Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  It does not make much sense to ask what the universe is expanding into. We picture the balloon universe as expanding into the surrounding space, but this does not make any difference for its inhabitants. They are confined to the surface of the balloon and are not aware of the third, radial dimension. Similarly, for observers in a closed universe, the three-dimensional spherical space is all the space there is, with nothing else outside it.

  Shortly after publishing these results, Friedmann discovered another class of solutions with a different geometry. Instead of curving back on itself, the space in these solutions curves, in a certain sense, away from itself, resulting in an infinite (open) universe. A two-dimensional analogue of this type of space is the surface of a saddle (Figure 3.2).

  Figure 3.1. An expanding and recontracting spherical universe.

  Once again, Friedmann found that the distance separating any pair of galaxies in an open universe grows, starting from zero at the initial singularity. The expansion slows down initially, but in this case the force of gravity is not strong enough to turn it around, so at late times galaxies move apart at nearly constant speeds.

  Figure 3.2. A two-dimensional analogue of an open universe.

  On the borderline between the open and closed models is the universe with a flat, Euclidean geometry.2 It expands without limit, but barely so, with the expansion rate becoming smaller and smaller with time.

  A remarkable feature of Friedmann’s solutions is that they establish a connection between the geometry of the universe and its ultimate fate. If the universe is closed, it must recollapse, and if it is open or flat, it will expand forever.c In his papers Friedmann gave no preference to either model.

  Unfortunately, Friedmann did not live to see his work become the foundation of modern cosmology. He died of typhoid fever in 1925, at the age of thirty-seven. Although Friedmann’s papers were published in a leading German physics journal, they went almost unnoticed.3 His papers were unearthed in the 1930s, in the wake of Hubble’s discovery of the expansion of the universe.d

  THE MOMENT OF CREATION

  Whatever Friedmann’s solutions have to say about the future of the universe, their most unexpected and intriguing aspect is the presence of the initial singularity—the big bang, where the mathematics of general relativity breaks down. At the singularity, matter is compressed to infinite density, and the solutions cannot be extended to earlier times. Thus, taken literally, the big bang should be interpreted as the beginning of the universe. Was that the creation of the world? Could it be that the whole universe began in a singular event a finite time ago?

  For most physicists this was too much to take. A singular jump-starting of the universe looked like a divine intervention, for which they thought there should be no place in physical theory. But although the “beginning of the world” was—and to a large degree remains—a source of discomfort for most scientists, it also had some benefits to offer. It helped to resolve some perplexing paradoxes that haunted the picture of a static, eternally unchanging universe.

  To begin with, an eternal universe appears to be in conflict with one of the most universal laws of nature: the second law of thermodynamics. This law says that physical systems evolve from ordered to more disordered states. If you neatly organize papers into piles on your desk and the wind suddenly blows into the window, the papers are scattered randomly all over the floor. However, you never see the wind picking up papers from the floor and assembling them into neat piles on your desk. Such a spontaneous reduction of disorder is not impossible in principle, but it is so unlikely that it is never seen to occur.

  Mathematically, the amount of disorder is characterized by the quantity called entropy, and the second law says that the entropy of an isolated system can only increase. This relentless increase of disorder leads eventually to the state of maximum possible entropy, thermal equilibrium. In this state all the energy of ordered motion has been turned into heat and a uniform temperature has been established throughout the system.

  The cosmic implications of the second law were first pointed out in the mid-1800s by the German physicist Hermann von Helmholtz. He argued that the whole universe can be regarded as an isolated system (since there is nothing external to the universe). If so, then the second law is applicable to the universe as a whole, and thus the universe should be headed toward an inevitable “heat death” in the state of thermal equilibrium. In that state the stars will all be dead and have the same temperature as their surroundings, and all motion will come to a halt, other than the disordered thermal jostling of the molecules.

  Another consequence of the second law is that if the universe existed forever, it should have already reached thermal equilibrium. And since we do not find ourselves in the state of maximum entropy, it follows that the universe could not have existed forever.4

  Helmholtz did not emphasize this second conclusion and was more concerned about the “death” part (which by the way inspired much apocalyptic prose in the late nineteenth and early twentieth centuries). But other physicists, including giants like Ludwig Boltzmann,e were well aware of the problem. Boltzmann saw the way out in the statistical nature of the second law. Even if the universe is in the maximally disordered state, spontaneous reductions of disorder will occasionally happen by chance. Such events, called thermal fluctuations, are common on the microscopic scale of a few hundred molecules, but become increasingly unlikely as you move toward larger scales. Boltzmann suggested that what we are observing around us is a huge thermal fluctuation in an otherwise disordered universe. The probability for such a fluctuation to happen is unbelievably small. However, improbable things do eventually happen if you wait long enough, and they will definitely happen if you have infinite time at your disposal. Life and observers can exist only in the ordered parts of the universe, and this explains why we are observing this incredibly rare event.5

  The problem with Boltzmann’s solution is that the ordered part of the universe appears to be excessively large. For observers to exist, it would be enough to turn chaos into order on the scale of the solar system. This would have a much higher probability than a fluctuation on the scale of billions of light-years that would be needed to account for the observed universe.

