Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  If successful, this line of reasoning would drive the Creator entirely out of the picture. Inflation relieved him of the job of setting up the initial conditions of the big bang, quantum cosmology unburdened him of the task of creating space and time and starting up inflation, and now he is being evicted from his last refuge—the choice of the fundamental theory of nature.

  Tegmark’s proposal, however, faces a formidable problem. The number of mathematical structures increases with increasing complexity, suggesting that “typical” structures should be horrendously large and cumbersome. This seems to be in conflict with the simplicity and beauty of the theories describing our world.8 It thus appears that the Creator’s job security is in no immediate danger.

  MANY WORLDS IN ONE

  Philosophers and theologians have been arguing for centuries, trying to decide whether the universe is finite or infinite, stationary or evolving, eternal or transient. You might have thought that all possible answers to these questions have already been anticipated. However, the worldview emerging from recent developments in cosmology is not what anyone had expected. Instead of choosing between conflicting options, it suggests that each of them has some element of truth.

  At the heart of the new worldview is the picture of an eternally inflating universe. It consists of isolated “island universes,” where inflation has ended, immersed in the inflating sea of false vacuum. The boundaries of these postinflationary islands are rapidly expanding, but the gaps that separate them are widening even faster. Thus there is always room for more island universes to form, and their number increases without bound.

  Viewed from the inside, each island is a self-contained infinite universe. We live in one of these island universes, and our observable region is one of the infinite number of O-regions that it contains. It is conceivable that billions of years from now our descendants will travel to other O-regions, but a voyage to another island universe is impossible, even in principle. No matter how long we travel and how fast, we are forever confined to our own island universe.

  The entire eternally inflating spacetime originated as a minuscule closed universe. It tunneled, quantum-mechanically, out of nothing and immediately plunged into the never-ending fury of inflation. Thus the universe is eternal, but it did have a beginning.

  Inflation rapidly blows the universe up to an enormous size, but from a global viewpoint it always remains closed and finite. And yet, due to the peculiar structure of inflationary spacetime, it contains an unlimited number of infinite island universes.

  Constants of nature that shape the character of our world take different values in other island universes. Most of these universes are drastically different from ours, and only a tiny fraction of them are hospitable to life.9 Observers in each habitable island will find that their universe evolves from a big bang to a big crunch. However, in the global view, all types of islands at all stages of their evolution are present simultaneously. This situation is analogous to that of the human population of the Earth. Each person starts as a baby and grows older with time, but the entire population includes people of all ages at any given moment. Although the total volume of the universe grows with time, the fraction of space occupied by each type of island does not change. In this sense, the eternally inflating universe is stationary.

  A striking feature of the new worldview is the existence of multiple “other worlds” beyond our observable region. Some of them are rather uncontroversial. Very few people, for example, would question the reality of other O-regions, even though they cannot be observed. We do have some circumstantial evidence for multiple island universes with diverse properties. As for the other, disconnected spacetimes that nucleated out of nothing, we have no idea how to test their existence observationally.

  The picture of quantum tunneling from nothing raises another intriguing question. The tunneling process is governed by the same fundamental laws that describe the subsequent evolution of the universe. It follows that the laws should be “there” even prior to the universe itself. Does this mean that the laws are not mere descriptions of reality and can have an independent existence of their own? In the absence of space, time, and matter, what tablets could they be written upon? The laws are expressed in the form of mathematical equations. If the medium of mathematics is the mind, does this mean that mind should predate the universe?

  This takes us far into the unknown, all the way to the abyss of great mystery. It is hard to imagine how we can ever get past this point. But as before, that may just reflect the limits of our imagination.

  Epilogue

  To: Galactic Council

  From: WSX–23EDJ

  Greetings! As required by the Protocol, I have completed my inspection of the planet Earth, located in sector S—16 in the peripheral zone of the Galaxy. The human race populating this planet has made good progress in the 1000 Earth years since the last inspection. I have upgraded their status from “budding” to “technologically challenged.”

  You will be amused to know that humans believe they are close to discovering the final theory of the universe. I envy their youthful enthusiasm … On certain issues they have come close to the right answers—surprisingly, I would say, for a primitive civilization such as this. In other matters, though, they are pretty far behind. They have not even figured out the right questions.

  Overall, this race is still rather immature. I recommend against inclusion in the Galactic Union at this time. Further details will be forthcoming in my regular report.

  Yours respectfully,

  WSX—23EDJ

  Notes

  1. WHAT BANGED, HOW IT BANGED, AND WHAT CAUSED IT TO BANG

  1 A. H. Guth, The Inflationary Universe (Addison-Wesley, Reading [Mass.], 1997, p. 2).

  2. THE RISE AND FALL OF REPULSIVE GRAVITY

  1 Einstein to Ehrenfest, January 16, 1916 (as quoted in A. Pais, Subtle is the Lord (Oxford University Press, Oxford, 1982).

