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Landau, Lev
Langevin, Paul
last scattering
Lebedev Institute
Lemaître, Georges
Leslie, John
Li, Li-Xin
life, evolution of

anthropic selection and
in closed universe
constants of nature and

light

from distant galaxies
Doppler shift of
quantum nature of
spectrum of
speed of

light-years
Linde, Andrei
lithium
Livio, Mario
Local Group of galaxies
Loeb, A.
logarithms, “natural”
Long Island University
Lou Gehrig’s disease
Ludwig-Maximilians University

magnetic fields,
see
electromagnetism
many-worlds theory

see also
multiverse hypothesis; parallel universes

Martel, Hugo
Marxism-Leninism
Massachusetts Institute of Technology (MIT)
mathematics, nature and
Mayer, Jean
McCarthy, Kathryn
McMullin, Ernan
mediocrity, principle of
Mendeleyev, Dmitry
Mermin, David
messenger particles
microwaves, cosmic

polarization of

Milky Way galaxy

replicas of

Milne, Edward
Minkowski, Hermann
Mohammed, Gul
Moon
Moscow State University
motion

inertial
planetary

Mukhanov, Slava
multiverse hypothesis
muons

Nagamine, K.
Nambu, Yoichiro
nanosecond
Nature
Ne’eman, Yuval
Nernst, Walter
neutrinos

mass of
weakly interacting

neutrons

mass of

neutron stars
New Scientist
Newton, Isaac
New York University
Niels Bohr Institute
Nielsen, Holger
night sky paradox
Nobel Prize
nuclear physics
nuclear reactions
nucleation

see also
bubble nucleation

nucleons

decay of

Nuffield Workshop (Cambridge, 1982)

Olum, Ken
Omega parameter
Omnes, Roland
O-regions

histories of
possible states of

Oxford University
oxygen

Page, Don
Pagels, Heinz
pair annihilation
parallel universes

mathematical structures of

particle physics

calculation of magnetic moment in
cosmic strings in
cosmological constant and
gauge symmetry in
scalar fields in
search for final theory in
Standard Model of
string theory and
strong and electroweak interactions in
variable constants in
see also
elementary particles

pendulum, dynamics of
Penrose, Roger
Penzias, Arno
periodic table
Perlmutter, Saul
Perry, Malcolm
Petrograd University
photons

interaction of

Physical Review
Physical Review Letters
Physics Letters
pi
Pi, So-Young
Pius XII, Pope
Planck, Max
Planck length
Planck satellite
planets

formation of
motion of

Plato
pocket universes,
see
island universes
polarization
Polchinski, Joseph
Pontifical Academy of Sciences
Popper, Karl
Port Alguer (Cadaqués)
(Dalí)
positrons

annihilation into photons of
virtual

primeval fireball,
see
fireball, cosmic
Princeton University
probabilities, quantum-mechanical
protons

in hydrogen nucleus
mass of

Ptolemy
Pythagoras
Pythagorean theorem

quantum kicks
quantum theory

gravity in
histories in
parallel universes in
probabilities in
tunneling in,
see
tunneling, quantum
uncertainty in
vacuum in

quarks

masses of
in string theory

quarternion
Queen Mary College
QUIET Observatory
quintessence model

Rabi, Isidor
radiation

cosmic
electromagnetic

radioactivity
radio astronomy
radio waves
redshift
Rees, Martin
relativity theory

general
special

repulsive gravity

anthropic selection and
in de Sitter spacetime
of false vacuum

Riess, Adam
Rockefeller University
Roman Catholic Church
Rosenfeld, Leon
Rubakov, Valery
Russian Revolution
Rutherford, Ernest
Ryle, Martin

Sakharov, Andrei
Salam, Abdus
Sato, Katsuhiko
scalar fields

in chaotic state
quintessence
and end of universe
energy landscape of
random walk of

Scherk, Joel
Schmidt, Brian
Schwartz, John
Shapiro, Paul
Siding Springs Observatory
Simpsons, The
(television show)
singularities

initial

solar system

formation of

solids, properties of
Solvay Congress (Brussels, 1933)
Sommerfeld, Arnold
sound waves
Space Telescope Science Institute
spacetime

curvature of
de Sitter
eternally inflating,
see
eternal inflation
quantum fluctuations in
singularities
without past boundary

special theory of relativity,
see
relativity theory, special
Spinoza, Baruch
spiral galaxies
Stalinism
standard candles
Standard Model
Stanford University
Starobinsky, Alexei
stars
stars

age of
dark matter and
death of
element formation in
formation of
masses of

steady-state cosmology
Steinhardt, Paul
stock market crash of 1929
strings, cosmic
string theory

landscape of
see also
superstring theory

strong force
Sun

lifetime of
motion of planets around
nuclear reactions in

superconductivity
Supernova Cosmology Project
supernovae
superstring theory
supersymmetric theories
surface of last scattering
Susskind, Leonard

