Contents
About the Author
Also by John D. Barrow
Dedication
Title Page
Epigraph
Preface
0. Nothingology – Flying to Nowhere
Mysteries of Non-existence
Nothing Ventured
Nothing Gained
1. Zero – The Whole Story
The Origin of Zero
Egypt – In Need of Nothing
Babylon – The Writing Is On the Wall
The No-entry Problem and the Babylonian Zero
The Mayan Zero
The Indian Zero
Indian Conceptions of Nothingness
The Travelling Zeros
The Evolution of Words for Zero
A Final Accounting
2. Much Ado About Nothing
Welcome to the Hotel Infinity
Greeks, Bearing Gifts
Islamic Art
St Augustine
The Medieval Labyrinth
Writers and Readers
Shakespearean Nothings
Paradox Lost
3. Constructing Nothing
The Search for a Vacuum
A Tale of Two Nothings
How Much of Space Is Space?
4. The Drift Towards the Ether
Newton and the Ether: To Be Or Not To Be?
Darkness in the Ether
Natural Theology of the Ether
A Decisive Experiment
The Amazing Shrinking Man
Einstein and the End of the Old Ether
5. Whatever Happened to Zero?
Absolute Truth – Where Is It To Be Found?
Many Zeros
Creation Out of the Empty Set
Surreal Numbers
God and the Empty Set
Long Division
6. Empty Universes
Dealing With Entire Universes on Paper
Vacuum Universes
Ernst Mach – A Man of Principle
Lambda – A New Cosmic Force
Deep Connections
7. The Box That Can Never Be Empty
It’s a Small World After All
The New Vacuum
All At Sea in the Vacuum
The Lamb Shift
Forces of the World Unite
Vacuum Polarisation
Black Holes
8. How Many Vacuums Are There?
Vacuum Landscape Appreciation
The Unification Road
Vacuum Fluctuations Made Me
Inflation All Over the Place
Multiple Vacuums
Eternal Inflation
Inflation and New Lambda
Falling Downstairs
Bits of Vacuum
9. The Beginning and the End of the Vacuum
Being Out of Nothingness
Creation Out of Nothing
Philosophical Problems About Nothing and How We Escaped From It
Creation Out of Nothing in Modern Cosmology
No Creation Out of Anything?
The Future of the Vacuum
Notes
Index
Copyright
Also available from Vintage
The Limits of Science and the Science of Limits
‘If you are fascinated, as I am, by the limits of knowledge, you will be richly rewarded by this book’
New Scientist
‘Around the theme that what is impossible may define the universe more clearly than the list of possibilities, Barrow conducts a tour of many of the most interesting topics in recent popular science, giving most of them a new twist in the telling . . . Barrow shows how there are limits on the kinds of questions to which we can expect answers . . . his book leaves one feeling that this kind of impossibility is no cause for despondency. Rather, trying to improve our understanding of just what is possible, and what is not, seems a vital part of the enterprise our kind of consciousness has called science’
Financial Times
‘A thoughtful, careful and insightful book that is presented in a skilfully woven narrative, guiding the reader gently through the thicket of logic, physics, and mathematics. I highly recommend it, especially if you like dizzying, mind-bending ideas that will make your head swim’
New Scientist
In memory of Dennis Sciama
The page references in this index correspond to the printed edition from which this ebook was created. To find a specific word or phrase from the index, please use the search feature of your ebook reader.
absolute zero 7
Adams, Robert M. 5
‘Aftermath’ 2
air pressure 64, 99–106, 111–13, 114, 117
Alhambra, Spain 70, 71
Ali G 5
Allen, Woody 256
American Indians: counting system 15
Anaxagoras 64–65
Anderson, Poul 271
Anselm, Saint, Archbishop of Canterbury 172, 173
anti-gravitation 252
anti-matter 280
anti-quarks 236
Apollonius 46
Aquinus, Thomas 74
Arab culture:
counting 46
Indian mathematics assimilated by 46–47, 48, 49
numerals and 47–48
Archimedes 46
Aristotle:
Christianity, synthesis with 69, 75
creation from nothing and 81–82
God’s constraints and 81
logic 59, 93, 153–54, 157
uncreated Universe and 82
vacua and 60, 68, 76, 79, 97
world view 69
as-sifr 49
asymptotic freedom 236, 237
