Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  11. THE KING LIVES!

  1 J. Garriga and A. Vilenkin, “Many worlds in one,” Physical Review, vol. D64, p. 043511 (2001).

  2 A. D. Sakharov, Alarm and Hope (Knopf, New York, 1978).

  3 G.F.R. Ellis and G. B. Brundrit, “Life in the infinite universe,” Quarterly Journal of the Royal Astronomical Society, vol. 20, p. 37 (1979).

  4 For a thought-provoking discussion of the many-world interpretation, see the book by David Deutsch, The Fabric of Reality (Penguin, New York, 1997).

  5 As quoted in G. Edelman, Bright Air, Brilliant Fire: On the Matter of the Mind (Penguin, New York, 1992, p. 216).

  6 This formulation is David Mermin’s; see Physics Today, April 1989, p. 9.

  7 From President Clinton’s testimony to the grand jury on August 17, 1998.

  8 An example of energy landscape designed to avoid eternal inflation is shown in the figure on p. 214 (compare with Figure 6.4).

  The flat hilltop responsible for eternal inflation is removed and replaced with a steep spike. At the same time, the flattened slope of the hill needs to be preserved, since otherwise we would have no inflation at all. Such landscapes are not likely to arise from particle physics. Inflation is eternal in practically all models suggested so far.

  9 Some ethical implications of the new worldview are discussed in the paper I wrote with the philosopher Joshua Knobe and my Tufts colleague Ken Olum, “Philosophical implications of inflationary cosmology,” to appear in the March 2006 issue of The British Journal for the Philosophy of Science.

  12. THE COSMOLOGICAL CONSTANT PROBLEM

  1 The first convincing measurement of electromagnetic vacuum fluctuations was performed only in the late 1990s, using the idea proposed decades earlier by the Dutch physicist Hendrik Casimir. Two metal plates are placed in a vacuum parallel to one another. Electromagnetic oscillations are suppressed in metal, and this has the effect of reducing vacuum fluctuations in the space between the plates. The pressure exerted by the fluctuating fields on the outer surfaces of the plates is therefore greater than the pressure acting from the inside, so there is a net force pushing the plates together. This force is very small and rapidly drops as the distance between the plates is increased. The measurement was performed for plates separated by about 1 micron (one-millionth of a meter).

  2 This is exactly what happens in particle theories that have a special kind of symmetry, called supersymmetry. Bosons and fermions in such theories come in pairs, so that each Bose particle has a fermionic “partner” and vice versa. Partner particles in each pair have the same mass, and the vacuum energies of fermions and bosons exactly cancel one another. Hence, the total energy density of the vacuum is zero.

  This would be a neat solution to the cosmological constant problem, but the trouble is that our world is definitely not supersymmetric. Otherwise, we would see the partners of electrons, quarks, and photons copiously produced in particle accelerators. But none of these partner particles has ever been observed. Moreover, even in a supersymmetric world, the cancellation of the cosmological constant works only in the absence of gravity. The vacuum energy gets large and negative when gravity is taken into account.

  13. ANTHROPIC FEUDS

  1 C. J. Hogan, “Quarks, electrons and atoms in closely related universes,” in Universe or Multiverse, ed. by B. J. Carr (Cambridge University Press, Cambridge, 2006).

  2 Numerous examples of the apparent fine-tuning of the constants of nature are discussed in the article by Bernard J. Carr and Martin J. Rees in Nature, vol. 278, p. 605 (1979), and in the books The Accidental Universe (Cambridge University Press, Cambridge, 1982) by Paul C. W. Davies; The Anthropic Cosmological Principle (Oxford University Press, Oxford, 1986) by John D. Barrow and Frank J. Tipler; and Universes (Routledge, London, 1989) by John Leslie. For a lucid popular account, see Martin Rees’s books Before the Beginning: Our Universe and Others (Addison-Wesley, Reading, 1997) and Just Six Numbers (Basic Books, New York, 2001).

