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Authors: Alex Vilenkin
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11. THE KING LIVES!
1
J. Garriga and A. Vilenkin, “Many worlds in one,”
Physical Review
, vol. D64, p. 043511 (2001).
Physical Review
, vol. D64, p. 043511 (2001).
2
A. D. Sakharov,
Alarm and Hope
(Knopf, New York, 1978).
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).
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).
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).
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.
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
).
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
.
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.
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.
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).
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).
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).
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 10
40
times weaker than the electromagnetic force. He also noticed that the visible universe is 10
40
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.
40
times weaker than the electromagnetic force. He also noticed that the visible universe is 10
40
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 10
11
per year—much less than required by the Dirac hypothesis.
11
per year—much less than required by the Dirac hypothesis.
6
N. Bostrom,
Anthropic Bias
(Routledge, New York, 2002).
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).
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.
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.
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).
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, galaxies 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.
Q
gets larger, galaxies 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).
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).
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).
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).
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).
Physical Review
, vol. D61, p. 023503 (2000). The same idea was independently suggested by Sidney Bludman, in
Nuclear Physics
, vol. A663, p. 865 (2000).
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