Tegmark, Max
temperature, scalar field of
tension
Texas, University of
Theory of Everything,
see
final theory of nature
thermal equilibrium
thermal fluctuations
thermodynamics, second law of
’t Hooft, Gerard
time

Euclidean
see also
spacetime

Tipler, Frank
top quark
tritium
true vacuum

energy density of (
see also
cosmological constant)
quantum fluctuations of

Tryon, Edward
Tufts University

Institute of Cosmology

tunneling, quantum
Turner, Michael
Turok, Neil
Twain, Mark

uncertainty, quantum
unified theory,
see
final theory of nature
universe

age of
beginning of (
see also
big bang)
bubbling
closed
cyclic
density of
disordered
exhaustive randomness of
expanding (
see also
inflation)
fine-tuning of
geometry of
observable, end of
Ptolemy’s model of
as quantum fluctuation
spherical
steady-state theory of
structure of
super-large-scale view of
without past boundary
see also
island universes, parallel universes

Unruh, Bill
Upanishads
uranium

vacuum

in cyclic universe
creation of matter out of
decay of
fluctuations in
gravity of
in string theory
see also
false vacuum; true vacuum

Vanchurin, Vitaly
Vaucouleurs, Gerard de
virtual particles
visible light

Wadlow, Robert Pershing
weak force
Weinberg, Steven
white dwarfs
Wigner, Eugene
Wilkinson, David
Wilkinson Microwave Anistropy Probe (WMAP) satellite
Wilson, Robert
Winitzki, Serge
Witten, Edward
WMAP satellite,
see
Wilkinson Microwave Anistropy Probe (WMAP) satellite
world lines
wormholes
W particles

X rays

Yeshiva University
Young, Thomas

Zel’dovich, Yakov
Z particles
Zurich Polytechnic
Zweig, George

Notes

For example, time can be measured in years and distance in light-years. (A light-year is the distance traveled by light in a year.) Then the speed of light is
c
= 1.

In fact, Einstein did not offer any physical explanation for the new constant. The modern interpretation in terms of the vacuum energy and pressure was later suggested by the Belgian physicist Georges Lemaître.

The simple connection between the geometry of the universe and its fate holds only assuming that the vacuum energy density (or cosmological constant) is equal to zero. More on this in Chapter 18.

The expanding universe model was reinvented in 1927 by Georges Lemaître. Just like Friedmann’s work, Lemaître’s paper remained completely unknown until Hubble’s discovery.

Boltzmann established the connection between entropy and disorder and elucidated the meaning of the second law.

In the kelvin scale, often used by physicists, the temperature is measured in centigrade units starting from absolute zero (–273.15 degrees Celsius). For the very high temperatures we are discussing here, there is little difference between the Celsius and kelvin scales.

Also present in the fireball were very light, weakly interacting particles called neutrinos.

Radioactive elements, such as uranium, which spontaneously decay into lighter elements, are an important exception. A uranium atom decays into lead with an average lifetime of 4.5 billion years, so the amount of uranium is gradually decreasing. In fact, our best estimate for the age of the Earth comes from measurements of the relative abundances of uranium and lead.

See footnote on p. 14 for a definition of “light-year.”

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.

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.

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.

Mukhanov is now at the Ludwig-Maximilians University in Munich; see his photo on p. 60.

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.

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.

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 10
¹³times 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.

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.

Guth calls these islands “pocket universes.” But, as Leonard Susskind has noted, this tends to ruin the prose.

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.

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.

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.”

See the second footnote on p. 42.

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.

Remember that we agreed to identify the big bang with the end of inflation.

As before, “A.B.” stands for “after the big bang.”

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.

Except, of course, that a closed universe is like a three-dimensional sphere, while the surface of the Earth has two dimensions.

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.

From “googolplex”—the name for the number 10 to the power 10
¹⁰⁰.

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.

This latter view is close to the Copenhagen picture, except it does not insist on the presence of external observers.

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.

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.

A nanosecond is one-billionth of a second.

So named after Satyendra Bose and Enrico Fermi, who elucidated their distinctive properties.

Named after the nineteenth-century German mathematician Hermann Grassmann, who first introduced them.

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
.

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.

The values of some of these constants, particularly those characterizing the properties of neutrinos, are still unknown.

The decay is accompanied by emission of an antineutrino.

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.

Note that even after a millionfold enhancement, gravity would still be 10
³⁴times weaker than electromagnetism.

Now at Meudon Observatory in France.

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.

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.

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.”

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.

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.

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.

This story was related to me by Sean Carroll of the University of Chicago.

Mukhanov is the same fellow who first calculated the density perturbations resulting from quantum processes during inflation (see his photo on p. 60).

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.”

Another important contribution that Mendeleyev gave to humanity was perfecting the recipe for Russian vodka.

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.

Positrons are antiparticles of the electrons. Muons are unstable particles, very similar to electrons, but 200 times heavier.

Most of these new particles are unstable and decay into the familiar, stable particles after a brief period of time.

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.

BOOK: Many Worlds in One: The Search for Other Universes

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