than Einstein’s. In a chapter called “The Rise and Fall of the Brans-Dicke Theory” the author explains why knowledge of the sun’s precise shape remains cloudy. The sun’s brightness, and the fact that it constantly throbs like a beating heart, make its shape extremely difficult to determine. Some observations reported in 1985 seem to show that the sun’s core rotates slower than its surface. In any case, support for the Brans-Dicke theory has been rapidly eroding.
The most precise measurements supporting Einstein over Brans-Dicke are described in the chapter “Do the Earth and the Moon Fall the Same?” Einstein’s field equations require an absolute equivalence in the way all matter is influenced by gravity. “If we were to drop the Earth and a ball of aluminum in the gravitational field of some distant body,” Will writes, “…the two would fall at the same rate.” A 1969 experiment, using lasers, verified that the earth and moon fall toward the sun with the same acceleration, and to a precision of one part in a hundred billion. Because the BransDicke theory does not accept what is called the “strong equivalence principle,” this test counted heavily against it. Had Einstein been told of its result, Will surmises, he would have replied, “Of course!”
Ephraim Fischbach of Purdue University has announced (too recently to be in this book) that he and his associates have found evidence for a hitherto undetected repulsive force which they call “hypercharge.” If it exists it would be much weaker than gravity, but it could cause gravity to act differently on different kinds of matter. A feather would not fall in a vacuum with exactly the same acceleration as an iron ball. Such a new force would be a revolutionary challenge to the strong equivalence principle. Although Fischbach’s claims have been widely publicized, most physicists remain skeptical.
Numerous tests since 1960 of the bending of light by gravity, as well as tests of the gravitational red shift, have strongly favored Einstein’s equations. Will gives a detailed account of the first good measurement (in 1960) of this shift. The difference in shifting between the top of Harvard’s Jefferson Tower and its base, where earth’s gravity is stronger, confirmed Einstein’s equations with a 10 percent margin of error. Later, the experiment was improved to an error of 1 percent. Measurements of the sun’s influence on starlight were abandoned in the 1970s because results were too muddied by the sun’s corona and other annoying factors. Different and more accurate tests have since been made in other ways, all in agreement with Einstein’s field equations.
The famous twin paradox of relativity, involved in many science-fiction stories, is closely related to the gravitational red shift. It says that if one twin makes a long journey into space and returns, he will be younger than his brother who stayed home. If he goes far and fast enough, he could come back to find that centuries on earth had sped by. Time travel into the past remains logically flawed (if you went back to your childhood and shot yourself, you would simultaneously be alive and dead), but traveling to the earth’s distant future is theoretically possible.
In the general theory of relativity the difference in aging can be explained by the fact that the stay-at-home twin does not move much relative to the universe, whereas the traveling twin does. A handful of stubborn skeptics have argued in the past that relativity does not imply the twin paradox, or if it does it must be wrong, but in the light of recent tests, their voices are seldom heard today. The book gives colorful details about how the twin paradox was validated in 1971 by flying two atomic clocks around the earth, one westward, the other eastward, then comparing them with an atomic clock that remained on the ground.
A fourth kind of test, not proposed by Einstein, involves the way gravity delays a light signal. Professor Will explains it with a rubber-sheet model. Put a heavy ball on the center of a flat elastic sheet supported at its perimeter. The ball will produce a depression—a three-dimensional distortion of the sheet’s two-dimensional space. This causes a marble, placed anywhere outside the depression, to roll toward the ball. The ball doesn’t pull the marble. The marble moves because of the sheet’s curvature. If you imagine a light ray on the sheet, entering and leaving the depression, it will travel farther than it would if the sheet were flat. This is similar to what happens when light goes through a region strongly warped by a star’s mass. Because the path has lengthened, there is what is called the Shapiro time delay, after Irwin Shapiro who worked out the mathematics in the early 1960s. Complex measurements of this delay by Viking spacecraft have confirmed Einstein’s field equations with an error of one part in one thousand. Will calls it “still the most accurate test of the theory ever performed.”
In general relativity the strength of gravity never alters. However, the discovery that the universe originated in a monstrous explosion, and has been expanding ever since, raised the possibility that perhaps gravity is slowly weakening. This is especially plausible if Mach’s principle holds. Paul Dirac, the British physicist who introduced special relativity into quantum mechanics, was among the first to suggest that gravity is getting weaker. The Brans-Dicke theory makes the same claim. A chapter titled “Is the Gravitational Constant Constant?” skillfully summarizes the latest experimental evidence that gravity is indeed constant, although definitive tests have yet to be made.
In brief, the book answers the question posed by its title with a resounding yes. Einstein was right. Not only have his equations been confirmed over and over again, the general theory has become indispensable for understanding the incredible new objects that modern telescopes have detected: the pulsars believed to be fast-spinning neutron stars, and the fardistant quasars suspected of having black holes at their centers because there seems no other way to account for their enormous energy output. The day has long passed, writes Will, when cosmologists can remain ignorant of relativity. Every year astrophysicists find new phenomena that only the general theory can explain. The most recent are the powerful gravity fields outside our galaxy that act like mammoth lenses, magnifying and refracting what is seen through them. Such lenses were predicted by Einstein in 1936.
Galileo and Newton made experiments, but the extraordinary thing about Einstein is that he made no experiments. Moreover, he was often unaware of significant tests that had strong bearings on his speculations. He just sat alone, thinking deeply about the secrets of the Old One, as he liked to call the universe. Newton was a devout Anglican who spent half his life struggling to unravel the mysteries of biblical prophecy. Einstein had no interest in any religion except in the sense that Spinoza, whose secular pantheism he admired, was religious. Yet he and Newton, in addition to their giant intellects and creative intuitions, shared a strong sense of wonder toward the Old One, and humility before the unanswerable riddle of existence. Both were Platonists in their conviction that what science knows is an infinitesimal portion of what it doesn’t know.
Newton, in an often quoted passage, likened himself to a boy playing on the shore of a vast “ocean of truth,” amusing himself by picking up a smooth pebble or a patterned shell. Einstein made the same point with a different metaphor. He told an interviewer that he thought of himself as a child who has entered an enormous library, its books written in many languages. He takes down one volume and manages to translate a few pages. What a far cry from those now trying to persuade us that physics is on the brink of discovering Everything!
December 4, 1986