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Infinity in the Palm of Your Hand: Einstein’s Far-Reaching Vision

I myself am of Mach’s opinion, which can be formulated in the language of the theory of relativity thus: all the masses in the universe determine the [gravitational] field…. In my opinion, inertia is in the same sense a communicated mutual action between the masses of the universe.

Albert Einstein (response to Ernst Reichenbaecher)

The fault, dear Brutus, is not in our stars, but in ourselves.

William Shakespeare (Julius Caesar)

TOUCHED BY THE STARS

The ancients believed that celestial patterns steered the individual fortunes of human beings and the collective destinies of civilizations. For example, if a particular constellation, or stellar grouping, was high in the sky on the night a certain king was born, he would be blessed with the fiery gifts of a warrior. Another heavenly configuration and he was doomed to die in battle. If Venus kissed Jupiter in the chapel of lights, then a royal marriage was brewing. But if the stars were all wrong on the night of marital bliss, the bride would alas be barren.

Is it lunacy to believe that there is a deep connection between earthly and celestial events? Not if one takes the concept literally.



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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos 2 Infinity in the Palm of Your Hand: Einstein’s Far-Reaching Vision I myself am of Mach’s opinion, which can be formulated in the language of the theory of relativity thus: all the masses in the universe determine the [gravitational] field…. In my opinion, inertia is in the same sense a communicated mutual action between the masses of the universe. Albert Einstein (response to Ernst Reichenbaecher) The fault, dear Brutus, is not in our stars, but in ourselves. William Shakespeare (Julius Caesar) TOUCHED BY THE STARS The ancients believed that celestial patterns steered the individual fortunes of human beings and the collective destinies of civilizations. For example, if a particular constellation, or stellar grouping, was high in the sky on the night a certain king was born, he would be blessed with the fiery gifts of a warrior. Another heavenly configuration and he was doomed to die in battle. If Venus kissed Jupiter in the chapel of lights, then a royal marriage was brewing. But if the stars were all wrong on the night of marital bliss, the bride would alas be barren. Is it lunacy to believe that there is a deep connection between earthly and celestial events? Not if one takes the concept literally.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos The term “lunacy” itself derives from beliefs in periodic influences of the Moon. As the shining beacon of the nocturnal sky, Earth’s satellite was thought to exert quite a pull on terrestrial affairs. There is little evidence that the Moon has driven anyone mad, or induced anyone to sprout extra facial hair. Yet, especially for those attuned to the rhythms of the sea, it clearly exerts a pull on many lives. For those who earn their living hauling in lobsters from the Bay of Fundy off the coast of maritime Canada, each working day is shaped by lunar forces. Amid some of the highest tides in the world, one could not help but concede that the sandstone of human destiny is carved by heavenly guided waters. Today we distinguish between scientific forces and spiritual influences. To the ancients this distinction was not so clear. Early astronomers did double duty, serving both to record the positions of the celestial spheres and to apply this information for astrological forecasts. Their expertise in predicting eclipses, planetary conjunctions, and other celestial events, as well as offering critical navigational knowledge, earned them the mantel of exalted prophets. Even as late as the 16th century, many scientific researchers, such as the German mathematician Johannes Kepler, sold horoscopes on the side for extra income. Kepler, in his first astrological calendar, proudly predicted a cold spell and a Turkish invasion of Styria (now Austria). Not only did he peddle forecasts, he deeply believed that they offered special insight into the determinants of human character. He once wrote that his father was “vicious, inflexible, quarrelsome and doomed to a bad end” because of the clashing influences of Venus and Mars. How did the heavenly orbs set the pace of their own motions and influence the course of earthly events? Kepler originally thought this happened because the planets somehow possessed minds of their own. However, after he developed a clearer understanding of celestial mechanics, he realized this could not be the case. “Once I firmly believed that the motive force of a planet was a soul,” he wrote. “Yet as I reflected, just as the light of the Sun diminishes in proportion to