  2 Einstein to Sommerfeld, February 8, 1916, ibid.

  3 It was later realized that Einstein’s static cosmological model is not acceptable even on purely theoretical grounds, because the balance between attractive and repulsive gravity in this model is unstable. If for some reason the size of the universe is slightly increased, the matter density will go down (since the distances between galaxies will grow), while the vacuum energy density will remain the same, being fixed by the cosmological constant. Hence, the repulsive gravity of the vacuum will now be stronger than the attractive gravity of matter and will cause the universe to expand. This will lead to a further increase of volume and to even greater imbalance between the attractive and repulsive forces. The universe will thus enter a regime of runaway expansion. Similarly, if the size of Einstein’s static universe is slightly decreased, the attractive gravity of matter will win over the repulsion of the vacuum and the universe will collapse to a point. Small fluctuations in the size of the universe are inevitable according to the quantum theory, and thus Einstein’s universe cannot remain in balance for an infinite time.

  3. CREATION AND ITS DISCONTENTS

  1 As quoted in E. A. Tropp, V.Y. Frenkel, and A. D. Chernin, Aleksandr Aleksandrovich Fridman (Nauka, Moscow, 1988, p. 133).

  2 Friedmann did not consider the case of a spatially flat universe. It was studied by Einstein and Willem de Sitter in 1932.

  3 A notable exception was Einstein’s reaction to Friedmann’s work. Initially, Einstein thought that Friedmann had made a mistake and wrote a brief note to the journal pointing to what he thought was an error. However, in less than a year he had to withdraw his criticism after a conversation with Friedmann’s friend, Yuri Krutkov. Krutkov reported home that he had won a debate with Einstein and that “Petrograd’s honor is saved!” But Einstein, though he agreed with Friedmann’s mathematics, still believed that the universe was static and that Friedmann’s work was therefore of purely formal interest. In his second note to the journal, he wrote that he was “convinced that Mr. Friedmann’s results are both correct and c
larifying.” He added in the original draft that the results could hardly be of any physical significance, but then crossed this phrase out, perhaps realizing that it was based more on his philosophical prejudice than on any known fact. Quotes are from Helge Kragh, Cosmology and Controversy, (Princeton University Press, Princeton [N.J.], 1996).

  4 The source of stellar energy was not known in Helmholtz’s time, but now we know that stars are burning nuclear fuel by turning hydrogen into helium and then into heavier nuclei. This is an irreversible process accompanied by an increase of entropy, and eventually stars run out of nuclear fuel. Some stars turn off their nuclear engines without much fanfare and then gradually cool down, while others explode, throwing their constituent gas into the interstellar space and leaving behind a compact remnant (a neutron star or a black hole). The expelled gas can be reprocessed to form new stars, but sooner or later the gas supply will be exhausted, as more and more of it ends up in cold stellar remnants. In a trillion years from now, galaxies will probably be noticeably dimmer than they are today. The process of gradual dimming of lights may be rather protracted, but one thing is clear: the universe as we know it could not have existed forever.

  5 Boltzmann’s fluctuation idea is probably the first example of what will later be known as anthropic arguments (see Chapter 13).

  6 The first persuasive evidence for the galactic evolution was presented in the 1950s by the Cambridge astronomer Martin Ryle. He found that powerful radio emission from galaxies was much more common a few billion years ago than it is now.

  7 Arthur Conan Doyle, The Sign of Four.

  4. THE MODERN STORY OF GENESIS

  1 Quoted from R. H. Stuewer, in The Kaleidoscope of Science, ed. by E. Ullmann-Margalit (Reidel, Dordrecht [Netherlands], 1986, p. 147).

  2 The description of Gamow’s life in this section is based mostly on his unfinished autobiography, My World Line (Viking Press, New York, 1970).

  3 Atoms are made of small, positively charged nuclei and negatively charged electrons “orbiting” around them. (I put “orbiting” in quotation marks, because quantum uncertainties are important in the atom, so instead of picturing electrons as moving in an orderly way along their orbits, like planets around the Sun, it is more accurate to picture them as being “smeared” around the orbits.) The nuclei consist of two types of subatomic particles: protons, which have a positive electric charge, and neutrons, which are electrically neutral. The chemical properties of an atom are determined solely by the number of electrons (which is equal to the number of protons, so that the atom is electrically neutral).

  4 The origin of this imbalance between matter and antimatter is one of the active areas of research in modern cosmology. For a discussion, see A. H. Guth, The Inflationary Universe (Addison-Wesley, Reading [Mass.], 1997).

  5 A more detailed discussion of the hot fireball and element formation can be found in Steven Weinberg’s classic bestseller The First Three Minutes (Bantam, New York, 1977).

  6 M. J. Rees, Before the Beginning (Addison-Wesley, Reading [Mass.], 1997, p. 17).

  7 S. Weinberg, op. cit., p. 123.

  5. THE INFLATIONARY UNIVERSE

  1 The twists and turns of Alan Guth’s path to the discovery of inflation are described in his excellent book The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (Addison-Wesley, Reading [Mass.], 1997).

  2 It is conceivable that our vacuum is not, in fact, the lowest-energy one. String theory, which is now the prime candidate for the fundamental theory of nature, suggests the existence of negative-energy vacua. If they do exist, then our vacuum may eventually decay, with catastrophic consequences for all the material objects it contains. We shall discuss string theory in Chapter 15 and the possibility of our vacuum decay in Chapter 18. Until then we shall assume that we live in the true vacuum.

