The Elegant Universe (12 page)

To do so, we revisit George and Gracie, no longer in the deep darkness of empty space, but floating near the outskirts of the solar system. They are still each wearing large digital clocks on their space suits that are initially synchronized. To keep things simple, we ignore the effects of the planets and consider only the gravitational field of the sun. Let’s further imagine that a spaceship hovering near George and Gracie has reeled out a long cable extending all the way down to the vicinity of the sun’s surface. George uses this cable to slowly lower himself toward the sun. As he does so, he periodically stops so that he and Gracie can compare the rate at which time is elapsing on their clocks. The warping of time predicted by Einstein’s general relativity implies that George’s clock will run slower and slower compared with Gracie’s as the gravitational field he experiences gets stronger and stronger. That is, the closer he gets to the sun the slower his clock will run. It is in this sense that gravity distorts time as well as space.

You should note that unlike the case in Chapter 2 in which George and Gracie were in empty space moving relative to each other with constant velocity, in the present setting there is no symmetry between them. George, unlike Gracie, feels the force of gravity getting stronger and stronger—he has to hold the cable tighter and tighter as he gets closer to the sun to avoid being pulled in. Each of them agrees that George’s clock is running slow. There is no “equally valid perspective” that exchanges their roles and reverses this conclusion. This is, in fact, what we found in Chapter 2 when George experienced an acceleration by turning on his jetpack to catch up with Gracie. The acceleration George felt resulted in his clock definitively running slow relative to Gracie’s. Since we now know that feeling accelerated motion is the same as feeling a gravitational force, the present situation of George on the cable involves the same principle, and once again we see that George’s clock, and everything else in his life, runs in slow motion compared with Gracie’s.

In a gravitational field such as that at the surface of an ordinary star like the sun, the slowing of clocks is quite small. If Gracie stays put at a billion miles from the sun, then when George has climbed to within a few miles of its surface, the rate of ticking of his clock will be about 99.9998 percent of Gracie’s. Slower, but not by much.9 If, however, George lowered himself on a cable so that he hovered just above the surface of a neutron star whose mass, roughly equal to that of the sun, is crushed to a density some million billion times that of solar density, the larger gravitational field would cause his clock to tick at about 76 percent of the rate of Gracie’s. Stronger gravitational fields, such as those just outside a black hole (as discussed below), cause the flow of time to slow even further; stronger gravitational fields cause a more severe warping of time.

Experimental Verification of General Relativity

Most people who study general relativity are captivated by its aesthetic elegance. By replacing the cold, mechanistic Newtonian view of space, time, and gravity with a dynamic and geometric description involving curved spacetime, Einstein wove gravity into the basic fabric of the universe. Rather than being imposed as an additional structure, gravity becomes part and parcel of the universe at its most fundamental level. Breathing life into space and time by allowing them to curve, warp, and ripple results in what we commonly refer to as gravity.

Aesthetics aside, the ultimate test of a physical theory is its ability to explain and predict physical phenomena accurately. Since its inception in the late 1600s until the beginning of this century, Newton’s theory of gravity passed this test with flying colors. Whether applied to balls thrown up in the air, objects dropped from leaning towers, comets whirling around the sun, or planets going about their solar orbits, Newton’s theory provides extremely accurate explanations of all observations as well as predictions that have been verified innumerable times in a wealth of situations. The motivation for questioning this experimentally successful theory, as we have emphasized, was its property of instantaneous transmission of the gravitational force, in conflict with special relativity.

The effects of special relativity, although central to a fundamental understanding of space, time, and motion, are extremely small in the slow-velocity world we typically inhabit. Similarly, the deviations between Einstein’s general relativity—a theory of gravity compatible with special relativity—and Newton’s theory of gravity are also extremely small in most common situations. This is both good and bad. It is good because any theory purporting to supplant Newton’s theory of gravity had better closely agree with it when applied in those arenas in which Newton’s theory has been experimentally verified. It is bad because it makes it difficult to adjudicate between the two theories experimentally. Distinguishing between Newton’s and Einstein’s theories requires extremely precise measurements applied to experiments that are very sensitive to the ways in which the two theories differ. If you throw a baseball, Newtonian and Einsteinian gravity can be used to predict where it will land, and the answers will be different, but the differences will be so slight that they are generally beyond our capacity to detect experimentally. A more clever experiment is called for, and Einstein suggested one.10