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos distance from the Sun, I came to the conclusion that this force must be something substantial.” Thus, what ultimately changed Kepler’s opinions on these matters was the realization that planetary motion could be explained through simple mathematical rules. This revelation came through a systematic study of the orbital behavior of the planet Mars and generalizing these results to other bodies in the solar system. Kepler discovered that each planet travels along an elliptical path around the Sun, sweeping out equal areas (of the region inside the ellipse) in equal times. He also found relationships between each planet’s orbital period and its average distance from the Sun. These discoveries, known as Kepler’s laws, led him to conclude that rock-solid mathematical principles, not ethereal spiritual influences, govern celestial mechanics. Picking up where Kepler left off, Isaac Newton brilliantly revealed the mainspring of this clockwork cosmos. He discovered that the same force that guides acorns down from oak trees and cannonballs down to their targets similarly steers the Moon around Earth and the planets around the Sun. Calling this force gravitation, from the Latin gravitas or heavy, he showed that it exerts an attractive pull between any pair of massive objects in the universe. The Moon, for instance, is pulled toward Earth just like a ripe fruit from its branch. Earth is similarly drawn toward the Moon—which explains the movements of the tides. Newton further demonstrated that the strength of gravity varies in inverse proportion to the square of the distance between any two masses. That is, if two objects are flung twice as far away from each other, their gravitational attraction drops by a factor of 4. This reduction in strength with distance explains why the Moon, rather than any of the stars (as massive as they are by comparison), lifts and lowers Earth’s ocean waters. Some contemporary believers in astrology have asserted that the marching parade of constellations exerts a changing gravitational influence on the temperaments of children born under these signs.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos When disaster strikes they like to think that the fault lies not in ourselves but in our stars. (Indeed, the word “disaster” derives from the Latin for “the unfavorable aspects of stars.”) However, as the late astronomer Carl Sagan was fond of pointing out, the gravitational attraction of the delivering obstetrician, hands cupping the baby’s head, outweighs the pull of any distant star. Though the stars are far more massive, the obstetrician is much, much closer. Besides, it’s unclear how any gravitational force could affect thought processes, unless one hangs upside down to permit greater blood flow to the brain. When applied to the proper venue, material objects in space, Newtonian theory is remarkably successful. Yet it harbors an essential mystery. Why do bodies orbit their gravitational attractors, rather than moving directly toward them? Why doesn’t the Moon, for instance, immediately plunge toward Earth and destroy all civilization? Newton’s answer was to propose a property called inertia that keeps still objects at rest and moving objects traveling in a straight line at a constant speed. Like a universal hypnotist, inertia places each object in a trance to continue doing what it is already doing. The only thing that can break inertia’s spell is the application of an external force (or unbalanced set of forces). Still, the magic is lifted only provisionally, allowing the body to change paths only during the interval in which the force is applied. Then it resumes its straight-line motion, until perhaps another force takes hold. Now consider the case of the Moon. Inertia compels the Moon to keep going in a straight line, but gravity continuously pulls it toward Earth. The compromise is a curving motion, resulting in an essentially circular path. Though gravity is a force, inertia is not. Rather, inertia represents the state of nature in the absence of all forces. As strange as it might seem, according to Newtonian theory, if all the forces in the universe suddenly “turned off,” every object would continue moving forever uniformly. This state of affairs would result from no specific cause but rather from a lack of causes.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos In trying to fathom the underlying reason for inertia, one is reminded of the Taoist paradox that, in trying to pin down something’s definition, its true meaning slips away. The machinery of inertia is remarkable in that there is no machinery. Nevertheless, from Newton’s time onward, physicists and philosophers have sought a deeper understanding of why constant linear motion constitutes nature’s default mode. To make matters even trickier, all motion is relative. This principle was put forth by Galileo and firmed up by Newton, well before the time of Einstein. The speed of any object depends on the frame (point of view) in which it is observed. For instance, if two truck drivers, traveling at the same speed but in opposite directions, wave to each other on a highway, each will observe the other to be moving twice as fast as their speedometers would indicate. If, on the other hand, each is traveling at identical speeds in the same direction, each will appear to the other to be at rest—presuming they ignore all background scenery. You would think that the property of inertia would similarly be relative. If, according to one reference frame, inertial motion appears unblemished by extra forces, why not in all frames? Strangely, though, while this is true for observers moving at constant velocities with respect to each other, it is emphatically not true for accelerating observers. Newton cleverly demonstrated this principle by means of a simple thought experiment involving a spinning bucket of water. BEYOND THE PAIL Sometimes the most ordinary household objects can offer deep insights about the physical universe. If we concoct the right experiment, there is no need for an expensive particle accelerator to probe the mysteries of force, nor a high-powered telescope to reveal the enigmas of the cosmos. A visit to our basement or backyard might well provide all the materials required.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Take, for example, an ordinary pail. Fill it to the brim with plain tap water. Suspend the bucket from a rope, attached to the limb of a tree. If the bucket is still, the water should appear completely level. Not the stuff of Nobel prizes, so far, but here’s where things get strange. Spin the bucket. Twirl it around gently but resolutely. As the bucket turns, you notice several things. First, the water remains in the pail. Thanks to inertial tendencies, it pushes against the walls of the bucket but doesn’t spill out. Yet something does change about the fluid. Its surface begins to hollow out, as if sculpted by a potter. In short order, the once-level top has become as curved as a soup bowl. The principle of inertia can explain this concavity, but only if you adopt the right perspective. From your point of view, the reason is simple: The water is building up against the sides because, despite the spinning of its container, it wants to travel in a straight line. This lowers the central part of the fluid, hollowing it out. Consider, however, the perspective of a tiny observer (a savvy ant, perhaps) perched on the side of the pail. If he ignores the world beyond the bucket, he might well believe that the bucket isn’t spinning at all. For him, therefore, inertia should keep everything inside the bucket at rest. Then, imagine his surprise if he looks down at the water and sees it change shape. What bizarre supernatural effect, he might wonder, could deliver such a targeted punch? Newton used his bucket argument to make the point that, while the principle of inertia does not depend on the relative velocity of two reference frames, it clearly does depend on the relative acceleration of the frames. In physics, acceleration refers not just to alterations in speed but also to changes in direction. Therefore, a spinning bucket is accelerating because the motion of any point within it keeps changing direction. But indeed that is true about Earth itself—rotating about its own axis as it revolves around the Sun. Therefore, given all these gyrating vantage points, how can we uniquely define inertia’s unmistakable action? Where in this whirling cosmic carnival can we find solid ground?