  3 B. Carter, “Large number coincidences and the anthropic principle in cosmology,” in Confrontation of Cosmological Theories with Observational Data, ed. by M. S. Longair (Reidel, Boston, 1974, p. 132).

  4 Stars less massive than the Sun have longer lifetimes. However, they tend to be unstable and are subject to flare-ups that can extinguish planetary life. We assume that planets orbiting such stars are disqualified as potential homes for observers.

  5 Dicke presented this argument in 1961, in response to the intriguing hypothesis advanced by Paul Dirac, the famous British physicist. Dirac was struck by the weakness of gravity, which is 1040 times weaker than the electromagnetic force. He also noticed that the visible universe is 1040 times larger than the proton. Dirac thought this could not be a pure coincidence and suggested that the two numbers should somehow be connected. But the size of the visible universe grows with time, so its ratio to the size of the proton will be greater at later epochs. This led Dirac to conclude that the other number, expressing the weakness of gravity, should also grow: gravity must be getting progressively weaker.

  Now, Dicke’s argument gave a completely different perspective on the large-number coincidence. We are observing the universe not at some arbitrary epoch, but at the time when its age is comparable to the lifetime of a star. Dicke showed that at that particular time Dirac’s large numbers are indeed close to one another. (This is not an accident: the visible universe is large because the stellar lifetimes are long, and long stellar lifetimes are in turn related to the weakness of gravity, thus establishing the connection between the two large numbers.) Thus the coincidence is automatically satisfied at the epoch when observers can exist, and there is no need to postulate any weakening of gravity. Precise astronomical measurements later showed that the strength of gravity remains constant with a very high accuracy. If there is any change, it must be smaller than 1 part in 1011 per year—much less than required by the Dirac hypothesis.

  6 N. Bostrom, Anthropic Bias (Routledge, New York, 2002).

  7 As quoted in A. L. Macay, A Dictionary of Scientific Quotations (Institute of Physics Publishing, Bristol [U.K.], 1991, p. 244).

  8 David Gross, as quoted in “Zillions of universes? Or did ours get lucky?” by Dennis Overbye in The New York Times, October 28, 2003.

  9 Paul Steinhardt, as quoted in “Out in the cold” by Marcus Chown in New Scientist, June 10, 2000.

  14. MEDIOCRITY RAISED TO A PRINCIPLE

  1 The doomsday argument is a fascinating and controversial subject. For a thought-provoking discussion, see The End of the World by John Leslie (Routledge, London, 1996) and Time Travel in Einstein’s Universe by Richard Gott (Houghton Mifflin Company, Boston, 2001).

  2 In an infinite universe, the volume factor can be defined as the fraction of volume occupied by regions of a given type. This definition, however, can lead to ambiguities. To illustrate the nature of the problem, consider the question, What fraction of all integers are odd? Even and odd integers alternate in the sequence 1,2,3,4,5, … , so you might think that the answer is obviously “half.” The integers, however, can be ordered in a different way. For example, we could write 1,2,4,3,6,8, … This sequence still includes all integers, but now each odd integer is followed by two even ones; it appears that only a third of all integers are odd. The same sort of ambiguity arises in calculations of the volume factor in models of eternal inflation. Some interesting ideas have been proposed on how to deal with this difficulty, but at present the problem is still unresolved.

  3 This is a bit of an oversimplification. Galaxies come in different sizes, from dwarfs to giants, with very different numbers of stars and, therefore, of observers. However, the vast majority of stars are in giant galaxies like ours. So the problem can be fixed by simply counting only giant galaxies and disregarding the rest.

