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Authors: Alex Vilenkin
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15. A THEORY OF EVERYTHING
1
Quoted in Nigel Calder,
The Key to the Universe
(Penguin Books, New York, 1977), p. 69.
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).
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).
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.
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.
Free Republic
, December 2004.
10
Leonard Susskind, interviewed by John Brockman,
Edge
, 2003.
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).
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).
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?”
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).
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.)
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.
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).
Physical Review Letters
, vol. 90, p. 151301 (2003).
10
E. A. Milne,
Modern Cosmology and the Christian Idea of God
(Clarendon, Oxford, 1952).
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.
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).
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.
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.
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).
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, 10
20
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.
20
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.
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).
The Inflationary Universe
(Addison-Wesley, Reading [Mass.], 1997, p. 273).
7
Saint Augustine,
Confessions
(Sheed and Ward, New York, 1948).
Confessions
(Sheed and Ward, New York, 1948).
8
A. Vilenkin, “Quantum origin of the universe,”
Nuclear Physics
, vol. B252, p. 141 (1985).
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.
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).
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).
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).
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.
Physical Review
, vol. D67, p. 043503 (2003). We pointed out, however, that this prediction was not likely to be tested anytime soon.
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