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Newton’s answer was to define a fixed, universal reference frame, called “absolute space,” placed in an exalted position above any other framework. “Absolute space,” he wrote, “in its own nature, without relation to anything else, remains always similar and immovable.” To the concept of absolute space, Newton added another expression, called “absolute time.” Absolute time represents the uniform ticking of an ideal universal clock. Together, absolute space and time serve to define absolute motion—an inviolate description of movement through the cosmos. Common parlance, Newton pointed out, fails to distinguish between relative motion (measured with respect to any fleeting frame) and absolute motion (defined with regard to the steel scaffolds of absolute space and time). The bucket example, however, demonstrates why such confusion of terms won’t do. To understand dynamics properly, he emphasized, one must reject the ephemeral and take a firm universal perspective. “Relative quantities,” he wrote, “are not the quantities themselves whose names they bear….” Those who mistake transient measures for true quantities, he continued, “violate the accuracy of language, which ought to be kept precise….” Despite Newton’s admonition, in the centuries after his death a growing community of scholars came to find his distinction rather artificial. With everything in the cosmos in ceaseless motion, why should any one reference frame stand still? By the 19th century, a number of scientists replaced Newton’s artifice with an all-pervading invisible substance, known as the aether. Absolute motion could thereby be defined with respect to the aether stream. Nobody, however, could detect the aether; it seemed as elusive as a ghost. Viennese physicist Ernst Mach took a different approach. In his popular book on mechanics, he dismissed the notion of an absolute frame. Rather, he argued that it is the combined pull of distant stars that keeps inertia’s hammock aloft. “Instead of referring a moving body to [absolute] space,” he wrote, “let us view directly its relation to the bodies of the universe, by which alone such a system of coordinates can be determined.” Hence, objects resist acceleration

