i See footnote on p. 14 for a definition of “light-year.”
j We say that electromagnetic waves are scattered when they are absorbed and re-emitted by charged particles. The last scattering surface could therefore be equally well characterized as the surface where the cosmic radiation was emitted.
k The Wilkinson Microwave Anisotropy Probe, so named after David Wilkinson of Princeton University. Wilkinson originated the idea of the probe and was a major inspiration in its design. Sadly, he died shortly before the satellite was launched.
l After the end of inflation, the matter density is diluted by the expansion of the universe. Therefore, regions of space that were in a hurry to end inflation are already diluted by the time other sluggish regions finally end inflation.
m Mukhanov is now at the Ludwig-Maximilians University in Munich; see his photo on p. 60.
n As the scalar field slowly rolls down the energy slope, the kicks get weaker and the resulting perturbations smaller. But the downhill roll of the field is so slow that it does not move much during the time that it generates perturbations on all astrophysically relevant scales.
o Erast Gliner, Starobinsky, and Linde in Russia; Katsuhiko Sato in Japan; and Robert Brout, François Englert, and Edgard Gunzig in Belgium were all considering a possible period of exponential expansion in the early universe. Sato was also aware of the graceful exit problem.
p This is the maximum distance over which communication is possible in the inflating universe. It is the same as the critical size necessary for a chunk of false vacuum to inflate (see Chapter 6): 1 millimeter for electroweak vacuum and 1013 times smaller for grand-unified vacuum. This distance plays the role of the horizon in the inflating universe; I use a different term—“kickspan”—to avoid confusion with the present horizon.
q The term “half-life” is borrowed from nuclear physics, where it refers to the time during which half of the atoms in a sample of radioactive material will decay.
r Guth calls these islands “pocket universes.” But, as Leonard Susskind has noted, this tends to ruin the prose.
s To avoid confusion, from now on I will reserve the term “big bang” for the end of inflation and use the term “singularity” for the initial (or final) state of infinite curvature and density.
t The distance to a supernova, which is determined from how bright it appears as viewed from Earth, tells us how long its light has traveled and, thus, when the explosion occurred. The reddening of the light (the Doppler redshift) can then be used to evaluate the speed of cosmic expansion at that time. More on this in Chapter 14.
u Some other options will be mentioned in the following chapters. Many physicists take an agnostic attitude toward the cause of cosmic acceleration and refer to it as “dark energy.”
v See the second footnote on p. 42.
w The Planck satellite is named after one of the discoverers of quantum mechanics, Max Planck, who also derived a formula describing how the energy of thermal radiation is distributed between waves of different frequency. The satellite is scheduled to be launched in 2007.
x Remember that we agreed to identify the big bang with the end of inflation.
y As before, “A.B.” stands for “after the big bang.”
z The state of motion of the observers also affects the readings of their clocks. In a Friedmann universe, it is most natural to assume that the observers are at rest relative to galaxies (or matter particles) at their respective locations. These are the “co-moving” observers.
aa Except, of course, that a closed universe is like a three-dimensional sphere, while the surface of the Earth has two dimensions.
ab This bound does not apply to regions much greater than the cosmic horizon. It is expected to be marginally valid for an O-region, which has the same size as the horizon.
ac From “googolplex”—the name for the number 10 to the power 10100.
ad We wrote our paper in 2001, right after the contentious presidential election in the United States, when George Bush won over Al Gore by a very narrow margin.
ae This latter view is close to the Copenhagen picture, except it does not insist on the presence of external observers.
af We shall see later, in Chapter 17, that there may in fact be a good reason to believe in the existence of other, completely disconnected universes.
ag Our ability to travel to other O-regions may be hindered if the observed accelerated expansion of the universe is due to a constant vacuum energy. In this case, galaxies in other O-regions will continue moving away faster and faster, and we will never be able to catch up with them. Some models, however, predict that the vacuum energy will gradually subside, as it did during inflation. Then there is no limit, in principle, to how far we can travel.
ah A nanosecond is one-billionth of a second.
ai So named after Satyendra Bose and Enrico Fermi, who elucidated their distinctive properties.
aj Named after the nineteenth-century German mathematician Hermann Grassmann, who first introduced them.
ak An equation is said to have symmetry if there is some operation that leaves it unchanged. For example, the equation x + y = 1 does not change if we swap x and y.
al The numerical value of the mass depends on the units used to measure it (e.g., grams, ounces, or atomic units), but a ratio of two masses, like 1836, is independent of this choice.
am The values of some of these constants, particularly those characterizing the properties of neutrinos, are still unknown.