atmosphere 102, 105–6, 111–13, 117
atomism 65–68, 69, 82, 95–96
Augustine, Saint 5, 72–75
Aztecs 24
Babylonians:
astronomers 25, 29
mathematicians 25, 51
numerals’ positioning 25–26
separator symbol 27
Sumerians and 20
zero and 26–29, 51
see also Sumerians
Bacon, Roger 77, 78, 94
Badra: Azerbaijan 70
Baghdad 47:
Caliph of 47
barometers 100
bases 15–16, 20, 24
Basilides 295–96
Beatles, The 8
Being and Nothingness (Sartre) 57
Bell, Graham Alexander 143
Ben Ezra 46
Bentley, Richard 126, 129, 134
Bergson, Henri 299–300
beta particles 146
Bible 181, 294–95, 296
Big Bang:
black holes and 240
forces’ unification and 249
gravitational waves 188
radiation from 197, 258–59, 283
vacuum fluctuations from 260
Bihârîlâl 38
binary arithmatic 4
binary pulsars 183, 184
bindu 40, 44, 49
black holes:
definition 238
event horizon 239
explanation of 238–39
explosions and 240
gravity and 239, 241
gravity waves and 184
identifying 239
large galaxies and 238
mass 239
quantum vacuum and 239–40, 241
Universe’s future and 314
black-body radiation 211–13, 217, 240
Blasius of Parma 79
Boersma, Sipko 223, 225
Bohr, Niels 206
Bolyai, Janos 155
Bonaparte, Napoleon 52
Bondi, Hermann 196, 312
Book of Number (Ben Ezra) 46
Boole, George 164–65
Boomerang 259, 261, 262
Born, Max 209
bosons 227
Boyle, Robert 10, 102–3, 124, 128
Brahmagupta 38
Brahmasphutasiddhanta 47
Bridgewater Treatises 135
Bruno, Giardano 114
Buber, Martin 57
Burley, Walter 78, 79–80, 94
Cage, John 6–7, 30
Cantor, Georg 165, 171, 174
Carroll, Lewis 58
Casimir, Hendrick 217, 219, 220
Casimir Effect 217, 219, 221, 223, 224
cefirum 49
‘chaos’ 59
Chesterton, G. K. 287
chiffre 50
China:
Indian counting system and 46
numerals 26
zero and 37
Christianity:
creation and 72–73, 292–98, 313
Greek and Jewishes influences 59, 75
science and 293
Chrysippus of Soli 68
cifra 49
cipher 2–3, 49, 50
ciphra 51
circulus 51
Clarke, Arthur C. 188
Clarke, Samuel 83
classical physics: end of 150
clepsydra see water-catcher experiment
Clermont 111
Cleveland, Richard 167
Cook, John 135
Colie, Rosalie 85
colour charge 227, 228, 235
computers 4
constants: non-uniformity of 264–66
Conway, John 169, 171
Copernicus, Nicholas 102
Cornford, Francis 298
Cosmic Background Explorer satellite 214, 258
cosmological constant see lambda
cosmology: vacuum and xiii
counting 14–15
creation field 196
creation out of nothing:
Christianity and 72–73,292–98
impossibility of 58
modern cosmology and 302–7, 311
myths and 290–91
problems of 11
vacuum and 106
creation out of something 289–90
Curie temperature 245
Da̦browski, Mariusz 310
dark matter 119
De Rerum Natura (Lucretius) 65
de Sitter universe 315, 316
Dead Souls (Gogol) 7
death 8
Debeye, Paul 221
Democritus 65, 67, 116
Desaguliers, Mr 98–99
Descartes, René:
air pressure and 111, 115
matière subtile 126
matter and 130
Pascal and 115
vacuum denied by 126, 130
vortex theory 126–28, 130
Dialogue Concerning Two World Systems (Galileo) 91–92
Dirac, Paul 51, 206
distances, measuring 197–203
Doppler shift 201, 202
Dyson, Freeman 315
Egypt:
hieroglyphic numerals 17, 18
numbers 16–19
zero absent 19
Einstein, Albert:
curved space and 181
empty universes and 186
equations of motion 178, 185
ether and xii 10, 146–51, 205
field equations 178, 180, 181, 182, 185, 188, 191, 192, 303
general theory of relativity (gravity) 148, 176, 177–80, 182–85, 188–94, 254, 302–3, 307, 315
lambda and 189–93, 195, 196, 205–6, 272, 310, 314
motion and 147–48, 149
Newton and 176–77
predictions confirmed 177
quantum theory and 204, 206
space/time and 177–80
special theory of relativity 148, 151, 177
successors to theories of 148
Universal homogeneity and 189
Universe expanding and 303
Universes and 181–85
vacua and 181
vacuum energy 11
Eldridge, Niles 277
Elea, school of 66
electromagnetism 227, 230, 233–36, 248
electrons:
electromagnetic repulsion between 235
firing at each other 232–33
mass 146
orbits of 210, 225
quantum vacuum and 233–34, 235
speed 146
weak force and 227
zero point motions around 225
elementary particles:
Universe and 205
wavelength 208
