Many Worlds in One: The Search for Other Universesby Alex Vilenkin
A Leading Figure in the Development of the New Cosmology Explains What It All Means
Among his peers, Alex Vilenkin is regarded as one of the most imaginative and creative cosmologists of our time. His contributions to our current understanding of the universe include a number of novel ideas, two of which—eternal cosmic inflation and the quantum/p>/b>
A Leading Figure in the Development of the New Cosmology Explains What It All Means
Among his peers, Alex Vilenkin is regarded as one of the most imaginative and creative cosmologists of our time. His contributions to our current understanding of the universe include a number of novel ideas, two of which—eternal cosmic inflation and the quantum creation of the universe from nothing—have provided a scientific foundation for the possible existence of multiple universes.
With this book—his first for the general reader—Vilenkin joins another select group: the handful of first-rank scientists who are equally adept at explaining their work to nonspecialists. With engaging, well-paced storytelling, a droll sense of humor, and a generous sprinkling of helpful cartoons, he conjures up a bizarre and fascinating new worldview that—to paraphrase Niels Bohr—just might be crazy enough to be true.
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Many Worlds in One
The Search for Other Universes
By Alex Vilenkin
Farrar, Straus and GirouxCopyright © 2006 Alex Vilenkin
All rights reserved.
What Banged, How It Banged, and What Caused It to Bang
In the context of inflationary cosmology, it is fair to say that the universe is the ultimate free lunch.
On a Wednesday afternoon, in the winter of 1980, I was sitting in a fully packed Harvard auditorium, listening to the most fascinating talk I had heard in many years. The speaker was Alan Guth, a young physicist from Stanford, and the topic was a new theory for the origin of the universe. I had not met Guth before, but I had heard of his spectacular rise from obscurity to stardom. Only a month before, he belonged to the nomadic tribe of postdocs—young researchers traveling from one temporary contract to another, in the hope of distinguishing themselves and landing a permanent job at some university. Things were looking bleak for Guth: at age thirty-two he was getting a bit old for the youthful tribe, and the contract offers were beginning to dry out. But then he was blessed with a happy thought that changed everything.
Guth turned out to be a short, bouncy fellow, full of boyish enthusiasm, apparently untarnished by his long wanderings as a postdoc. From the outset, he made it clear that he was not trying to overthrow the big bang theory. There was no need to. The evidence for the big bang was very persuasive, and the theory was in good shape.
The most convincing evidence is the expansion of the universe, discovered by Edwin Hubble in 1929. Hubble found that distant galaxies are moving away from us at very high speeds. If the motion of the galaxies is traced backward in time, they all merge together at some moment in the past, pointing to an explosive beginning of the universe.
Another major piece of evidence in favor of the big bang is the cosmic background radiation. Space is filled with microwaves of about the same frequency as we use in microwave ovens. The intensity of this radiation dwindles as the universe expands; hence what we now observe is the faint afterglow of the hot primeval fireball.
Cosmologists used the big bang theory to study how the fireball expanded and cooled, how atomic nuclei formed, and how the grand spirals of galaxies emerged from featureless gas clouds. The results of these studies were in excellent agreement with astronomical observations, so there was little doubt that the theory was on the right track. What it described, however, was only the aftermath of the big bang; the theory said nothing about the bang itself. In Guth's own words, it did not say "what 'banged,' how it 'banged,' or what caused it to 'bang.'"
To compound the mystery, on closer examination the big bang appeared to be a very peculiar kind of explosion. Just imagine a pin balancing on its point. Nudge it slightly in any direction and it will fall. So it is with the big bang. A large universe sprinkled with galaxies, like the one we see around us, is produced only if the power of the primordial blast is fine-tuned with an incredible precision. A tiny deviation from the required power results in a cosmological disaster, such as the fireball collapsing under its own weight or the universe being nearly empty.
The big bang cosmology simply postulated that the fireball had the required properties. The prevailing attitude among physicists was that physics can describe how the universe evolved from a given initial state, but it is beyond physics to explain why the universe happened to start in that particular configuration. Asking questions about the initial state was regarded as "philosophy," which, coming from a physicist, translates as a waste of time. This attitude, however, did not make the big bang any less enigmatic.
Now Guth was telling us that the veil of mystery surrounding the big bang could be lifted. His new theory would uncover the nature of the bang and explain why the initial fireball was so contrived. The seminar room fell suddenly silent. Everybody was intrigued.
The explanation the new theory gave for the big bang was remarkably simple: the universe was blown up by repulsive gravity! The leading role in this theory is played by a hypothetical, superdense material with some highly unusual properties. Its most important characteristic is that it produces a strong repulsive gravitational force. Guth assumed that there was some amount of this material in the early universe. He did not need much: a tiny chunk would be sufficient.
The internal gravitational repulsion would cause the chunk to expand very rapidly. If it were made of normal matter, its density would be diluted as it expanded, but this antigravity stuff behaves completely differently: the second key feature of the strange material is that its density always remains the same, so its total mass is proportional to the volume it occupies. As the chunk grows in size, it also grows in mass, so its repulsive gravity becomes stronger and it expands even faster. A brief period of such accelerated expansion, which Guth called inflation, can enlarge a minuscule initial chunk to enormous dimensions, far exceeding the size of the presently observable universe.