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos because they are in some mysterious way “connected” to the myriad other bodies in the cosmos. Even a lowly pail on Earth responds to mammoth energies trillions of miles away. This far-reaching concept has come to be known as Mach’s principle. It’s strange to think of remote stars steering the water in a bucket. Yet the idea that the Moon guides the tides of Fundy seems perfectly normal. Mach’s principle just stretches such cosmic connections much, much further—until they engulf the entirety of space itself. When Mach published his treatise, he freely admitted that he had no experimental proof for his hypothesis. Yet because it was based on the actions of real celestial bodies, he asserted that his explanation was heads above Newton’s abstract design. This argument stirred the youthful imagination of Albert Einstein, who dreamed of putting Mach’s ideals into practice. COMPASSES AND CLOCKS Albert Einstein, the greatest physicist of modern times, was born in Ulm, Germany, on March 14, 1879. As a child he had a keen curiosity about the principles underlying the way things work. In an autobiographical essay, he recalled his wonder at the age of 4 or 5 when he was lying ill in bed and his father presented him with his first compass. “The fact that the needle behaved in such a definite manner did not fit at all into the pattern of occurrences which had established itself in my subconscious conceptual world (effects being associated with ‘contact’). I remember to this day—or I think I remember— the deep and lasting impression this experience made on me. There had to be something behind the objects, something that was hidden.” Then, at the age of 12, a family friend gave him a book on Euclidean geometry. The young thinker marveled at the crisp certainty of the mathematical arguments presented. Soon he learned how to construct his own proofs, creating geometric rules from simple propositions.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Like many philosophers before him, Einstein was intrigued by the contrast between the imperfect arena of sensory experiences and the ideal realm of abstract concepts. He wondered which aspects of the world required hands-on experimentation and which could be deduced through pure thought. His life’s journey stepped carefully between these two positions. Ultimately, the latter would win out, and his mathematical side would overtake his more practical side. He would become obsessed by the idea of finding inviolable mathematical principles, elegant and beautiful in their simplicity of expression, that could explain all of nature. One of Einstein’s first “thought experiments” involved a seeming contradiction between Newtonian physics and the known properties of light. At the age of 16 he imagined chasing a light wave and trying to catch up with it. He pictured himself running faster and faster until he precisely matched the speed of the flash. Then, he wondered, would the signal seem still to him, like two trains keeping pace? Newtonian physics would suggest the affirmative. Any two objects moving at the exact same velocity should observe each other to be at rest—that is, their relative velocity should be zero. However, by Einstein’s time, physicists knew that light was an electromagnetic wave. James Clerk Maxwell’s well-known equations of electro-magnetism made no reference to the velocities of observers. Anyone recording the speed of light (in a vacuum) must measure the same value. Hence, two of the giants of physics, Newton and Maxwell, appeared locked in a conceptual battle. Others tried to find a way out of this dilemma by proposing effects due to the invisible aether (which by that time had experimentally been discredited), but it was Einstein who developed the definitive solution. In a breakthrough known as the special theory of relativity, he demonstrated that Newtonian mechanics and Maxwellian electrodynamics could be reconciled by abandoning the notions of absolute space and time. By asserting that measured distances and durations depend on the relative velocities of the observer and the observed, Einstein developed dynamical equations that preserve the constancy of the speed of light.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Let’s see how special relativity works. Suppose a runner tries to catch up to a light wave. As he moves faster and faster, approaching light speed, his personal clock (as measured by his thoughts, his metabolism, and any timepieces he is wearing) would slow down relative to that of someone standing still. Compared to the tortoise-like ticking of his own pace, light would still seem to be whizzing by at its gazelle-like speed. He wouldn’t know that his own time is moving slower, unless he later compares his findings with a stationary observer. Then he would realize that he had experienced fewer minutes while running than he would have just by standing. All this ensures that any observer, whether moving or still, records exactly the same value for light speed. This phenomenon, of clocks ticking more slowly if they move close to the speed of light, is called time dilation. Time dilation is nature’s hedge against anyone catching up with its fastest sprinter. Nature would rather slow down stopwatches than allow runners carrying them to violate its sacred speed limit. A related mechanism, called length contraction (or sometimes Lorentz-Fitzgerald contraction), involves the shortening of relativistic objects along the direction of their motion. This is a clear consequence of time dilation and the constancy of light. If one uses a light signal to measure a length (by recording how long it takes to go from one end to the other) but one’s clock is slower, one would naturally find the object to be shorter. In 1907, two years after Einstein published his special theory of relativity, the Russian-German mathematician Hermann Minkowski proposed an extraordinary way to render it through pure geometry. Minkowski suggested that Einstein’s theory could be expressed more eloquently within a four-dimensional framework. With a thunderous speech, he proclaimed the very end to space and time as separate entities, replacing them with unified four-dimensional space-time. Within this framework, known as Minkowski space-time, anything that happens in the universe is called an “event.” Spilling a

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos morning cup of coffee in a Ganymede café could be one event; shipping out emergency supplies of Venusian organically grown house blend on a sweltering afternoon could be another. The “distance” between these two occurrences, called the space-time interval, involves combining the differences in time and space between the two events. How, you might ask, can time be “added to” space? The answer involves using nature’s universal constant velocity, the speed of light. Multiplying velocity (in miles per hour, for example) by time (in hours) yields length (in miles). The time units cancel out, leaving only length units. Multiplying all time values by the speed of light converts them into length values in a consistent way. Then we can employ a modified form of the Pythagorean theorem—the geometric relationship that relates the hypotenuse and sides of a right triangle— to find the space-time interval. Technically, the procedure is as follows: Take the spatial distances in all three directions and square them. Next, take the time difference, multiply by the speed of light, and square the result. Finally, subtract that value from the sum of the squares of the spatial distances, yielding the square of the space-time interval. Notice that the spatial distances are added, but the time difference (multiplied by light speed) is subtracted. The procedure that governs which terms to add and which to subtract is called the signature. In standard Euclidean geometry, of the sort Einstein studied as a child, all distances are additive. Hence, the signature is fully positive. In Minkowski space-time, on the other hand, the temporal “distance” is subtracted, yielding a mixed signature of three “plusses” (for space) and one “minus” (for time). The mechanism, in general, to determine the space-time interval for any given set of events and region of the universe is called the metric. For Minkowski space-time, the metric is relatively simple: Add the squares of the spatial terms and subtract the square of the temporal term (multiplied by the speed of light). It is known as a