  A more serious problem is that the density of matter and other characteristics of galaxies may change because of variation of life-neutral constants. For example, if the density perturbation parameter Q gets larger, gala
xies form earlier and have a higher density of matter. As a result, close encounters between stars, which can disrupt planetary orbits and extinguish life, become more common. (This point was made by Max Tegmark and Martin Rees in their paper published in Astrophysical Journal in 1998.) Even if the encounter is not close enough to affect the planets, it may disturb the swarm of comets in the outer stellar system, sending a rain of comets toward the inner planets and extinguishing life. Another danger in a denser galaxy is the potentially devastating effect of nearby supernova explosions. Quantifying the impact of all these factors on the density of habitable stellar systems is a challenging, but not intractable problem. At present, however, it is hard to go beyond order-of-magnitude estimates.

  4 A. Vilenkin, “Predictions from quantum cosmology,” Physical Review Letters, vol. 74, p. 846 (1995).

  5 Efstathiou’s approach was somewhat different from mine. He assumed that we are typical only among the presently existing observers (galaxies), while my choice was to include all observers—present, past, and future. If we are truly typical, and live at the time when most observers live, the two methods should give similar results—as in fact they do. The choice of the reference class of observers among which we expect to be typical is generally an important issue. It has been discussed in detail by the philosopher Nick Bostrom.

  6 There is in fact some variation in the power of type Ia supernovae, probably due to differences in the chemical composition of the white dwarfs. But this variation can be accounted for by measuring the duration of the explosion: the power depends on the duration in a well-studied way.

  7 Doppler shift is the change in frequency of electromagnetic waves when the source of waves and the observer move relative to one another. If you move toward a source of light, the frequency of the waves increases, just as a boat hits the waves more frequently as it goes against oncoming waves. The same effect occurs when the source of light moves toward a stationary observer: only the relative motion of the observer and the source is important. Quite similarly, the frequency of light emitted by a galaxy gets lower (shifts toward the red end of the spectrum) if the galaxy moves away from the observer.

  8 As quoted in R. Kirshner, The Extravagant Universe (Princeton University Press, Princeton [N.J.], 2002, p. 221).

  9 The possibility that a cosmological constant could resolve the age discrepancy between the oldest stars and the universe was advocated in the 1980s by Gerard de Vaucouleurs. More recently, it was emphasized, together with other potential benefits of a cosmological constant, by Lawrence Krauss and Michael Turner in their paper “The cosmological constant is back,” published in General Relativity and Gravitation, vol. 27, p. 1137 (1995).

  10 For a popular review of the quintessence idea, see Quintessence: The Mystery of the Missing Mass by Lawrence Krauss (Basic Books, New York, 2000).

  11 Another problem with the quintessence model is that the flat plateau at the bottom of the hill is assumed to be at zero energy density. This amounts to the assumption that the energies of the fluctuating fermions and bosons miraculously cancel one another (see Chapter 12).

  12 It is probably not an accident that we live in the disc of a giant galaxy. Galaxy formation is a hierarchical process, with smaller and denser objects merging to form larger and more dilute ones. Early dense galaxies are less suitable for life, for the reasons indicated in note 3 above.

  13 This explanation of the coincidence was given in the paper I wrote with Jaume Garriga and Mario Livio, “The cosmological constant and the time of its dominance,” published in the Physical Review, vol. D61, p. 023503 (2000). The same idea was independently suggested by Sidney Bludman, in Nuclear Physics, vol. A663, p. 865 (2000).

  15. A THEORY OF EVERYTHING

  1 Quoted in Nigel Calder, The Key to the Universe (Penguin Books, New York, 1977), p. 69.

  2 During the 1970s and 1980s physicists tried to achieve a more unified description of particles and their interactions in the framework of the grand unified theories. The first model of this type was proposed by Howard Georgi and Sheldon Glashow of Harvard, who showed that the entire standard model, with its separate symmetries for strong and electroweak interactions, could be elegantly incorporated into a theory that had a single, but larger, symmetry pattern. Moreover, the model gave a unified description for the three basic interactions. Grand unification is a very attractive idea, and most physicists believe that it will survive as part of the final theory. But grand unified theories still have most of the shortcomings of the standard model. In particular, they require an even larger number of adjustable parameters, and gravity is still left out.