The dramatic increase in mass during inflation may at first appear to contradict one of the most fundamental laws of physics, the law of energy conservation. By Einstein's famous relation, E = mc2, energy is proportional to mass. (Here, E is energy, m is mass, and c is the speed of light.) Sothe energy of the inflating chunk must also have grown by a colossal factor, while energy conservation requires that it should remain constant. The paradox disappears if one remembers to include the contribution to the energy due to gravity. It has long been known that gravitational energy is always negative. This fact did not appear very important, but now it suddenly acquired a cosmic significance. As the positive energy of matter grows, it is balanced by the growing negative gravitational energy. The total energy remains constant, as demanded by the conservation law.
In order to provide an ending for the period of inflation, Guth required that the repulsive gravity stuff should be unstable. As it decays, its energy is released to produce a hot fireball of elementary particles. The fireball then continues to expand by inertia, but now it consists of normal matter, its gravity is attractive, and the expansion gradually slows down. The decay of the antigravity material marks the end of inflation and plays the role of the big bang in this theory.
The beauty of the idea was that in a single shot inflation explained why the universe is so big, why it is expanding, and why it was so hot at the beginning. A huge expanding universe was produced from almost nothing. All that was needed was a microscopic chunk of repulsive gravity material. Guth admitted he did not know where the initial chunk came from, but that detail could be worked out later. "It's often said that you cannot get something for nothing," he said, "but the universe may be the ultimate free lunch."
All this assumes, of course, that the repulsive gravity stuff really existed. There was no shortage of it in science fiction novels, where it had been used in all sorts of flying machines, from combat vehicles to antigravity shoes. But could professional physicists seriously consider the possibility that gravity might be repulsive?
They sure could. And the first to do that was none other than Albert Einstein.CHAPTER 2
The Rise and Fall of Repulsive Gravity
"We have conquered gravity!" the Professor shouted, and crashed to the floor.
—J. WILLIAMS and R. ABRASHKIN, Danny Dunn and the Anti-Gravity Paint
THE FABRIC OF SPACE AND TIME
Einstein created two theories of stunning beauty that forever changed our concepts of space, time, and gravitation. The first of the two, called the special theory of relativity, was published in 1905, when Einstein was twenty-six and by most standards could be regarded a failure. His fierce independence and his casual class attendance did not make him popular among the professors at Zurich Polytechnic, where he got his diploma. When the time came to apply for jobs, all his fellow graduates were appointed assistants at the Polytechnic, while Einstein failed to get any academic position. He thought himself lucky to have a job as a clerk at the patent office in Berne, which he got with the help of a former classmate. On the positive side, the patent office work was not without some interest and left plenty of time for Einstein's research and other intellectual pursuits. He spent evenings with friends, smoking a pipe, reading Spinoza and Plato, and discussing his ideas about physics. He also played string quintets in the unlikely company of a lawyer, a bookbinder, a schoolteacher, and a prison guard. None of them suspected that their second violin had something profound to say about the nature of space and time.
Einstein completed the special theory of relativity in less than six weeks of frenzied work. The theory shows that space and time intervals do not by themselves have absolute meaning, but rather depend on the state of motion of the observer who measures them. If two observers move relative to one another, then each of them will find that the other's clock ticks more slowly than his own. Simultaneity is also relative. Events that are simultaneous for one observer will generally occur at different times for the other. We do not notice these effects in our everyday life because they are completely negligible at ordinary velocities. But if the speed of the two observers relative to each other is close to the speed of light, the discrepancies between their measurements can be very large. There is one thing, though, that all observers will agree upon: light always travels at the same speed, approximately 300,000 kilometers per second.
The speed of light is the absolute speed limit in the universe. As you apply a force to a physical object, the object accelerates. Its velocity grows, and if you keep up the force, the velocity of the object will eventually approach the speed of light. Einstein showed that it would take increasingly large amounts of energy to get closer and closer to the speed of light, so the limit can never be reached.
Perhaps the best-known consequence of special relativity is the equivalence of energy and mass, expressed in Einstein's formula E = mc2. If you heat an object, its thermal (heat) energy grows, so it should weigh more. This may give you the idea to take a cold shower before you step on the scale. But this trick is likely to decrease your weight by no more than a few billionths of a pound. In conventional units, like meters and seconds, the conversion factor c2 between energy and mass is very large, and it takes a huge amount of energy to noticeably change the mass of a macroscopic body. Physicists often use another system of units, where c = 1, so that energy is simply equal to mass and can be measured in kilograms.a I will mostly follow this tradition and make no distinction between energy and mass.
The word "special" in "special relativity" refers to the fact that this theory applies only in special circumstances when the effects of gravity are unimportant. This limitation is removed in Einstein's second theory, the general theory of relativity, which is essentially a theory of gravitation.