an The decay is accompanied by emission of an antineutrino.
ao On a more fundamental level, protons and neutrons are made up of quarks, so it is more appropriate to regard their masses as derived quantities and the quark masses as fundamental constants of nature. This, however, does not change the general conclusions. A few percentage points’ variation of the quark masses drives us either into a neutron world or into a hydrogen world.
ap Note that even after a millionfold enhancement, gravity would still be 1034 times weaker than electromagnetism.
aq Now at Meudon Observatory in France.
ar Philosophers often define the universe as “everything there is.” Then, of course, there cannot be any other universes. Physicists do not usually use the term in this broadest sense and refer to completely disjointed, self-contained spacetimes as separate universes. Here I follow the physics tradition.
as It is conceivable that advanced civilizations can survive the death of stars using nuclear energy or the energy of tides to sustain life. But it appears more likely that civilizations are relatively short-lived. I will touch upon this subject in Chapter 14.
at Carter himself contributed to the confusion by introducing an alternative version of the principle, called the “strong anthropic principle,” which states that “the universe … must be such as to admit the creation of observers within it at some stage.” Many people interpreted this in a mystical sense, as referring to some sort of theological necessity. In this book I adopt Carter’s original formulation, which he referred to as the “weak anthropic principle.”
au In order to get to a noticeably different elevation, a random walker would have to travel a long distance along the very flat slope. In the meantime, the universe would expand by a huge amount.
av It is not clear whether or not scalar fields of the kind postulated by Linde really exist. We shall return to this issue in Chapter 15.
aw The anthropic bound derived by Weinberg was somewhat too high for comfort—about 500 times greater than the average density of matter in the universe. In the mid-1990s, observations already indicated that the cosmological constant in our region was at least 50 times smaller. Besides, Weinberg’s bound was based on the most distant galaxies known in the late 1980s. By now, even more distant galaxies have been discovered, and the corresponding bound would be 4000 times the average matter density.
ax This story was related to me by Sean Carroll of the University of Chicago.
ay Mukhanov is the sa
me fellow who first calculated the density perturbations resulting from quantum processes during inflation (see his photo on p. 60).
az Here, the term “universe” is used in the sense of “visible universe,” and “the age of the universe” in the sense of “the time since the big bang in our local region.”
ba Another important contribution that Mendeleyev gave to humanity was perfecting the recipe for Russian vodka.
bb In other words, any two atoms with a different number of populated shells, but with the same number of electrons in the outer shell, will display similar chemical behavior.
bc Positrons are antiparticles of the electrons. Muons are unstable particles, very similar to electrons, but 200 times heavier.
bd Most of these new particles are unstable and decay into the familiar, stable particles after a brief period of time.
be The theory also includes a host of other entities (e.g., fluxes, which are similar to magnetic fields), but I will omit them in this discussion.
bf Polchinski is largely responsible for the realization that string theory must include branes of different dimensions.
bg Bubbles of higher energy density can also be formed, though with a much smaller probability.
bh Edward Witten, one of the leading string theorists, was awarded the 1990 Fields Medal—the mathematics equivalent of the Nobel Prize.
bi The minimum radius of the de Sitter sphere is roughly equal to the distance traveled by light during one doubling time of inflation.
bj The existence of such a class of observers can be taken as a definition of an expanding universe.
bk More precisely, the quantity called the wave function is found by adding up the contributions of different histories. The probability is given by the square of the wave function.
bl The error in my original paper was independently noticed and corrected by Andrei Linde, by Valery Rubakov, and by Yakov Zel’dovich and Alexei Starobinsky.
bm The following day Hawking had another important engagement: he went to Hollywood to have his electronic voice recorded for a special episode of the animated television show The Simpsons.
bn The quaternion is a generalization of the more familiar complex number. It has one real and three imaginary parts.
Copyright © 2006 by Alex Vilenkin
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eISBN 9780374707149
First eBook Edition : June 2011
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First paperback edition, 2007
The Library of Congress has cataloged the hardcover edition as follows: Vilenkin, A. (Alexander)
Many worlds in one : the search for other universes / Alex Vilenkin.—1st ed.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-8090-9523-0 (hardcover : alk. paper)
ISBN-10: 0-8090-9523-8 (hardcover : alk. paper)
1. Cosmology. 2. Cosmogony. 3. Cosmography. I. Title.
QB981.V526 2006
523.1—dc22
2005027057
Paperback ISBN-13: 978-0-8090-6722-0
Paperback ISBN-10: 0-8090-6722-6
Many Worlds in One: The Search for Other Universes Page 24