wavelike behaviour 208
see also under names of individual types
Empedocles 62, 63, 77
energy:
conservation 271
electromagnetic interaction and 235
forms of 180, 250
of motion 271
potential 271
quantum theory and 207–8, 210
space and 254
wavelengths 211
wavelike character 210, 211–14
entropy 309, 310
Epicurus 65, 67, 122
Epimenides 92
Escher, Mauritz 71
Essay on Silence (Hubbard) 7
ether:
beginning of belief in 62–63, 123–24
darkness of night sky and 132
detecting 139–44
Einstein and xii 10, 146–51, 205
Empedocles 62
existence disproved 141–44
gravity and 130
light and 135
natural theology of 134–36
nature of xii
Newton and 124, 125, 128–30
pneuma and 68
popularity of idea 136
tragedy of 204
Euclid 92, 93, 110, 153–58
Europe:
numbers system introduced 48
zero and 46
European Space Agency 260
event horizon 238, 239
existentialists 57
extracosmic void 76, 80–81, 83, 131, 151
Fernando II, Grand Duke 99
Feynman, Richard 207
fine structure constant 231–32
FitzGerald, George 145, 146, 149
FitzGerald–Lorenz contraction 145, 146, 149
forces of nature:
distinct forms 226
temperature and 244
underlying unity 229
unity 229, 230, 236–37, 248–56, 280
4 minutes 33 seconds 6–7
Friedmann, Alexander 191, 199
funiculus 103
galaxies 118
clusters 120
origins of 281, 282-84
vacuum region surrounding 132
Galbraith, John K. 4
galgal 46
Galilei, Galileo 10, 92, 96–97, 103, 114
Gamaliel, Rabbi 294
Gardner, Martin 7
gases under pressure 96 see also air pressure
Gassendi, Pierre 82
Gauss, Carl Friedrich 155
geometry 153–57
Gerbert of Aurillac 48
Gersdorf, Johannes von 106–7
Gibbs, Josiah Willard 145
Gjertsen, Derek 122
gluons 227, 235, 236
Gnostic philosophies 295, 297
God:
Design Argument and 82, 126, 134
empty sets and 171–73
Nature and 293
ontological argument for existence of 172
space and 82, 83–84
vacua and 81–82
Gödel, Kurt 92–93, 301
Gogol, Nikolai 7
Gold, Thomas 196, 312
Gombrich, Ernst 72
Gore, John 131, 133
Gould, Stephen Jay 277
Graham, Ronald 158
‘grand unification’ temperature 249
Grant, President Ulysses Simpson 138
graphs 163
gravitational instability 258
gravity:
all matter has 118–19
complexity of 180
Einstein and 177–80
Einstein dispenses with 178
energy and 241
ether and 130
gravitons 227, 228
as innate property 125
interaction with itself 180
mass and 184, 186
quantum theory and 306, 311
repulsive 195, 306, 307, 310
vacua and 126
waves 184–85, 187
weakness of 229
see also lambda
Greeks:
counting system 24
creation out of nothing and 297
logic 42, 44, 93
nothing and 9, 42, 44–45, 52, 59–62, 64
zero and 13, 51–52
Guericke, Otto von 103–8
Guth, Alan 252, 280
Guy, Richard K. 26
Hamlet (Shakespeare) 87, 88
Harary, Frank 163
Hartshorne, Charles 172
Hawking, Stephen 239, 240, 241, 306, 311, 314
Hebrew tradition:
creation out of nothing 293–94
Indian counting system and 46
nothing and 42
numerals’ positioning 46
zero 46
Hegel, Georg Friedrich Wilhelm 58
Heidegger, Martin 299
Hein, Piet 95
Heisenberg, Werner 206, 207, 215:
Uncertainty Principle 215, 233, 257
Helmholtz, Hermann von 143
Hero 82
Hilbert’s Hotel 55–56
histories 304–5
Hodges, Andrew 300
Hoffman, Banesh 204
Hollywood, John of 50
Homer 60
Hooke, Robert 102
Hoyle, Fred 117, 196, 312
Hubbard, Elbert 7
Hubble, Edwin 199, 202
Hubble Space Telescope (HST) 12, 200, 201, 202, 285
Huguenots 3
Huxley, Aldous 172
Huygens, Christiaan 115, 124, 135
hydrogen atom 225–26
hyperinflation 4
ideal forms 54, 94, 297–98
Ifrah, Georges 35, 44
India:
astronomers 36
counting system 35–42, 45–46
mathematics assimilated by Arabs 46–47, 48, 49
non-being and 42, 44
nothing and 9, 40, 42–45, 52
numerals 36, 37
numerals positioning 35, 36
zero and 35–42, 51, 52
Indus: numerals 35
Indus valley culture 35
infinity 55–58, 59:
paradoxes and 58
inflation, cosmological 251, 252, 253–54, 255, 256
information storage and precessing 315–16
interferometer 143, 145–46, 184
intracosmic void 76
inverse square law 190
Irenaeus 295
Isaac of Nineveh 69
Islamic art 69–72
Johns, Jasper 6
Johnson, Samuel 13
Jolson, Al 1
Joseph, Tim 292, 302