The general theory of relativity grew out of a simple observation, that the motion of objects under the action of gravity is independent of their mass, shape, or any other properties, as long as all nongravitational forces can be neglected. This was first recognized by Galileo, who forcefully argued the point in his famous Dialogues. The accepted view at the time, that of Aristotle, was that heavier objects fall faster. Indeed, a watermelon does fall faster than a feather, but Galileo realized that the difference was due only to air resistance. Legend has it that Galileo dropped rocks of different weight from the Leaning Tower of Pisa, to make sure that they landed at the same time. We do know that he experimented with marbles rolling down an inclined plane and found that the motion was independent of the mass. He also offered a theoretical proof that Aristotle could not be right. Suppose, says Galileo, that a heavy rock falls faster than a light rock. Imagine then tying them together with a very light string. How will this affect the fall of the heavy rock? On the one hand, the slower-moving light rock should make the fall of the heavy rock somewhat slower than it was before. On the other hand, viewed together, the two rocks now constitute one object that is more massive than the heavy rock was initially, and thus the two rocks together should fall faster. This contradiction demonstrates that Aristotle's theory is inconsistent.
Einstein was pondering this peculiar kind of motion, which is completely independent of what is moving. It reminded him of inertial motion: in the absence of forces, an object moves along a straight line at a constant speed, regardless of what it is made of. In effect, the motion of the object in space and time is the property of space and time themselves.
Here Einstein made use of the ideas of his former mathematics professor, Hermann Minkowski. As a student, Einstein did not think much of Minkowski's lectures, while Minkowski remembered Einstein as a "lazy dog" and did not expect him to do anything worthwhile. To Minkowski's credit, he changed his mind quickly after reading Einstein's 1905 paper.
Minkowski realized that the mathematics of special relativity becomes simpler and more elegant if space and time are not regarded as separate, but are united in a single entity called spacetime. A point in spacetime is an event. It can be specified by four numbers: three for its spatial location and one for its time. Hence, spacetime has four dimensions. If you had all of spacetime in front of you, then you would know all the past, present, and future of the universe. The history of each particle is represented by a line in spacetime, which gives the position of the particle at every moment of time. This line is called the world line of the particle. (George Gamow, one of the founders of the big bang cosmology, called his autobiography My World Line.)
The uniform motion of particles in the absence of gravity is represented by straight lines in spacetime. But gravity makes particles deviate from this simple motion, so their world lines are no longer straight. This led Einstein to a truly astonishing hypothesis: even deviant particles with curved world lines might still be following the straightest possible paths in spacetime, but the spacetime itself must be curved around massive bodies. Gravity, then, is nothing but the curvature of spacetime!
The distortion of spacetime geometry by a massive body can be illustrated by a heavy object resting on a horizontally stretched rubber sheet (see Figure 2.1). The rubber surface is warped near the object, just as spacetime is warped near a gravitating body. If you try playing billiards on this rubber sheet, you will discover that the billiard balls are deflected on the curved surface, especially when they pass near the heavy mass. This analogy is not perfect—it illustrates only the warping of space, not that of spacetime—but it does capture the essence of the idea.
It took Einstein more than three years of truly heroic effort to express these ideas in mathematical terms. The equations of the new theory, which he called the general theory of relativity, relate the geometry of spacetime to the matter content of the universe. In the regime of slow motion and not-too-strong gravitational fields, the theory reproduced Newton's law, with the force of gravity being inversely proportional to the square of the distance. There was also a small correction to this law, which was utterly negligible for planetary motion, except in the case of Mercury, the planet closest to the Sun. The effect of the correction was to cause a slow precession, or advance, of Mercury's orbit. Astronomical observations did in fact show a tiny precession, which remained unexplained in Newton's theory, but was in perfect agreement with Einstein's calculation. At this point Einstein was certain that the theory was correct. "I was beside myself with ecstasy for days," he wrote to his friend Paul Ehrenfest.
Perhaps the most remarkable thing about the general theory of relativity is how little factual input it required. The essential fact that Einstein placed at the foundation of the theory—that the motion of objects under the action of gravity is independent of their mass—was known already to Galileo. With this minimal input, he created a theory that reproduced Newton's law in the appropriate limit and explained a deviation from this law. If you think about it, Newton's law is in some sense arbitrary. It states that the gravitational force between two bodies is inversely proportional to the second power of their distance, but it does not say why. It could equally well be the fourth power or the 2.03rd power. In contrast, Einstein's theory allows no freedom. The picture of gravity as curvature of spacetime inevitably leads to Einstein's equations, and the equations yield the inverse square law. In this sense the general theory of relativity not only describes gravity, it explains gravity. So compelling was the logic of the theory and so beautiful its mathematical structure that Einstein felt it simply had to be right. In a letter to a senior colleague, Arnold Sommerfeld, he wrote, "Of the general theory of relativity you will be convinced, once you have studied it. Therefore I am not going to defend it with a single word."
Excerpted from Many Worlds in One by Alex Vilenkin. Copyright © 2006 Alex Vilenkin. Excerpted by permission of Farrar, Straus and Giroux.
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Meet the Author
Alex Vilenkin is a professor of physics at Tufts University, where he also serves as director of the Tufts Institute of Cosmology. The author of more than 150 research papers in cosmology, he has introduced a number of novel ideas to the field.
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