  3 A broad range of issues surrounding the existence (or not) of a final theory of nature is discussed in Dreams of a Final Theory by Steven Weinberg (Vintage, New York, 1994).

  4 An interesting possibility of an observational test of string theory comes from cosmology. Strings of astronomical size could be formed as a result of high-energy processes at the end of inflation. Like “ordinary” cosmic strings (see Chapter 6), these fundamental strings would then be accessible to observation. Strings do not emit light, so they cannot be seen directly, but they can betray their presence through their gravitational effects. Light rays from a distant galaxy located behind a long string are bent by the string gravity, and we can see two images of the galaxy next to one another, from the rays passing on the two sides of the string. Oscillating loops of string are powerful sources of gravitational waves. Existing and future gravitational wave detectors will search for their characteristic signal.

  5 Recent work by Nima Arkani-Hamed of Harvard, Gia Dvali of New York University, and Savas Dimopoulos of Stanford suggests that the compact dimensions may be much larger than previously thought. In this case, the sizes of vibrating string loops are also greatly increased. The next generation of particle accelerators could then be powerful enough to reveal the “stringy” nature of the particles.

  6 An eloquent expression of this philosophy, together with details of string theory, can be found in Brian Greene’s book The Elegant Universe (Vintage Books, New York, 2000).

  7 In the presence of branes, strings can have the form of closed loops, as before, but can also be open, with their ends attached to the branes. Such open string segments can move along the branes, but can never leave them. Branes play a central role in braneworld cosmological models, which assume that we live on a three-dimensional brane floating in a higher-dimensional space. The familiar particles, like electrons and quarks, are then represented by open strings with their ends attached to our brane.

  8 The spacetime structure of expanding bubbles is similar to that of island universes, as described in Chapter 10. The bubbles are finite as viewed from the outside, but from the inside each bubble appears to be a self-contained, infinite universe. Eternal inflation with bubble island universes was envisaged by Richard Gott in 1982 and was discussed by Paul Steinhardt in a more realistic model in 1983.

  9 Quoted by Davide Castelvecchi, “The growth of inflation,” Free Republic, December 2004.

  10 Leonard Susskind, interviewed by John Brockman, Edge, 2003.

  11 Ibid.

  16. DID THE UNIVERSE HAVE A BEGINNING?

  1 Interesting parallels between ancient myths and scientific cosmology are discussed in The Dancing Universe: From Creation Myths to the Big Bang by Marcelo Gleiser (Dutton, New York, 1997).

  2 A. Jinasena, Mahapurana, in A. T. Embree, ed., Sources of Indian Tradition (Columbia University Press, New York, 1988).

  3 The same criticism applies to the idea of the universe coming out of chaos, as in models of chaotic inflation. This point is highlighted in the “joke” related by Timothy Ferris in his book The Whole Shebang (Simon & Schuster, New York, 1997). An atheist claims that the world came out of chaos, to which a believer replies, “Ah, but who made the chaos?”

  4 A. K. Coomaraswamy, Dance of Shiva (Farrar, Straus and Giroux, New York, 1957).

  5 To implement this scenario, Steinhardt and Turok introduced a
scalar field with a judiciously designed energy landscape. Cosmologists are generally skeptical about their model, because the landscape appears rather contrived. Moreover, the value of the vacuum energy density, which plays a crucial role in this model, is simply put in by hand, without an explanation of why it is so small or why it dominates the universe at about the epoch of galaxy formation.

  6 This method of proving spacetime incompleteness by showing that certain past- or future-directed histories have a finite duration dates back to Hawking and Penrose’s work in the 1960s and ’70s.

  7 One way to avoid the conclusion of the theorem is to assume that the expansion rate gets smaller and smaller as we go backward in time, so the universe becomes static at past infinity. This sort of scenario was suggested in 2004 by George Ellis and his collaborators. They assumed that the universe started out as a static Einstein world. The problem, however, is that Einstein’s universe is unstable and could not have existed for an infinite time. (See note 3 to Chapter 2 on p. 209.)