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos stacked inside each other like Russian dolls and then placed in a cryogenic (ultracold) vacuum flask. Superconducting shielding will protect the apparatus from external disturbances. (Superconductivity is a low-temperature quantum effect that allows certain materials to maintain electrical currents and magnetic fields indefinitely. It offers a buffer against external electromagnetic influences.) Highly sensitive SQUIDs (Superconducting Quantum Interference Devices) will measure the concentric cylinders’ relative motions as the satellite circles through Earth’s gravitational field. They’ll be able to detect motions as fine as 50-quadrillionths of an inch. Like an overzealous traffic cop, they’ll record even the slightest inkling of a violation. The equivalence principle is not the only aspect of gravitational physics being tested in space. An orbiting satellite called GP-B (Gravity Probe B) is currently engaged in a far-reaching study of two general relativistic predictions: frame dragging and the geodetic effect. These properties, specific to Einstein’s theory, are quite subtle and have never before been tested. Frame dragging involves the twisting of space-time due to the rotation of massive objects. Emanating from each body in the cosmos, like the streamers from a maypole, are manifold geodesics. These strands correspond to the shortest paths through that region of the universe—namely the routes traveled by light rays. When a body twirls around in its clockwork dance, it swings its streamers with it. Objects clinging to these streamers, like May Day revelers, must similarly whirl around, changing directions as they spin. Although relativistic frame dragging was first postulated by Austrian physicists Joseph Lense and Hans Thirring in 1918, it wasn’t until 1959 that Leonard Shiff of Stanford proposed a direct way of testing it. Shiff calculated that a spinning gyroscope orbiting 400 miles above Earth would change its tilt by a fraction of a milliarcsecond (an extremely tiny angle, roughly 300-billionths of a degree) each time it orbits. Though minute, this precession could potentially be detected; it is the main impetus for GP-B.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos A second source of tilting, the geodetic effect, arises from the denting of space-time by massive bodies. Dutch scientist Willem de Sitter discovered this property in 1916. When a car drives over bumps in the road, it may swing from side to side. Similarly, if a spinning gyroscope travels through warped space—near a planet, for instance—its axis of rotation tends to lean in various directions. This effect, approximately 6,600 milliarcseconds per year, is also minuscule but decidedly more pronounced than frame dragging. Both effects are so tiny that we might be tempted to ignore them, or dispute whether they are worth spending our hard-earned tax dollars on testing. However, effects that are small in our solar system can have profound implications for the wider cosmos. For example, Einstein’s theory accounts for a tiny change in the orbit of the planet Mercury of 43 arcseconds per century. That minuscule result helped confirm the space-bending properties of general relativity—leading, for example, to predictions about massive black holes in the centers of galaxies. Similarly, precise measurements of the frame-dragging and geodetic effects would undoubtedly produce a wealth of new cosmological conjectures. The GP-B apparatus is specially designed to accomplish this task. Inside an Earth-orbiting satellite is a dewar of superfluid helium, maintaining a temperature of 1.8 degrees above absolute zero. The dewar, in turn, houses a cigar-shaped quartz chamber. Within the chamber are four spinning spherical gyroscopes suspended in an electric field and encased by superconducting lead foil. The extreme cold, electrical levitation, and lead foil each cushion the gyroscopes from stray disturbances. Cold minimizes the random jostling of molecules; levitation minimizes the rocking due to the motion of the vessel; and the foil dampens the influence of Earth’s magnetic field. All this ensures that the gyroscopes are steered almost exclusively by gravitational effects. As in the case of the STEP project, superconductivity plays a second, even more vital role. The gyroscopes are encircled with