Judaism see Hebrew tradition
Judeo-Christian world view 69
Kafka, Franz 136
Kak, Subhash 38
Kant, Immanuel 172
Kaufmann, Walter 146
Kelvin, Lord 130, 136
Kepler, Johannes 128
Kerr, Philip 176, 226
Al-Kharizmi 46–47
Kibble, Tom 279
King Lear (Shakespeare) 89–90
Knuth, Donald 158, 169
Kohn, Marek 134
Krailsheimer, Alban 108
Kramer, Hilton 6
Kramers, Hendrick 207
Kushner, Laurence 91
Lamb shift 225–26
Lamb, Willis 226
lambda force 189–203, 205–6, 271–75, 306, 310, 311, 314, 315
Lamoreaux, Steve 219, 220
Lao-tzu 230
Laplace, Pierre Simon de 46
Latin, medieval 49
laws of Nature:
asymmetry of 248
symmetricality and 247–48
Laws of Thought, The (Boole) 165
Leibnitz, Gottfried 42, 83–84, 129, 298–99
Lemaître, Georges 194–95, 196, 272
leptons 227, 228, 229
Leucippus 65
Liar paradox 92
life: and future of Universe 315–18
light:
behaviour of 124–25
ether and 135
gravity and 179
particle characteristics 125
speed of 147, 148, 149, 177
wave characteristics 124–25
see also photons
light bulbs 11
Linde, Andrei 251, 267–68
Lobachevski, Nikolai 155
Logan, Robert 13
Lorentz, Hendrik 145, 146, 149, 150
Louis XIV 3
Lucretius 77, 82, 95
M theory 148
Macbeth (Shakespeare) 87
McCrea, William 196
McCrum, Robert xi
Mach, Ernst 186–88
Mach’s Principle 186–88
‘Magdeburg Hemispheres’ 103–5
magnetism 245–47
MAP (Microwave Background Explorer) 260
Mare, Father de la 113
Maric, Mileva 150
Marvell, Andrew 152
Marx, Groucho 319
Masefield, John 223
mass:
gravity waves and 184, 186
space and 182, 254
wavelike character 210
mathematical modelling 158
mathematics:
absolute truth and 92–93
different structures of 158–59, 161, 162, 173–75
existence and 299, 300, 302
groups 159–62
importance to theologians and philosophers 153
infinity and 55
metaphysical influences 175
natural world, gap from 157, 158, 162
new directions 152
physical existence and 162, 299, 300, 302
pure 174, 175
relativism of 157
science, difference from 158
teaching 169–70
see also sets
matter:
creation of 196
excess over anti-matter 280
hierarchy of systems 118
Matthew Effect 258
Maxwell, James Clerk:
ether and 139
light and electromagnetism 145
vacuum and 215
Mayans:
calculations, distinctions in sophistication 30
calendar 33–34
counting system 30–31
numerals 31
numerals’ positioning 31
zero 30–34
zero, hieroglyphs for 34
Mearns, Hughes 1
mercury 99, 101, 103:
vacuum at top of column 99, 102, 103, 113, 124
Mercury 179
Mersenne, Marin 110, 114
Michelson, Albert: ether and 10, 137–44, 145, 147, 149, 184
Michelson, Samuel 137
microwave photons 120
microwave radiation 258, 260
middle ages:
experiments and 94
vacuum and 9, 75–84
Milky Way 118, 188
Millennium Bug 14
Moon: gravity experiment on 98
More, Henry 82
Morley, Edward 144, 145, 147, 149
motion:
curved space and 178–79
length and mass and 147
Much Ado about Nothing (Shakespeare) 87
muons 227
musicians 6–7
Nâgarî script 36
‘napoo’ 3
Napoleon Bonaparte 52
Narmer, King 17, 18
NASA 214, 258
natural numbers 168
natural selection 277
Nature:
God and 293
vacuum and 76–77
neutrino-like particles 119
neutrinos:
quarks and 229
weak force and 227
Newcomb, Simon 132, 133
Newton, Sir Isaac:
absolute space and 123
atomic structure of matter 131
cosmos, conceptions of 131
ether and 124, 125, 128–30
forces’ instantaneous action and 62
God and 82, 84
gravity and 84, 122, 125–26, 128, 129, 176, 190, 191
laws of motion 84, 122–23, 147–48, 149
light and 124–25, 128
Opticks 83, 129
Principia 128, 129
space and 82, 83
space/time and 177
vacuum and 131
night sky, darkness of 130–34
Nihil (Passerat) 86
Nihil (Von Guericke) 107
Nimmo 4
Noël, Père 115–16
‘non-Euclidean’ 157
nothing:
artists and 5, 6–8
Christianity and 72–75
creation out of 11, 72, 73, 90
creation out of impossible 58
different traditions confronting 4–5
Eastern philosophies and xii
existence of 54
fascination of xi
importance of 9
literary fascination with 9, 60, 84–88, 91, 109
mathematics’ acceptance of 94
metaphysical 109
multiple meanings for 44, 109
perplexing nature 1–2
philosophical problems about 298–302
philosophy and 8–10