We see stars at night, but of course they are also there during the day. We usually don’t see them because their distant, pinpoint light is overwhelmed by the light emitted by the sun. During a solar eclipse, however, the moon temporarily blocks the light of the sun and distant stars become visible. Nevertheless, the presence of the sun still has an effect. Light from some of the distant stars must pass close to the sun on the way to earth. Einstein’s general relativity predicts that the sun will cause the surrounding space and time to warp and such distortion will influence the path taken by the starlight. After all, the photons of distant origin travel along the fabric of the universe; if the fabric is warped, the motion of the photons will be affected much as for a material body. The bending of the path of light is greatest for those light signals that just graze the sun on their way to earth. A solar eclipse makes it possible to see such sun-grazing starlight without its being completely obscured by sunlight itself.

The angle through which the light path is bent can be measured in a simple way. The bending of the starlight’s path results in a shift in the apparent position of the star. The shift can be accurately measured by comparing this apparent position with the star’s actual location known from observations of the star at night (in the absence of the sun’s warping influence), carried out when the earth is at an appropriate position, some six months earlier or later. In November of 1915, Einstein used his new understanding of gravity to calculate the angle through which starlight signals that just graze the sun would be bent and found the answer to be about .00049 of a degree (1.75 arcseconds, where an arcsecond is 1/3600 of a degree). This tiny angle is equal to that subtended by a quarter placed upright and viewed from nearly two miles away. The detection of such a small angle was, however, within reach of the technology of the day. At the urging of Sir Frank Dyson, director of the Greenwich observatory, Sir Arthur Eddington, a well-known astronomer and secretary of the Royal Astronomical Society in England, organized an expedition to the island of Principe off the coast of West Africa to test Einstein’s prediction during the solar eclipse of May 29, 1919.

On November 6, 1919, after some five months of analysis of the photographs taken during the eclipse at Principe (and of other photographs of the eclipse taken by a second British team led by Charles Davidson and Andrew Crommelin in Sobral, Brazil), it was announced at a joint meeting of the Royal Society and the Royal Astronomical Society that Einstein’s prediction based on general relativity had been confirmed. It took little time for word of this success—a complete overturning of previous conceptions of space and time—to spread well beyond the confines of the physics community, making Einstein a celebrated figure worldwide. On November 7, 1919, the headline in the London Times read “REVOLUTION IN SCIENCE—NEW THEORY OF THE UNIVERSE—NEWTONIAN IDEAS OVERTHROWN.”11 This was Einstein’s moment of glory.

In the years following this experiment, Eddington’s confirmation of general relativity came under some critical scrutiny. Numerous difficult and subtle aspects of the measurement made it hard to reproduce and raised some questions regarding the trustworthiness of the original experiment. Nevertheless, in the last 40 years a variety of experiments making use of technological advancements have tested numerous aspects of general relativity with great precision. The predictions of general relativity have been uniformly confirmed. There is no longer any doubt that Einstein’s description of gravity is not only compatible with special relativity, but yields predictions closer to experimental results than those of Newton’s theory.

Black Holes, the Big Bang, and the Expansion of Space

Whereas special relativity is most manifest when things are moving fast, general relativity comes into its own when things are very massive and the warps in space and time are correspondingly severe. Let’s describe two examples.

The first is a discovery made by the German astronomer Karl Schwarzschild while studying Einstein’s revelations on gravity in between his own calculations of artillery trajectories at the Russian front during World War I in 1916. Remarkably, just months after Einstein had put the finishing touches on general relativity, Schwarzschild was able to use the theory to gain a complete and exact understanding of the way space and time warp in the vicinity of a perfectly spherical star. Schwarzschild sent his results from the Russian front to Einstein, who presented them on Schwarzschild’s behalf to the Prussian Academy.