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos superconducting loops hooked up to SQUID devices. As they turn ever so slightly, the SQUIDs are sensitive enough to record minute magnetic changes resulting from these reorientations. These devices provide the jeweler’s tools needed to examine the fine facets of relativity. The gyroscopes themselves do not look like the archetypal toy spinning top (though mechanically they act in a similar fashion). Rather, each is a glassy sphere about the size of a Ping-Pong ball, machined to amazing smoothness. The surface of the ball does not depart from that of a perfect sphere by more than a millionth of an inch. To put this into perspective: If Earth were as spherical, its highest mountains and deepest oceans would represent deviations of only about 8 feet! The GP-B satellite follows a polar orbit 400 miles above Earth. To provide a steady reference point, the orbital plane lines up with a star named HR8703, in the constellation Pegasus. This guide star offers an absolute background against which astronomers can take their measurements. As you can see, nothing about the mission has been left to chance. The principal investigator of the GP-B experiment, who also happens to be the chief organizer and developer of the STEP project, is Stanford University physicist C. W. Francis Everitt. Born in 1934 in Sevenoaks, a town in the rolling Kentish countryside of south-eastern England, Everitt first learned about general relativity at an unusually young age. One day when he was 12 years old and was sitting at the family dinner table, his father fascinated him with compelling accounts of gravity’s actions in the universe. “My father,” relates Everitt, “who was an engineer/patent attorney with wide intellectual interests, talked to us about Einstein’s and Eddington’s popular books on the meaning of relativity. He contrasted these with quantum mechanics which, like Einstein, he found not entirely tasteful.” Everitt did not pursue general relativity as his specialty, however, until 1961 when he assumed a position at the University of Pennsylvania. In that scholarly setting, Stanford physicist Bill Fairbank, a

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos pioneering researcher in gravitational and space science, gave a series of talks describing a number of “far out” experiments. “I found them and him fascinating,” recalls Everitt. “Since GP-B was the ‘farthest out’ of the lot, I volunteered to join his group to work on it. At a deeper level I was also much influenced by a remark [Nobel Prize– winning physicist Patrick] Blackett made to me in London: ‘If you can’t think of what physics to do next, invent some new technology; it’ll always lead to new physics’.” Everitt has remarkable perseverance, given the decades taken for his major projects to reach fruition. From the time he began working on GP-B until the instant it blasted off into space, nine U.S. presidents took their oaths of office, musical tastes ran from Doo Wop to Hip Hop, and the world’s population more than doubled. Yet he persisted in his endeavors until he could set his creations free in space. Convincing NASA to construct GP-B in times of tightening budgets required the skills of an expert salesman. Costing hundreds of millions of dollars, it was the most expensive and technologically ambitious science spacecraft ever commissioned by NASA, and its development became the subject of acrimonious debate in the science community. By and large, theoretical physicists wanted it, while astronomers thought it was unnecessary. Like many things in California, it came to represent a focal point of discontent between those in the north and those in the south. Stanford researchers, from the San Francisco area, wanted it built; while many Caltech researchers, from the Los Angeles area, wanted it scrubbed. An exception in the latter camp was Kip Thorne, who consistently supported the mission and was present at the launch. The experiment came perilously close to being closed down several times by NASA, whose critical visits to the Stanford campus were likened by one senior figure as akin to interrogations by the Spanish Inquisition. Even the probe’s launch, from Vandenberg Air Force Base in south-central California, proved a nail-biting test of patience. From December 6, 2003, to April 17, 2004, the mission was held up

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos because of a revamping of its electronics. Then, a broken cord on the launch tower caused another delay. Finally, on April 19, things seemed ready to roll. The mission’s organizers bused several hundred people to the site—including various scientists and journalists keen to catch a glimpse of the historic event. Everything went well until the four-minute mark, when the launch was suddenly aborted due to unfavorable weather conditions. The wind profile at the time was not ideal, and nobody wanted to take any chances. Everybody then went back to their hotels, with some people drowning their sorrows at the local taverns. Everitt, however, did not seem downhearted. Sure enough, the next day when the launch experts tried again, fate was much kinder. First, the epochal words: “Five, four, three, two, one….” A tense pause and then: “We have liftoff for Gravity-Probe B to test Einstein’s theory of relativity in space!” A bright, unnatural light burst over the semiarid landscape of central California. The ball of radiation shot rapidly into the blue morning sky. Perceptibly later, a swath of ragged noise like an avalanche swept over the assembled onlookers. They appeared not to notice. Their eyes were fixed on the actinic light, now halfway up the sky, which marked the location of the spacecraft. It moved surprisingly quickly, heading out over the Pacific atop its Delta II rocket, accelerating to its final speed of about 17,000 miles per hour. In haste, cameras began to click, and a spontaneous cheer followed the probe upward. Heads craned back, hands sheltered narrowed eyes, and after little more than a minute, the sky was empty again, save for a few startled seagulls. “We did it!” exclaimed one of the onlookers, Dimitri Kalligas. His tone mixed triumph and relief. Having worked on the mission at Stanford for several years in the late 1980s and early 1990s, he relished his dreams finally coming alive. He had traveled from his native Greece, together with his wife and two children to savor the moment. His eyes remained transfixed on the rapidly disappearing probe, even as his kids started pulling him impatiently toward the waiting shuttle bus. With a heartfelt gesture, he did the sign of

