Many Worlds in One: The Search for Other Universes
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8 Another interesting attempt to avoid the beginning of the universe was made in the 1998 paper “Can the universe create itself?” written by J. Richard Gott and Li-Xin Li of Princeton University. (The paper is published in Physical Review D, vol. 58, p. 023501.) Gott and Li suggest that as one goes backward in time, one gets caught in a time loop, going through the same events over and over again. Einstein’s general relativity does allow, in principle, the existence of closed loops in time. (For an entertaining discussion, see Richard Gott’s wonderful book Time Travel in Einstein’s Universe.) However, as Gott and Li themselves point out, in addition to histories circling in a loop, the spacetime they envisage necessarily contains some incomplete histories, like the space traveler’s history discussed in the text. This means that the spacetime itself is past-incomplete, and therefore does not provide a satisfactory model of a universe without a beginning.
9 A. Borde, A. H. Guth, and A. Vilenkin, “Inflationary spacetimes are not past-complete,” Physical Review Letters, vol. 90, p. 151301 (2003).
10 E. A. Milne, Modern Cosmology and the Christian Idea of God (Clarendon, Oxford, 1952).
11 Pope Pius XII, Address to the Pontifical Academy of Sciences, November 1951; English translation is in P. J. McLaughlin, The Church and Modern Science (Philosophical Library, New York, 1957). The pope’s enthusiasm was not universally shared by all clergy. In particular, Georges Lemaître, who was both a Catholic priest and a renowned cosmologist, thought that religion should keep to the spiritual world, leaving the material world for science. Lemaître even tried to talk the pope out of endorsing the big bang. It appears that in later years the pope had second thoughts about his remarks. Neither he nor his successors ever repeated this attempt at direct verification of religion by science.
12 As quoted in C. F. von Weizsacker, The Relevance of Science (Harper and Row, New York, 1964).
17. CREATION OF UNIVERSES FROM NOTHING
1 A. Vilenkin, “Creation of universes from nothing,” Physics Letters, vol. 117B, p. 25 (1982). I later learned that the possibility of spontaneous nucleation of the universe from nothing was discussed about a year earlier by Leonid Grishchuk and Yakov Zel’dovich of Moscow State University in Russia. However, they did not offer any mathematical description for the nucleation process.
2 This story is based on a conversation I had with Edward Tryon when I visited him in New York in October of 1985.
3 At about the same time, an idea very similar to Tryon’s was put forward by Piotr Fomin of the Institute for Theoretical Physics in Kiev, Ukraine. In fact, the sequence of steps shown in Figure 17.3 was not clearly spelled out by Tryon and first appeared in Fomin’s paper. Unfortunately, Fomin had trouble finding a journal that would publish his work. In the end it was published in 1975 in an obscure Ukrainian physics journal.
4 E. P. Tryon, “Is the universe a vacuum fluctuation?” Nature, vol. 246, p. 396 (1973).
5 In the late 1970s and early ’80s there were some attempts to develop mathematical models of quantum creation from the vacuum. Richard Brout, François Englert, and Edgard Gunzig of the Free University of Brussels suggested in 1978 that superheavy particles, 1020 times heavier than the proton, could be spontaneously created in the vacuum. The particles would curve space, the growing curvature would trigger further particle creation, and the process will extend to a larger and larger region as an expanding bubble. Inside the bubble, the heavy particles will quickly decay into light particles and radiation, resulting in an expanding universe filled with matter. This model has the same problem as Tryon’s scenario: it does not really explain the origin of the universe. If flat empty space were indeed so unstable, it would be rapidly filled with expanding bubbles. Such an unstable space could not have existed forever and cannot, therefore, be taken as the starting point of creation.
David Atkatz and Heinz Pagels of Rockefeller University wrote a paper in 1982, suggesting that before the big bang the universe existed in the form of a small spherical space packed with exotic high-energy matter—a sort of “cosmic egg.” They designed a model in which the “egg” was classically stable, but could tunnel to a bigger radius and expand. (To my knowledge, this was the first discussion of quantum tunneling of the universe as a whole.) Once again, the problem is that the unstable “egg” could not have existed forever, and we are left with the problem of where the egg came from.
6 A. H. Guth, The Inflationary Universe (Addison-Wesley, Reading [Mass.], 1997, p. 273).
7 Saint Augustine, Confessions (Sheed and Ward, New York, 1948).
8 A. Vilenkin, “Quantum origin of the universe,” Nuclear Physics, vol. B252, p. 141 (1985).
9 I am grateful to Ernan McMullin for emphasizing to me the importance of requiring that the universes in the ensemble must be really existing, not merely possible universes.