physical 109
physicists’ concept 5
puns and paradoxes 9, 60, 84–88
quantum theory and 11
as something xi 107
something and 287
synonyms 1, 4
theology and 8, 72–75, 94
two types 108–17
zero and 175
see also vacuum; zero
Nothing Book, The 7
nuclear reactions 226
‘null’ 50
Number Zero, The (Johns) 6
numbers:
decimal 169
natural 170
negative 170
place value system 18, 19, 21, 24–26, 30–31, 51:
zero and 28, 36–37, 51
surreal 169–71
numerals, grouping in threes 47
Odyssey, The (Homer) 60
On the Letter O 86
Opticks (Newton) 83, 129
O’Shaughnessy, Arthur 307
outer space: vacuum 118
parallel postulate 154–55
Paris condemnations 81
Parmenides 44–45, 58, 59, 61–62
Pascal, Blaise:
achievements of 109
air pressure and 10, 111–13, 117
Descartes and 115
mathematics 109–10
Pensées 109
silence of space terrifies 56–57
vacua and 10, 111, 113–17, 124
Passerat, Jean 86
Patashnik, Owen 158
Paul, St 275
Penrose, Roger 304, 305, 306, 311
Pensées (Pascal) 109
Périer, Florin 111
Petit, Pierre 111
Philosophical Transactions of the Royal Society 98–99
photons:
electromagnetism and 226, 235
history of 120
numerousness of 120
Pisa, Leaning Tower of 98
Pisa, Leonardo of 49–50
Planck, Max 206, 211, 212, 213, 240
Planck Surveyor 260
Planck’s constant 208, 213, 233
Plato 45, 54, 94, 297–98
pneuma 68, 123–24
Porter, Cole 173
Poseidonius of Apamea 68
positrons:
quantum vacuum and 233–34
repelling chanrge 235
Prayse of Nothing, The 85
Principia (Newton) 128, 129
protons:
gravitational force between 229
strong force and 227
Proust, Marcel 287
pumps 98, 99
Puthoff, Harold 222
Pythagoreans: vacuum and 67–68
quantisation 207, 208
quantum theory:
accuracy of predictions 207
determinism in 209
gravity and 306
importance of 151
incompleteness of 229
light and 207
Newton’s laws and 209
nothing and 11
pioneers of 206
position and velocity 215
stability and 210
vacua and xiii 5, 10, 151, 228, 233–37, 239
wavelengths 208, 227
quarks:
anti-quarks 236
colour charge 227, 228, 235, 236
definition of 227
electric charge 228
families of 229
as most elementary particles 228
quasars 123, 197
radiation: energy and 119–20
radioactivity 226
Rauschenberg, Robert 6
Read, Ronald 163
Reinhardt, Ad 6
relativity: importance of 151
Renyi, Alfréd 13
Retherford, Robert 22
Ricci, Michelangelo 100, 101, 111
Roman numerals 16, 48
Rotman, Brian 59–60
Royal Society 103
Rucker, Rudy 194
Russell, Bertrand 174, 300
Salmon, Wesley 152
Sankheda 36
Sartre, Jean-Paul 57, 90–91
scalar fields 249–52, 253, 257, 258, 259, 262, 268, 273, 275, 306
Scholastics 78, 84
Schrödinger, Erwin 206, 208–9
Schwinger, Julian 222
science:
Christianity and 293
effectiveness of 287
experimental investigation and 93
mathematics, difference from 158
theories 148
Sen, Dev 219
sets:
definition 165
numbers and 166–67, 168, 169–71
sets within 167
see also following entry
sets, empty;
creation from 164–68, 169
God and 171–73
need for 166
zero and 166
Shackleton, Len 7
Shakespeare, William 87–91, 267
ships, rolling: attraction of 223–25
Simplicio 91
Simplicius 58
singularities 303, 304, 305, 307, 308, 314
Sitter, Willem de 315
something, rather than nothing 287, 298
sonoluminescence 222
sound, behaviour of 125
sound-wave energy: conversion into light 222
space:
beginning to 312
curved 178, 181, 185, 186, 189, 254
dimensions 265–66, 267
God and 82, 83–84
spacetime 180, 181, 182
Spain 46
Sparnaay, Marcus 219
Spinoza, Baruch 155
Sriyantra 40
stars:
nuclear fuel 314
variable 198, 199
steady-state theory 196–97, 312
Stein, Gertrude 117
Stewart, Balfour 136
Stoicism 68–69, 80, 82, 123
strong force 226, 227
Sumerians:
clay tablets 21
counting 16, 20
cuneiform signs 23
numerals 21, 22, 24
writing implements 23
see also Babylonians
Sun: motion of 146
sunya 38, 40, 49
supernovae 200–2, 260–62, 270
Sylvester II, Pope 48
symmetry breaking 247
Tait, Peter Guthrie 136
Tantric tradition 40
Tatian 297
tauons 227
telescopes, ground: advanced 200
temperature:
early Universe 249
forces and 244–47, 249
wavelength and 211–14
Tempier, Bishop Etienne 81
Tessimond, A. S. J. 278