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos the cross and turned away; the spacecraft was in the heavens where it belonged. Perfectly aligned with its guide star, it has been in orbit ever since. CATCHING WAVES Another critical test of general relativity doesn’t involve space probes; it is taking place right here on Earth. The LIGO (Laser Interferometer Gravitational-Wave Observatory) project is attempting to detect gravitational waves, the elusive ripples in the space-time fabric first predicted by Einstein in 1916. A joint project of scientists from Caltech and MIT, the observatory’s detectors began operation in 2001 and have scanned for signals ever since. Researchers believe cosmic catastrophes, such as supernova explosions or collisions between black holes, generate volleys of gravitational waves. These shock waves are thought to fan out in all directions from such disturbances, rattling any massive objects lying in their paths—in the same way that shops rumble when an elevated train passes overhead. Although they’ve yet to be found directly, astronomers Joseph Taylor and Russell Hulse have used binary pulsars (pairs of rapidly spinning neutron stars) to show that they are likely to exist. For this work they received the 1993 Nobel Prize for Physics. The LIGO project was proposed by physicist Rainer (Rai) Weiss of MIT, along with Kip Thorne, Ronald Drever, Rochus Vogt, and other researchers at Caltech. Born in Berlin in 1932 to a politically active family, Weiss emigrated with them at a young age to the United States to escape the terrors of the Nazi regime. Like Everitt, he was not originally trained in general relativity but rather in another branch of physics. Weiss received his Ph.D. at MIT, in the field of atomic physics under the supervision of Jerrold Zacharias. Zacharias had dedicated himself to building high-precision time-pieces based on the predictable rhythms of atoms, an extraordinarily important endeavor with broad implications for a variety of scien-

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos tific fields. As Weiss related, even Einstein in his final years, while engrossed in the search for a unified field theory, expressed interest in the MIT project to develop such clocks. If such devices could be perfected, one of their possible applications would be precise measurement of the effects of gravitation on time. This would help provide further confirmation of general relativity. Zacharias proudly introduced his project to Weiss. “Jerrold said to me,” recalled Weiss, “that he had made himself a clock called the ‘fountain clock,’ which was a brand new idea involving tossing atoms high into the air and timing them. The idea was to get a long observation time on the atom. He kept telling me that if we could get the clock running, I would travel to the Jungfraujoch, a scientific observatory high in the Swiss Alps. He would be with his clock in the valley and we would measure the Einstein redshift. That’s what set the bee in my bonnet about relativity. But the clock didn’t work; it was a total failure.” Nevertheless, Weiss’s interest in experimental tests of general relativity only grew. Obtaining a postdoctoral fellowship with Bob Dicke, he learned about attempts to measure gravitational radiation. “With Dicke I did something wacky,” continued Weiss. “I worked on a gravitometer to measure scalar waves [a hypothesized mode of radiation] hitting the Earth.” Dicke, a master at cutting through thorny mechanical dilemmas, also instilled in Weiss the value of solid experimental design. Returning to MIT as a professor, Weiss embraced the teachings of his mentors and became one of the world’s leading experts in high-precision measurements of gravity. The capstone of Weiss’s career is LIGO. Weiss developed the notion of using a special technique called laser interferometry to track minute movements of matter due to gravitational waves. Interferometry involves focused beams of light with well-defined frequencies (that is, laser beams) traveling along separate paths and then coming together again. The pattern created when the beams reunite provides precise information about the difference in path lengths.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Imagine the laser beam to be a troop of soldiers, marching down a road in perfect lockstep. At one point the band needs to cross a river, traversing two parallel bridges that at first glance appear to be identical. They split into two groups, continuing to march all the while. When they reunite, they realize that half of them are now marching out of cadence with the others. A member of the corps of engineers measures the bridges, and sure enough, one is 10 inches longer than the other. The extra length created the asynchrony. The same thing happens with light if it is forced to take several different trajectories. The results are characteristic interference patterns—bright and dark fringes that indicate where the beams are in or out of phase. The spacing of these fringes pertains to discrepancies between the routes. Weiss and his collaborators realized that such hairbreadth measures would be needed if science had any chance of sensing the ghostly touch of gravitational pulses. Imagine two black holes colliding thousands of light-years from Earth. The resulting catastrophe would send shock waves through the fabric of space, with these rumbles eventually reaching Earth. Nevertheless, even the signal from such a cataclysmic event would offer only a feather touch on earthly objects. The end points of a yard-long iron rod, if it were completely free to move, would be displaced trillions of times less than the diameter of a speck of dust. Thus, the Caltech and MIT researchers planned LIGO to be miles long (for maximum effect) and calibrated as finely as state-of-the-art technology permitted. The LIGO detectors, located in the states of Louisiana and Washington, are uniquely designed to record the murmurs of passing gravitational waves. Having two widely separated instruments helps rule out the effects of local terrestrial vibrations, such as miniearthquakes or other rumblings, that could masquerade as true signals. A team of planners selected each location to be as far away from urban noise as possible. No one would like a symphony of jackhammers, a band of tractor trailers, and an ensemble of landing jets to serenade the delicate equipment each day—not when it is listening for the subtler melodies of deep space.