  Another problem, having an even longer pedigree, arises if one assumes that the universe is infinite and that stars (or galaxies) are distributed more or less uniformly throughout the infinite space. If this were the case, then no matter where you looked in the sky, your line of sight would eventually hit upon a star. The sky would then constantly glare with a nearly uniform brilliance—which leaves us with a simple question: Why is it dark at night? The problem was first recognized in 1610 by Johannes Kepler, whose conclusion was that the universe could not be infinite.

  Both the entropy problem and the night sky paradox are naturally resolved if the age of the universe is finite. If the universe came into being only a finite time ago and was initially in a highly ordered (low entropy) state, then we are now observing the descent from that state into chaos and should not be surprised that the state of maximum disorder has not yet been reached. The night sky paradox is resolved because, in a universe of a finite age, light from very distant stars has not had enough time to reach us. We can only observe the stars within the horizon radius, equal to the distance traveled by light during the lifetime of the universe. The number of stars within that radius is clearly finite, even if the entire universe is infinite.

  Given these arguments, how could anyone ever believe that the universe as we know it has existed forever? The reason is, of course, that the idea of a cosmic beginning that occurred a finite time ago creates perplexing problems of its own. If the universe began a finite time ago, then what determined the initial conditions at the big bang? Why did the universe start in a homogeneous and isotropic state? It could in principle start in any state at all. Should we attribute the choice of the initial state to the Creator? Not surprisingly, physicists were slow to embrace the big bang cosmology and made nu
merous attempts to avoid dealing with the problem of “the beginning.”

  ACCEPTING THE INEVITABLE

  Some people initially suggested that the big bang singularity was an artifact of the assumptions of exact homogeneity and isotropy that Friedmann adopted to solve Einstein’s equations. In a collapsing universe, if all galaxies were moving radially toward us, it would be no wonder that they would all crush together in a big crunch. But if the motion of galaxies were even slightly nonradial, one might think that they would bypass one another and start flying apart afterward. The singularity would then be avoided, and contraction would be followed by an expansion. Thus, one might hope to construct an oscillating model of the universe, without a beginning, with alternating periods of expansion and contraction.

  It turns out, however, that the attractive nature of gravity makes this scenario impossible. The British physicist Roger Penrose and Stephen Hawking, who was a graduate student at the time, proved a series of theorems showing, under very general assumptions, that the cosmological singularity cannot be avoided. The main assumptions used in the proofs are that Einstein’s general theory of relativity is valid, and that matter has positive energy density and pressure everywhere in the universe. (More precisely, the pressure should not get so negative as to make gravity repulsive.) Thus, as long as we stay within the framework of general relativity and do not assume exotic repulsive-gravity matter, the singularity will be with us and the question of the initial conditions will remain unresolved.

  The most notorious attempt to avoid the problem of the beginning was no doubt the steady-state theory, suggested in 1948 by the British astrophysicist Fred Hoyle and two Austrian refugees, Hermann Bondi and Thomas Gold, all at Cambridge University. They boldly asserted that the universe has always remained unchanged in its broad features, so that it looks more or less the same at all places and at all times. This view seems to be in glaring contradiction with the expansion of the universe: If the distances between the galaxies grow, how can the universe remain unchanged? To compensate for the expansion, Hoyle and his friends postulated that matter is being continuously created out of the vacuum. This matter fills the voids opened by the receding galaxies, so that new galaxies can be formed in their place.

  The Cambridge physicists admitted that they had no evidence for the spontaneous creation of matter, but the required creation rate was so low—a few atoms per cubic mile per century—that there was no evidence against it either. They further defended their theory by pointing out that continuous creation of matter, in their view, was no more objectionable than creation of all matter at once in the big bang. In fact, the term “big bang” was coined by Hoyle as he ridiculed the competing theory in a popular BBC radio talk show.

  It did not take long, however, for the steady-state theory to run into serious problems. The most distant galaxies are seen as they were billions of years ago, because that is how long it takes for their light to reach us. If the steady-state theory is correct, and the universe at that time was the same as it is now, then these distant galaxies should look more or less the same as the galaxies we now see in our own neighborhood. With more data, however, it became increasingly clear that far-away galaxies are actually quite different and show distinct signs of their youth. They are smaller, have irregular shapes, and are populated with very bright, short-lived stars. Many of them are powerful sources of radio waves, a trait much less common among the older, nearby galaxies.6 There seemed to be no way in which the observations could be explained in terms of the steady-state theory.

  As Sherlock Holmes used to say, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”7 The prospects of the steady-state theory were getting dimmer, and with no other viable alternative in sight, attitudes began to shift. Physicists were gradually coming to terms with the picture of an evolving universe that started with a bang.

