Many Worlds in One: The Search for Other Universes (26 page)
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Authors: Alex Vilenkin
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19. FIRE IN THE EQUATIONS
1
Alan L. Mackay,
A Dictionary of Scientific Quotations
, Institute of Physics Publishing, Bristol [U.K.], 1991.
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.
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).
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.
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.
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.
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.
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
antiparticles
antiquarks
Archimedes
Aristotle
Arkani-Hamed, Nima
Aryal, Mukunda
Astrophysical Journal
Atkatz, David
atomic nuclei
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
antigravitypredictions drawn from
string theory and
antiparticles
antiquarks
Archimedes
Aristotle
Arkani-Hamed, Nima
Aryal, Mukunda
Astrophysical Journal
Atkatz, David
atomic nuclei
formation of
impact of heat on
atomsimpact of heat on
formation of
see also
atomic nuclei
Augustine, Saintsee also
atomic nuclei
Babson, Roger W.
bacteria, reproduction of
Barcelona, University of
Bardeen, Jim
Barrow, John
Bekenstein, Jacob
bell curves
Bell Telephone Laboratories
Bethe, Hans
big bang
biology
black holes
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.
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”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
biology
black holes
evaporation of
Bludman, SidneyBohr, 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
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
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
Copernicus, Nicolaus
Cosmic Background Explorer (COBE) satellite
cosmic background radiation
cosmic horizon
Cosmo-98 conference (Monterey)
cosmological constant
creation stories
Curie, Marie
curvature of spacetime
cyclic universe
California, University of
Berkeley
Santa Barbara
California Institute of Technology (Caltech)Santa Barbara
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, Billidentical
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 interpretationeternal inflation and
see also
cosmological constant
Copernicus, Nicolaus
Cosmic Background Explorer (COBE) satellite
cosmic background radiation
see also
microwaves, cosmic
cosmic eggmicrowaves, cosmic
cosmic horizon
Cosmo-98 conference (Monterey)
cosmological constant
accelerated expansion and
anthropic selection and
Einstein and
principle of mediocrity and
Coulomb, Charles-Augustin deanthropic selection and
Einstein and
principle of mediocrity and
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
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
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
deuteriumparameter
Q
of
see also
inhomogeneities, cosmic
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=mc
2
Earth
economic inflation
Edison, Thomas
Efstathiou, George
Ehrenfest, Paul
Einstein, Albert
electromagnetism
elementary particles
Ellis, George
empty space, gravity of
energy conservation, law of
Englert, François
entropy
equilibrium, thermal
eschatology, cosmic
eternal inflation
Euclidean time
Euler’s formula
European Center for Nuclear Research (CERN)
Everett, Hugh, III
Everett interpretation of quantum mechanics
evolution, Darwin’s theory of
2
Earth
evolution of intelligent life on
human population of
infinite duplicates of
magnetic field of
École Normale Supérieurehuman population of
infinite duplicates of
magnetic field of
economic inflation
Edison, Thomas
Efstathiou, George
Ehrenfest, Paul
Einstein, Albert
cosmological constant of
Friedman’s solutions to equations of
mass-energy relation (E=mc
2
) of
on observer dependency of time order of events
Stalinist rejection of theories of
see also
relativity theory
electric forceFriedman’s solutions to equations of
mass-energy relation (E=mc
2
) of
on observer dependency of time order of events
Stalinist rejection of theories of
see also
relativity theory
electromagnetism
in final theory of nature
in final theory of nature
quantum fluctuations of
in supernovae
electronsin final theory of nature
quantum fluctuations of
in supernovae
annihilation into photons of
magnetic moment of
mass of
in string theory
virtual
electroweak forcemagnetic moment of
mass of
in string theory
virtual
elementary particles
collisions of
masses of
elementsmasses of
chemical properties of
origins of
periodic table of
elliptical galaxiesorigins of
periodic table of
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 geometryand 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 time
Euler’s formula
European Center for Nuclear Research (CERN)
Everett, Hugh, III
Everett interpretation of quantum mechanics
evolution, Darwin’s theory of
false vacuum
fermions
Ferris, Timothy
final theory of nature
flatness problem
fluxes
foam, spacetime
Fomin, Piotr
Ford, Larry
fractals
French Communist Party
Friedmann, Alexander
see
final theory
in “chaotic” inflation
decay of
energy density of
island universes in
in parallel universes
repulsive gravity of
strings of
tunneling and
Fermi, Enricodecay of
energy density of
island universes in
in parallel universes
repulsive gravity of
strings of
tunneling and
fermions
Ferris, Timothy
final theory of nature
gravity and
mathematics of
search for
see also
string theory
fireball, cosmicmathematics of