  3 This conclusion is easy to understand from simple energy considerations. The force on a physical object always acts in the direction of reducing its energy (more precisely, its potential energy, that is, the part of energy not related to motion). For example, the force of gravity pulls objects down, so that their energy is decreased. (The gravitational energy grows with elevation above the ground.) For a false vacuum, the energy is proportional to the volume it occupies and can be reduced only by reducing the volume. Hence, there should be a force causing the vacuum to shrink. This is the force of tension.

  6. TOO GOOD TO BE WRONG

  1 A. H. Guth, “The inflationary universe: A possible solution to the horizon and flatness problems,” Physical Review, vol. D23, p. 347 (1981).

  2 The Starobinsky model is based on a modified form of Einstein’s gravitational equations. The modification becomes important only when the curvature of spacetime gets very high. The magnitude of the curvature plays the role of a scalar field in this theory.

  3 True to the Russian style, Mukhanov and Chibisov wrote their paper “for Landau,” stating their result and providing little detail of how it was derived. Some of the Nuffield participants argue that an important step may be missing in this derivation and that Mukhanov and Chibisov may not, therefore, deserve full credit for the result. In my opinion, they do.

  8. RUNAWAY INFLATION

  1 A. Vilenkin, “The birth of inflationary universes,” Physical Review, vol. D27, p. 2848 (1983). This paper is about quantum cosmology; eternal inflation is discussed in sections IV and V.

  2 An exponentially expanding region would quickly cover the whole computer screen, forcing us to stop the simulation. We dealt with this problem by using an expanding distance scale, which grew at the same rate as the inflating regions. Measured by this expanding ruler, the size of the inflating false-vacuum volume does not change in time, so it occupies a fixed area on the screen. In the economic inflation analogy that we used in Chapter 5, this method of measurement corresponds to expressing prices in “original dollars,” so that the effect of inflation is factored out.

  3 M. Aryal and A. Vilenkin, “The fractal dimension of the inflationary universe,” Physics Letters, vol. B199, p. 351 (1987).

  4 A. D. Linde, “Eternally existing self-reproducing chaotic inflationary universe,” Physics Letters, vol. B175, p. 395 (1986). The term “eternal inflation” was introduced by Linde in this paper.

  9. THE SKY HAS SPOKEN

  1 The accelerated expansion of the universe was discovered by the High-Redshift Supernova Search Team, led by the Harvard astronomer Robert Kirshner and by Brian Schmidt of Siding Springs Observatory in Australia, and by the Supernova Cosmology Project team, led by Saul Perlmutter. For a witty firsthand account of this discovery, see Robert Kirshner’s book The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos (Princeton University Press, Princeton, [N.J.], 2004).

  2 Inflation can be reconciled with density smaller than critical at the expense of making the theory more complicated and less attractive. To this end, the scalar field energy landscape needs to be specially designed. It needs to have a barrier, as in Guth’s original model (Figure 6.2). But instead of dropping steeply toward the minimum, the barrier must be followed by a very gentle slope. The resulting model combines the features of Guth’s old inflation scenario with the improved scenario by Linde and others. The field tunnels through the barrier via bubble nucleation and completes its journey to the minimum by slowly rolling downhill within individual bubbles. In his analysis of vacuum bubbles, Sidney Coleman showed that from within they look like open Friedmann universes with density smaller than critical. By carefully adjusting the height and the slope of the hill, one can arrange for the density to be close, but not too close, to the critical density. Physicists find such fine-tuning very distasteful, so the hope is that it will not be needed.

  If, on the other hand, observations point to a density greater than critical, by more than one part in 100,000, the implication would be that the universe is a relatively small three-dimensional sphere, not much larger than the present horizon. This would pose a severe problem for inflation.
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  3 The origin of gravitational waves is similar to that of the density perturbations (see Chapter 6). They are produced as quantum fluctuations during inflation, with amplitudes independent of their length scale. The prediction of gravitational waves follows from the work that Alexei Starobinsky did in 1980, before Guth proposed the idea of inflation.

  4 Clover will start operating in 2008. It will be able to detect gravitational waves from inflation only if the false vacuum had a grand-unification energy scale. For a lower-energy vacuum, a more sensitive instrument will be needed.

  10. INFINITE ISLANDS

  1 A. D. Linde, “Life after inflation,” Physics Letters, vol. B211, p. 29 (1988).

  2 In flat spacetime, the square of the interval between two events is defined as (time separation)2 – (space separation)2. Except for the minus sign, this quantity is very similar to the length squared in the Pythagorean theorem. To calculate the interval, time and space separations have to be expressed in compatible units. For example, if time is measured in years, then length should be measured in light-years. The interval is timelike if its square is positive, and is spacelike if it is negative. For the class reunion and superball events discussed in the text, the time separation is 3 years, the space separation is 4 light-years, so the interval squared is 32 – 42 = –7. Hence, the interval is spacelike.