Thales 44, 61
Theaetetus 45
theca 51
theology:
creation and 292–93
nothing and 8, 72–75, 94
vacuum and 9
Theophilus of Antioch 297
time:
beginning to 312
Creation and 82
curved 186
dimensions 265–66, 267
energy and 182
mass and 182
time travel 187, 304
time-keeping in 60s 20, 26
Tipler, Frank 315, 316
Tolkien, J. R. R. 264
Torricelli, Evangelista:
air pressure and 10, 64, 99–102, 111, 113–14, 117
interests of 102
vacua and 124
transformation rules 159, 162
Turing, Alan 300
Universe:
beginning 11, 289–92, 303, 305, 307, 312, 313
change, necessity for 189, 190, 193
cyclic 307–10
density differences 253
density low 121
early stages of 119, 205, 213, 214, 237, 249
energy fields in 249–50
elementary particles and 205
future of 313–18
matter clustering 120–21
myths about 289–90
non-uniformity 256, 257, 258, 264, 270, 303
nuclear reactions in early history 119
past hotter and denser 205
quantum-transition into another type of universe 317
rotation 187
stability of may be temporary 276
static 191
temperature differences 253
ultimate theory of 288
vacuum 181–85, 186–88
see also following entry
Universe, expanding:
acceleration of 197–203, 251, 280–81, 314
critical dividing line 252–53, 255, 259
direction, uniformity of 253–54
gravity and 185, 188
inflation 251, 252, 253–54, 255, 256, 257–58, 259, 262–64, 267–75, 277, 281, 284, 306, 307, 310–11
lambda and 203
necessity for 193
non-spherical 185
temperature and 259, 260, 314
vacuum energy and 12, 56
varieties of 192
WIMPS and 119
vacuum:
before creation 81
changes in 5, 252–53, 279, 317
concept first used 65
cosmic strings 279, 282–86
definition 242
different types 242–48, 277
electromagnetic oscillation and 220
empty space and 115–16
experimental science and 10
fluctuations 256–62
God and 81–82
importance of 5
inflation and 256
lambda and 195, 205–6
landscapes 249, 277, 288, 317
life and 121
mass, wavelike character and 210
monopoles 279, 280–82
necessary for change 66
nothing and 5
physical reality of 95, 109
pieces of 279
polarisation 230–37, 244
possibility of doubted 10, 54, 96, 115, 137
quantum theory and xiii 5, 10, 151, 216–17, 228, 233–37, 237, 239, 241
searching for 95–108
shape changes 279
smooth surfaces’ separation and 77–80
states 11, 250–51, 264–67, 277, 279
Uncertainty Principle and 216
Universes 181–85, 205
Universe’s future and 313–18
walls 279
vacuum, cosmic 10, 203, 315
vacuum energy 11–12, 203, 206, 218, 306, 313, 315, 316–17
vacuum tubes 11
‘vanishing point’ 6
Vâsavadattâ 37
Velentius 295
Vilenkin, Alex 268
Vinci, Leonardo da 53
water-catcher experiment 63, 64–65, 77, 80
wave function 209
weak force 226, 227, 229–30, 248
West, Mae 225
Whewell, William 135–36
Whitehead, Alfred North 176
WIMPS (weakly interacting massive particles) 119
Winter’s Tale, The (Shakespeare) 87
Wittgenstein, Ludwig 299, 300
wordplay 9, 60, 84–88
X-ray binary systems 239, 240
X-rays 11, 239
zefiro 50
zefirum 49
zefro 50
Zeno 58, 59, 79:
paradoxes 59, 60, 61
Zeno of Cition 68
zero:
Babylonians and 26–29, 51
circumlocutions 2
complication of 164
derogatory associations 2–3
etymology 49–50
Greeks and 14, 51–52
India and 35–42, 51, 52
infinity and 55–58
mathematical fragmentation and 163
Moslems and 71–72
no-entry 28, 29, 38
nothingness and 175
numbers’ relative positioning and 19, 28
as operator 37–38
Romans and 16
sets and 166
shape of 38–39
spread of 45–49
strings 4
usefulness of 52
words for 39–40, 49–51
see also nothing; zero
zero-point energy 216, 217–22
zevero 50
Ziffer 51
‘zilch’ 2
‘zip’ 2
“Deciding on a book’s beginning is as complex as determining the origins of the universe.”
Robert McCrum
‘Because it’s not there’ might be reason enough to write a book about Nothing, especially if the author has already written one about Everything. But, fortunately, there are better reasons than that. If one looks at the special problems that were the mainsprings of progress along the oldest and most persistent lines of human inquiry, then one finds Nothing, suitably disguised as something, never far from the centre of things.