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos Each detector is L shaped, with two perfectly straight vacuum pipes meeting at the corner. Like a colossal bowling alley, each pipe stretches out 2.5 miles long, with target masses on both ends. The idea is that gravitational waves would roll through the tubes, nudge the targets in each arm, and slightly alter their mutual separations. Along one arm, the masses would be pushed slightly closer, while along the other they’d be jostled slightly farther apart. Twin laser beams, meeting at the corner, would record these relative differences through the mechanism of light inference. The characteristic inference patterns would offer a telltale sign of gravitational disturbances (like from eons-old cosmic collisions) faintly touching Earth. The direct detection of gravitational waves would be a crowning achievement for Einstein’s theory. It would well justify all the time and money spent on detectors and probes. As Weiss emphasized, “Observing gravitational waves would yield an enormous amount of information about the phenomenon of strong-field gravity. If we could detect black holes colliding that would be amazing.” Such observations would offer a window into regions in which Einstein’s theory differs most greatly from Newton’s. General relativity is the foundation of modern-day astrophysics and cosmology. We cannot know if our theories of the cosmos are correct unless we can trust Einstein. MACH REVISITED While future experiments may indicate a need for its modification, general relativity remains the gold standard. Yet despite its mathematical elegance and predictive success, some physicists are disappointed that it has never fully incorporated Mach’s principle. Einstein’s scheme never established a direct connection between local inertia and distant matter. In the 1950s, British astrophysicist Dennis Sciama made a well-regarded attempt to bridge the gap. He wrote down equations

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos designed to make the locally measured mass of a particle depend on the rest of the matter in a continuously expanding universe. According to his calculations, the enormity of material in the cosmos would outweigh disparate regional influences and produce the uniform tendencies we know as inertia. Sciama never fully developed his model, however—he passed away in 1999 before completing his grand vision. Other physicists have launched similar efforts to encompass Machian notions, but none of their schemes have panned out so far. Perhaps their imaginations haven’t been properly nourished, say with cheap, wholesome cuisine. Enter a trio of hungry cosmologists, famished for truth and a hearty meal. One of us (Paul Wesson), invited colleagues Sanjeev Seahra and Hongya Liu to a working dinner at a no-frills restaurant in Waterloo, Canada. Over heaping plates of seafood, the trio pondered ways of formulating Mach’s principle in terms of gravitational waves moving through an altered version of Einsteinian space-time. Through streams of relativistic calculations, hastily jotted down on available napkins, an intriguing picture emerged of a profoundly interconnected cosmos. The modified theory involves expressing the space-time metric (which measures distances between space-time points) in complex numbers, instead of real (ordinary) numbers. Complex numbers, including terms such as the square root of negative one, play little role in traditional gravitational physics. However, they comprise an important part of quantum mechanics, helping to explain hidden connections between particles. In particular, they permit a complete description of particles in terms of “wave functions”: entities that can stretch out over vast regions of space. By describing mass in terms of elongated waves rather than conventional clumps, the group found that it could express local inertia as a manifestation of the geometry of the universe as a whole. Thus, the combined effects of curvature throughout the entirety of space-time could exert a tug significant enough to affect the acceleration of

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Brave New Universe: Illuminating the Darkest Secrets of the Cosmos objects on Earth. The more matter in space-time (such as stars, galaxies, and quasars), the greater its fabric bends and the more pronounced the effect. This approach to Mach is compatible with Einstein’s standard theory but goes considerably further. In a mathematical sense it extends general relativity to complex numbers, opening the way to all sorts of wavelike phenomena that were formerly the purview of quantum mechanics. In a physical sense the idea that a particle is a wave—whose behavior depends on the rest of the matter in the universe—links the local to the remote. This result came as a surprise to both quantum and classical physicists familiar with the approach, since it shows a way of bridging the two topics. More work is under way to see if the bridge represents a broad boulevard or just a catwalk. Ancient mariners used to steer by the stars—relying on those distant beacons to help them sail across uncharted seas. If Mach’s principle is true, the stars guided their vessels in subtler ways than they ever could have imagined.