10 J. B. Hartle and S. W. Hawking, “The wave function of the universe,” Physical Review, vol. D28, p. 2960 (1983). Hawking outlined the basic idea of this work about a year earlier, in Astrophysical Cosmology: Proceedings of the Study Week on Cosmology and Fundamental Physics, edited by H. A. Bruck, G. V. Coyne, and M. S. Longair (Pontifica Academia, Vatican, 1982), but at that time he did not provide any mathematical details.
11 A firsthand account of the no-boundary proposal can be found in Hawking’s bestselling book A Brief History of Time (Bantam, New York, 1988, p. 136).
12 One caveat is that the string theory landscape may consist of several disconnected domains, with no possibility for bubbles from one domain to nucleate in another. Then bubbles formed during eternal inflation will only contain vacua belonging to the same domain as the initial vacuum that filled the universe when it came into being. In this case, the nature of the multiverse does depend on the initial state, and a test of quantum cosmology is in principle possible.
18. THE END OF THE WORLD
1 Physical processes in the distant future of the universe have been studied by Martin Rees and Don Page, among others. For a popular review, see the book by Paul Davies, The Last Three Minutes: Conjectures about the Ultimate Fate of the Universe (Basic Books, New York, 1994).
2 This scenario is based on the analysis by K. Nagamine and A. Loeb in “Future evolution of nearby large-scale structure in a universe dominated by a cosmological constant,” New Astronomy, vol. 8, p. 439 (2003).
3 The prediction that the local region of the universe will collapse to a big crunch was made in the paper I wrote with Jaume Garriga, “Testable anthropic predictions for dark energy,” Physical Review, vol. D67, p. 043503 (2003). We pointed out, however, that this prediction was not likely to be tested anytime soon.
19. FIRE IN THE EQUATIONS
1 Alan L. Mackay, A Dictionary of Scientific Quotations, Institute of Physics Publishing, Bristol [U.K.], 1991.
2 This situation, that an infinite ensemble is much simpler than one of its members, is very common in mathematics. Consider, for example, the set of all integers: 1,2,3, … It can be generated by a simple computer program, which takes only a few lines of code. On the other hand, the number of bits needed to specify a specific large integer is equal to the number of digits required to write it in a binary code, and can be much larger.
3 P.A.M. Dirac, “The evolution of the physicist’s picture of nature,” Scientific American, May 1963.
4 For an interesting discussion of beauty in scientific theories, see The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos by Mario Livio (Wiley, New York, 2000).
5 Needless to say, “simplicity” and “depth” are almost as difficult to define as “beauty.”
6 M. Tegmark, “Parallel universes,” Scientific American, May 2003.
7 Tegmark makes no distinction between mathematical structures and the universes they describe. He argues that mathematical equations describe every aspect of the physical world, so that each physical object corresponds to some entity in the Platonic world of mathematical structures and vice versa. In this sense the
two worlds are equivalent to one another, and Tegmark’s view is that our universe is a mathematical structure.
8 To address this problem, Tegmark suggested that mathematical structures might not all be equal; they might be assigned different “weights.” If these weights rapidly decline with increasing complexity, the most probable structures might be the simplest ones that can still contain observers. The introduction of weights may resolve the complexity problem, but then we are faced with the question, Who determines the weights? Should we recall the Creator from his exile? Or should we perhaps enlarge the ensemble of mathematical structures still further, to include all possible weight assignments? I am not sure that the notion of weights for the set of all mathematical structures is even logically consistent: it seems to introduce an additional mathematical structure, but all of them are supposed to be already included in the set.
9 Depending on the fundamental theory, the constants may vary within the island universes as well. Our own island universe is then mostly barren, with rare habitable enclaves.
Acknowledgments
My friends and colleagues, whose opinion is very important to me, read the manuscript and kindly offered their critique and suggestions. Alan Guth, Steven Weinberg, and Jaume Garriga gave me their advice and very useful comments about parts of the book. Paul Shellard and Ken Olum provided extensive feedback on the entire text, and straightened me out on some important details of science. I am deeply grateful to all of them.
Special thanks to Delia Schwartz-Perlov, who turned my sketches into wonderful illustrations, refined some of my cartoons, and suggested many improvements in the text. I also benefited from stimulating correspondence with Frank McCormick and Max Tegmark.
Thanks to my editor, Joseph Wisnovsky, for his enthusiasm for the project and guidance throughout the production of this book. Many thanks to Vitaly Vanchurin, who was always ready to help whenever I ran into trouble with my computer, to Marco Cavaglia and Xavier Siemens for historical references, and to Susan Mader for her assistance with photographs. I also owe a debt of gratitude to Susan Rabiner for her vital advice at the early stages of this work.