Nothing, in its various guises, has been a subject of enduring fascination for millennia. Philosophers struggled to grasp it, while mystics dreamed they could imagine it; scientists strove to create it; astronomers searched in vain to locate it; logicians were repelled by it, yet theologians yearned to conjure everything from it; and mathematicians succeeded. Meanwhile, writers and jesters were happy to stir up as much ado about Nothing as ever they possibly could. Along all these pathways to the truth Nothing has emerged as an unexpectedly pivotal something, upon which so many of our central questions are delicately poised.
Here, we are going to draw together some of the ways in which our conceptions of Nothing influenced the growth of knowledge. We will see how the ancient Western addiction to logic and analytic philosophy prevented progress towards a fruitful picture of Nothing as something that could be part of an explanation for the things that are seen. By contrast, Eastern philosophies provided habits of thought in which the idea of Nothing-as-something was simple to grasp and not only negative in its ramifications. From this first simple step, there followed a giant leap for mankind: the development of universal counting systems that could evolve onwards and upwards to the esoteric realms of modern mathematics.
In science, we will see something of the quest to make a real vacuum, in the midst of a thousand years of tortuous argument about its possibility, desirability and place. These ideas shaped the future direction of many parts of physics and engineering while, at the same time, realigning the philosophical and theological debates about the possibility and desirability of the vacuum – the physical Nothing. For the theologians, these debates were, in part, the continuation of a crucial argument about the need for the Universe to have been created out of both a physical and a spiritual Nothing. But for the critical philosophers, they were merely particular examples of ill-posed questions about the ultimate nature of things that were gradually falling into disrepute.
At first, such questions about the meaning of Nothing seemed hard, then they appeared unanswerable, and then they appeared meaningless: questions about Nothing weren’t questions about anything. Yet, for the scientists, producing a vacuum appeared to be a physical possibility. You could experiment with the vacuum and use it to make machines: an acid test of its reality. Soon this vacuum seemed unacceptable. A picture emerged of a Universe filled with a ubiquitous ethereal fluid. There was no empty space. Everything moved through it; everything felt it. It was the sea in which all things swam, ensuring that no nook or cranny of the Universe could ever be empty.
This spooky ether was persistent. It took an Einstein to remove it from the Universe. But what remained when everything that could be removed was removed was more than he expected. The combined insights of relativity and the quantum have opened up striking new possibilities that have presented us with the greatest unsolved problems of modern astronomy. Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act. Only when the vacuum’s subtle quantum influence was discovered could we see how the diverse forces of Nature might unite in the seething microworld inhabited by the most elementary parts of matter.
The astronomical world is no less subservient to the properties of the vacuum. Modern cosmology has built its central picture of the Universe’s past, present and future on the vacuum’s extraordinary properties. Only time will tell whether this construction is built on shifting sand. But we may not have to wait very long. A series of remarkable astronomical observations now seem to be revealing the cosmic vacuum by its effects on the expansion of the Universe. We look to other experiments to tell us whether, as we suspect, the vacuum performed some energetic gymnastics nearly fifteen billion years ago, setting the Universe upon the special course that led it to be what it is today and what it will eventually become.
I hope that this story will convince you that there is a good deal more to Nothing than meets the eye. A right conception of its nature, its properties, and its propensity to change, both suddenly and slowly, is essential if we are to understand how we got to be here and came to think as we do.
The glyphs accompanying the chapter numbers throughout this book, from zero to nine, are reproductions of the beautiful Mayan head-variant numerals. They represent a spectrum of celebrated gods and goddesses and were widely used by the Mayans more than fifteen hundred years ago for recording dates and spans of time.
I would like to thank Rachel Bean, Malcolm Boshier, Mariusz Da̦browski, Owen Gingerich, Jörg Hensgen, Ed Hinds, Subhash Kak, Andrei Linde, Robert Logan, João Magueijo, Martin Rees, Paul Samet, Paul Shellard, Will Sulkin, Max Tegmark and Alex Vilenkin for their help and discussions at various times. This book is dedicated to the memory of Dennis Sciama without whose early guidance neither this, nor any of my other writing over the last twenty-five years, would have been possible.
This book has survived one move of house and three moves of office in the course of its writing. In the face of all these changes of vacuum state, I would also like to thank my wife Elizabeth for ensuring that something invariably prevailed over nothing, and our children, David, Roger and Louise, for their unfailing scepticism about the whole project.
J.D.B.
Cambridge, May 2000
Theories of Everything
The Left Hand of Creation
(with Joseph Silk)
The Anthropic Cosmological Principle
(with Frank J. Tipler)
The World Within the World
The Artful Universe
Pi in the Sky
Impossibility
The Origin of the Universe
Between Inner Space and Outer Space
The Universe that Discovered Itself
Nothingology – Flying to Nowhere“As I was going up the stair,
I met a man who wasn’t there.