  4

  The Modern Story of Genesis

  The elements were cooked in less time than it takes to cook a dish of duck and roast potatoes.

  —GEORGE GAMOW

  TUNNELING THROUGH THE IRON CURTAIN

  The idea of the primeval fireball was born in the mind of George Gamow, a flamboyant Russian-born physicist whom we shall encounter more than once as our story develops. A fellow physicist, Leon Rosenfeld, described him as “a Slav giant, fair haired and speaking a very picturesque German; in fact he was picturesque in everything, even in his physics.”1 Gamow took Friedmann’s course in general relativity in 1923-24, while he was a graduate student in Petrograd; thus he heard about the expanding universe solutions, so to say, from the horse’s mouth. He wanted to do research in cosmology under Friedmann, but this plan was ruined by Friedmann’s sudden death. Gamow ended up writing his thesis on the dynamics of a pendulum, a subject he characterized as “extremely dull.”2

  In 1928, at the instigation of his old professor, Orest Khvolson, Gamow was given a stipend to spend the summer at the University of Göttingen in Germany. That was the time when quantum mechanics was being developed, and Göttingen was one of the leading centers in this area of research. Physicists were trying to capture the essence of the new theory and to contribute to its rapid advance. Discussions that started in seminar rooms during the day continued in the streets and cafés in the evenings, and it was hard not to be infected by this atmosphere of excitement and discovery. Gamow decided to investigate what quantum mechanics could say about the structure of atomic nuclei, and very quickly he made his mark. He used what is called the tunneling effect—the penetration of a barrier by a quantum particle—to explain the radioactive decay of nuclei. His theory was in beautiful agreement with the experimental data.

  When the summer came to an end and it was time to return to Petrograd (now called Leningrad), Gamow decided to make a stop in Denmark and visit the legendary Niels Bohr, one of the founders of the quantum theory. He told Bohr about his work on radioactivity (which was not yet published), and Bohr was sufficiently impressed to offer Gamow a fellowship at his institute in Copenhagen. Of course, Gamow accepted with enthusiasm. He continued work in nuclear physics and soon became a recognized authority in this field.

  In 1930 Gamow was invited to give a major talk at the International Congress on Nuclear Physics in Rome. He was already preparing to cross Europe on his little motorcycle when he learned from the Soviet embassy that his passport could not be extended and that he had to return to the Soviet Union before traveling anywhere else.

  Back in Leningrad, Gamow immediately sensed that things had taken a drastic turn for the worse. The Stalinist regime was tightening its grip on the country. Science and art had to conform to the official Marxist ideology, and anyone accused of “bourgeois” idealistic views was severely persecuted. Quantum mechanics and Einstein’s theory of relativity were declared nonscientific and contrary to Marxism-Leninism. When Gamow mentioned quantum physics in a public lecture, a government representative interrupted the lecture and dismissed the audience. Gamow was warned that such mistakes were not to be repeated. Even before this incident, he was told he could forget about foreign travel and should not bother applying for a passport. The iron curtain was tightly closed. In Gamow’s mind, the writing was on the wall: he had to escape from the Soviet Union.

  With his wife Lyuba, whom he had married soon after his return to Leningrad, Gamow was preparing for the escape. The plan was to cross the Black Sea from the Crimean Peninsula to Turkey. Childish as it may seem, they wanted to do this in a kayak. They had a food supply for a week and a simple navigation plan: paddling straight to the south. But the Black Sea is not called black for nothing. Perfectly calm when the two adventurers left in the morning, the sea became increasingly rough toward the evening. During the night, it took all their efforts to keep the boat from turning over. Accepting defeat, they were now fighting to get back to the shore and felt fortunate when they finally made it the following day.

  It was totally unexpected when in the summer of 1933 Gamow
was informed that he had been appointed to represent the Soviet Union at the prestigious Solvay Congress on nuclear physics in Brussels. He was overjoyed, but had no idea what to make of it. The explanation came on arrival at the congress. When Gamow did not show up in Rome, Niels Bohr got concerned and wanted to see his old friend. He asked the French physicist Paul Langevin, a member of the French Communist Party, to use his connections to arrange Gamow’s appointment to the Solvay Congress. But, Gamow was horrified to find out, Bohr gave Langevin his personal assurance that Gamow was going to return to the Soviet Union! That evening at the dinner table Gamow sat next to Marie Curie, the famous discoverer of radium and plutonium, and told her about his impossible situation. Madame Curie knew Langevin very well (rumors said too well); she said she would talk to him. After a sleepless night and a day of anxious anticipation, Gamow finally heard from Curie that the issue was settled and he did not have to go back. The following year he accepted a professorship at George Washington University in the United States.

  THE PRIMEVAL FIREBALL

  Gamow realized that the early universe was not only superdense, it was also superhot. The reason is that gases get hotter when they are compressed and cool down when they expand. (People who ride bicycles tell me that they know this property firsthand: a bicycle tire gets warm when you pump it with air. The compressed air heats up and the surface of the tire gets warmer as a result.)