Beyond confirming and making mathematically precise the warping that was schematically illustrated in Figure 3.5, Schwarzschild’s work—which has now come to be known as “Schwarzschild’s solution”—revealed a stunning implication of general relativity. He showed that if the mass of a star is concentrated in a small enough spherical region, so that its mass divided by its radius exceeds a particular critical value, the resulting spacetime warp is so radical that anything, including light, that gets too close to the star will be unable to escape its gravitational grip. Since not even light can escape such “compressed stars,” they were initially called dark or frozen stars. A more catchy name was coined years later by John Wheeler, who called them black holes—black because they cannot emit light, holes because anything getting too close falls into them, never to return. The name stuck.

We illustrate Schwarzschild’s solution in Figure 3.7. Although black holes have a reputation for rapacity, objects that pass by them at a “safe” distance are deflected in much the same way that they would be by an ordinary star, and can proceed on their merry way. But objects of any composition whatsoever that get too close—closer than what has been termed the black hole’s event horizon—are doomed: they will be drawn inexorably toward the center of the black hole and subject to an ever increasing and ultimately destructive gravitational strain. For example, if you dropped feet first through the event horizon, as you approached the black hole’s center you would find yourself getting increasingly uncomfortable. The gravitational force of the black hole would increase so dramatically that its pull on your feet would be much stronger than its pull on your head (since in a feet-first fall your feet are always a bit closer than your head to the black hole’s center); so much stronger, in fact, that you would be stretched with a force that would quickly tear your body to shreds.

If, on the contrary, you were more prudent in your wanderings near a black hole and took great care not to trespass beyond the event horizon, you could make use of the black hole for a rather amazing feat. Imagine, for example, that you were to discover a black hole whose mass was about 1,000 times the mass of the sun, and that you were to lower yourself on a cable, much as George did near the sun, to about an inch above the black hole’s event horizon. As we have discussed, gravitational fields cause a warping of time, and this means that your passage through time would slow down. In fact, since black holes have such strong gravitational fields, your passage through time would slow way down. Your watch would tick about ten thousand times more slowly than those of your friends back on earth. If you were to hover just above the black hole’s event horizon in this manner for a year, and then climb up the cable to your waiting starship for a short, yet leisurely, journey home, upon arrival at earth you would find that more than ten thousand years had passed since your initial departure. You would have successfully used the black hole as a kind of time machine, allowing you to travel to earth’s distant future.

To get a sense of the extreme scales involved, a star with the mass of the sun would be a black hole if its radius were not its actual value (about 450,000 miles), but, instead, just under 2 miles. Imagine: The whole of the sun squeezed to fit comfortably within upper Manhattan. A teaspoonful of such a compressed sun would weigh about as much as Mount Everest. To make a black hole out of the earth we would need to crush it into a sphere whose radius is less than half an inch. For a long time physicists were skeptical about whether such extreme configurations of matter could ever actually occur, and many thought that black holes were merely a reflection of an overworked theoretician’s imagination.

Nevertheless, during the last decade, an increasingly convincing body of experimental evidence for the existence of black holes has accumulated. Of course, since they are black, they cannot be observed directly by scanning the sky with telescopes. Instead, astronomers search for black holes by seeking anomalous behavior of other more ordinary light-emitting stars that may be positioned just outside a black hole’s event horizon. For instance, as dust and gas from the outer layers of nearby ordinary stars fall toward the event horizon of a black hole, they are accelerated to nearly the speed of light. At such speeds, friction within the maelstrom of downward-swirling material generates an enormous amount of heat, causing the dust-gas mixture to “glow,” giving off both ordinary visible light and X rays. Since this radiation is produced just outside the event horizon, it can escape the black hole and travel through space to be observed and studied directly. General relativity makes detailed predictions about properties that such X ray emissions will have; observation of these predicted properties gives strong, albeit indirect, evidence for the existence of black holes. For example, mounting evidence indicates that there is a very massive black hole, some two and a half million times as massive as the sun, sitting in the center of our own Milky Way galaxy. And even this seemingly gargantuan black hole pales in comparison to what astronomers believe to reside in the core of the astonishingly luminous quasars that are scattered throughout the cosmos: black holes whose masses may well be billions of times that of the sun.