search for
see also
string theory
in cyclic universe
at end of universe
ignited by decaying false vacuum
images of
five-nucleon gapat end of universe
ignited by decaying false vacuum
images of
flatness problem
fluxes
foam, spacetime
Fomin, Piotr
Ford, Larry
fractals
French Communist Party
Friedmann, Alexander
big crunch predicted by models of
Gamow and
on geometry and density of universe
fundamental theory of nature,Gamow and
on geometry and density of universe
see
final theory
galaxies
gamma rays
Gamow, George
Gamow, Lyuba
Garriga, Jaume
gases, expansion of
gauge symmetry
Gell-Mann, Murray
general theory of relativity,
see
relativity theory, general
genetic code
geometry
Georgi, Howard
giant galaxies
Glashow, Sheldon
Gleiser, Marcelo
Gliner, Erast
gluons
God
Gold, Thomas
googol
googolplex
Gore, Al
Gott, Richard
Göttingen, University of
graceful exit problem
grand unified theories
grand-unified vacuum
Grassmann, Hermann
Grassmann numbers
gravitational constant
gravitational waves
gravitons
gravity
Greeks, ancient
Green, Brian
Green, Michael
Griffiths, Robert
Grishchuk, Leonid
Gross, David
Guinness Book of Records
Gunzig, Edgard
Guth, Alan
clusters of
in contracting universe
dark matter and
distant
distribution of
duplicate
formation of
helium content of
in island universes
in open universe
properties of
radio emissions from
type Ia supernova explosions in
Galileoin contracting universe
dark matter and
distant
distribution of
duplicate
formation of
helium content of
in island universes
in open universe
properties of
radio emissions from
type Ia supernova explosions in
gamma rays
Gamow, George
Gamow, Lyuba
Garriga, Jaume
gases, expansion of
gauge symmetry
Gell-Mann, Murray
general theory of relativity,
see
relativity theory, general
genetic code
geometry
Euclidean
spacetime
George Washington Universityspacetime
Georgi, Howard
giant galaxies
Glashow, Sheldon
Gleiser, Marcelo
Gliner, Erast
gluons
God
and cosmic egg scenario
before creation
existence of
as mathematician
goldbefore creation
existence of
as mathematician
Gold, Thomas
googol
googolplex
Gore, Al
Gott, Richard
Göttingen, University of
graceful exit problem
grand unified theories
grand-unified vacuum
Grassmann, Hermann
Grassmann numbers
gravitational constant
gravitational waves
gravitons
gravity
amplification of perturbations by
of dark matter
instability of
Newton’s theory of
quantum
and rate of cosmic expansion
repulsive,
see
repulsive gravity
strength of
in string theory
Great Depressionof dark matter
instability of
Newton’s theory of
quantum
and rate of cosmic expansion
repulsive,
see
repulsive gravity
strength of
in string theory
Greeks, ancient
Green, Brian
Green, Michael
Griffiths, Robert
Grishchuk, Leonid
Gross, David
Guinness Book of Records
Gunzig, Edgard
Guth, Alan
calculation of density perturbations
calculation of density perturbations by
graceful exit problem recognized by
on repulsive gravity
success of inflation theory of
calculation of density perturbations by
graceful exit problem recognized by
on repulsive gravity
success of inflation theory of
half-life
Hartle, James
Harvard University
Hawking, Stephen
heat-death problem
Heisenberg, Werner
Heisenberg’s uncertainty principle
helium
Helmholtz, Hermann von
Herman, Robert
High-Redshift Supernova Search Team
Hinduism
histories
Hogan, Craig
horizon, cosmic,
see
cosmic horizon
horizon problem
horoscopes
Hoyle, Fred
Hubble, Edwin
human race, longevity of
Hunter College
hydrogen
Hartle, James
Harvard University
Hawking, Stephen
heat-death problem
Heisenberg, Werner
Heisenberg’s uncertainty principle
helium
Helmholtz, Hermann von
Herman, Robert
High-Redshift Supernova Search Team
Hinduism
histories
Hogan, Craig
horizon, cosmic,
see
cosmic horizon
horizon problem
horoscopes
Hoyle, Fred
Hubble, Edwin
human race, longevity of
Hunter College
hydrogen
heavy
imaginary numbers
inertial motion
inflation
inhomogeneities, cosmic
see also
density perturbations
instability, gravitational
Institut des Hautes Études Scientifiques
intelligent life
International Congress on Nuclear Physics (Rome, 1930)
inverse square law
iron
island universes
inertial motion
inflation
chaotic
density perturbations from
eternal,
see
eternal inflation
graceful exit problem in
no-boundary proposal and
observational evidence for
quantum fluctuations during
repulsive gravity and
success of theory of
tunneling and
inflatondensity perturbations from
eternal,
see
eternal inflation
graceful exit problem in
no-boundary proposal and
observational evidence for
quantum fluctuations during
repulsive gravity and
success of theory of
tunneling and
inhomogeneities, cosmic
see also
density perturbations
instability, gravitational
Institut des Hautes Études Scientifiques
intelligent life
evolution of
future of
interference, quantumfuture of
International Congress on Nuclear Physics (Rome, 1930)
inverse square law
iron
island universes
computer simulation of
in de Sitter spacetime
frontiers of
time in
in de Sitter spacetime
frontiers of
time in
Jainism
Jinasena
Jinasena
Kac, Victor
kelvin scale
Kepler, Johannes
Khvolson, Orest
“kickspan”
Kiev Institute for Theoretical Physics
kicks, quantum
Kirshner, Robert
Knobe, Joshua
Kragh, Helge
Krauss, Lawrence
Krutkov, Yuri
kelvin scale
Kepler, Johannes
Khvolson, Orest
“kickspan”
Kiev Institute for Theoretical Physics
kicks, quantum
Kirshner, Robert
Knobe, Joshua
Kragh, Helge
Krauss, Lawrence
Krutkov, Yuri
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