Closer to home, my thanks go to Joshua Knobe and my daughter, Alina, for their useful suggestions, enthusiasm, and support, and to my wife, Inna, who served as editor, critic, and trusted advisor.
Index
The index that appeared in the print version of this title does not match the pages of your eBook. Please use the search function on your eReading device to search for terms of interest. For your reference, the terms that appear in the print index are listed below.
acceleration, cosmic
Albrecht, Andreas
alchemy
Alfonso the Wise, King of Castile
Alpha Centauri
Alpher, Ralph
Andromeda galaxy
anthropic selection
cosmological constant and
predictions drawn from
string theory and
antigravity
antiparticles
antiquarks
Archimedes
Aristotle
Arkani-Hamed, Nima
Aryal, Mukunda
Astrophysical Journal
Atkatz, David
atomic nuclei
formation of
impact of heat on
atoms
formation of
see also atomic nuclei
Augustine, Saint
Babson, Roger W.
bacteria, reproduction of
Barcelona, University of
Bardeen, Jim
Barrow, John
Bekenstein, Jacob
bell curves
Bell Telephone Laboratories
Bethe, Hans
big bang
afterglow of
cosmic radiation and
elements formed in
evidence of
and Friedman’s solutions to Einstein’s equations
as hot
inflationary universe and
nature of
repulsive gravity and
theological response to
“big crunch”
biology
black holes
evaporation of
Bludman, Sidney
Bohr, Niels
Boltzmann, Ludwig
Bondi, Herman
Borde, Arvind
Bose, Satyendra
bosons
Bostrom, Nick
Bousso, Raphael
branes
British Columbia, University of
Brout, Robert
Brundrit, G.
Brussels, Free University of
bubble nucleation
Bush, George W.
Caesar, Julius
California, University of
Berkeley
Santa Barbara
California Institute of Technology (Caltech)
Cambridge University
carbon
Carr, Bernard
Carter, Brandon
Casimir, Hendrik
CERN (European Center for Nuclear Research)
Chandrasekhar limit
chaotic inflation
charge, conservation of
Chibisov, Gennady
Chicago, University of
Churchill, Winston
civilizations
future of
identical
Clinton, Bill
closed-universe model
Clover Observatory
coarse-grained description
COBE satellite, see Cosmic Background Explorer (COBE) satellite
coincidence problem
Coleman, Sidney
Communist Party, French
compactification
complex numbers
Conference on General Relativity and Gravitation (Padova, 1983)
Confessions (Augustine)
conservation laws
constants of nature
anthropic selection and
eternal inflation and
see also cosmological constant
Copenhagen interpretation
Copernicus, Nicolaus
Cosmic Background Explorer (COBE) satellite
cosmic background radiation
see also microwaves, cosmic
cosmic egg
cosmic horizon
Cosmo-98 conference (Monterey)
cosmological constant
accelerated expansion and
anthropic selection and
Einstein and
principle of mediocrity and
Coulomb, Charles-Augustin de
creation stories
Curie, Marie
curvature of spacetime
cyclic universe
Dalí, Salvador
Damour, Thibault
dark energy
dark matter
Darwin, Charles
Davies, Paul C. W.
de Sitter, Willem
de Sitter spacetime
density perturbations
calculation of
parameter Q of
see also inhomogeneities, cosmic
deuterium
Deutsch, David
Dicke, Robert
dimensions, extra
Dimopoulos, Savas
Dirac, Paul
disorder
distance determination
DNA
doomsday argument
Doppler shift
double-slit experiment
Dvali, Gia
dwarf galaxies
E=mc2
Earth
evolution of intelligent life on
human population of
infinite duplicates of
magnetic field of
École Normale Supérieure
economic inflation
Edison, Thomas
Efstathiou, George
Ehrenfest, Paul
Einstein, Albert
cosmological constant of
Friedman’s solutions to equations of
mass-energy relation (E=mc2) of
on observer dependency of time order of events
Stalinist rejection of theories of
see also relativity theory
electric force
electromagnetism
in final theory of nature
in final theory of nature
quantum fluctuations of
in supernovae
electrons
annihilation into photons of
magnetic moment of
mass of
in string theory
virtual
electroweak force
elementary particles
collisions of
masses of
elements
chemical properties of
origins of
periodic table of
elliptical galaxies
Ellis, George
empty space, gravity of
energy conservation, law of
Englert, François
entropy
equilibrium, thermal
eschatology, cosmic
eternal inflation
computer simulation of
and future of intelligent life
island universes and
parallel universes and
necessity of a beginning
quantum processes during
string theory and
time and
versus end of universe
Euclidean geometry
Euclidean time
Euler’s formula
European Center for Nuclear Research (CERN)