He wasn’t there again today,
I wish, I wish he’d stay away.”
Hughes Mearns
“You ain’t seen nothing yet.”
Al Jolson1
‘NOTHING’, IT HAS been said, ‘is an awe-inspiring yet essentially undigested concept, highly esteemed by writers of a mystical or existentialist tendency, but by most others regarded with anxiety, nausea, and panic.’2 Nobody seems to know how to handle it and perplexingly diverse conceptions of it exist in different subjects.3 Just take a look at the entry for ‘nothing’ in any good dictionary and you will find a host of perplexing synonyms: nil, none, nowt,4 nulliform,5 nullity – there is a nothing for every occasion. There are noughts of all sorts to zero-in on, from zero points to zero hours, ciphers to nulliverses.6 There are concepts that are vacuous, places that are evacuated, and voids of all shapes and sizes. On the more human side, there are nihilists,7 nihilianists,8 nihilarians,9 nihilagents,10 nothingarians,11 nullifideans,12 nullibists,13 nonentities and nobodies. Every walk of life seems to have its own personification of nothing. Even the financial pages of my newspaper tell me that ‘zeros’14 are an increasingly attractive source of income.
Some zeros seem positively obscure, almost circumlocutory. Tennis can’t bring itself to use so blunt a thing as the word ‘nil’ or ‘nothing’ or ‘zero’ to record no score. Instead, it retains the antique term ‘love’, which has reached us rather unromantically from l’oeuf, the French for an egg which represented the round 0 shape of the zero symbol.15 Likewise, we still find the use of the term ‘love’ meaning ‘nothing’ as when saying you are playing for love (rather than money), hence the distinction of being a true ‘amateur’, or the statement that one would not do something ‘for love or money’, by which we mean that we could not do it under any circumstances. Other games have evolved anglicised versions of this anyone-for-tennis pseudonym for zero: ‘goose egg’ is used by American ten-pin bowlers to signal a frame with no pin knocked down. In England there is a clear tradition for different sports to stick with their own measure of no score, ‘nil’ in soccer, ‘nought’ in cricket, but ‘ow’ in athletics timings, just like a telephone number, or even James Bond’s serial number. But sit down at your typewriter and 0 isn’t O any more.
‘Zilch’ became a common expression for zero during the Second World War and infiltrated ‘English’ English by the channel of US military personnel stationed in Britain. Its original slang application was to anyone whose name was not known. Another similar alliterative alternative was ‘zip’. A popular comic strip portrays an owl lecturing to an alligator and an infant rabbit on a new type of mathematics, called ‘Aftermath’, in which zero is the only number permitted; all problems have the same solution – zero – and consequently the discipline consists of discovering new problems with that inevitable answer.16
Another curiosity of language is the use of the term ‘cipher’ to describe someone who is a nonentity (‘a cipher in his own household’, as an ineffectual husband and father was once described). Although a cipher is now used to describe a code or encryption involving symbols, it was originally the zero symbol of arithmetic. Here is an amusing puzzle which plays on the double meaning of cipher as a code and a zero:
“U 0 a 0, but I 0 thee
O 0 no 0, but O 0 me.
O let not my 0 a mere 0 go,
But 0 my 0 I 0 thee so.”
which deciphers to read
“You sigh for a cipher, but I sigh for thee
O sigh for no cipher, but O sigh for me.
O let not my sigh for a mere cipher go,
But sigh for my sigh, for I sigh for thee so.”
The source of the insulting usage of cipher is simple: the zero symbol of arithmetic is one which has no effect when added or subtracted to anything. One Americanisation of this is characteristically racier and derives from modern technical jargon. A null operation is technospeak for an action that has no consequence. Your computer cycles through millions of them while it sits waiting for you to make the next keystroke. It is a neutral internal computer operation that performs no calculation or data manipulation. Correspondingly, to say that someone ‘is a zero, a real null op’ needs no further elucidation. Of course, with the coming of negative numbers new jokes are possible, like that of the individual whose personality was so negative that when he walked into a party, the guests would look around and ask each other ‘who left?’ or the scientist whose return to the country was said to have added to the brain drain. The adjective ‘napoo’, meaning finished or empty, is a contraction of the French il n’y a plus, for ‘there is nothing left’.
Not all nominal associations with ‘nothing’ were derogatory. Sometimes they had a special purpose. When some of the French Huguenots fled to Scotland to escape persecution by Louis XIV they sought to keep their names secret by using the surname Nimmo, derived from the Latin ne mot, meaning no one or no name.
Our system of writing numbers enables us to build up expressions for numbers of unlimited size simply by adding more and more noughts to the right-hand end of any number: 11230000000000 . . . During the hyperinflationary period of the early 1920s, the German currency collapsed in value so that hundreds of billions of marks were needed to stamp a letter. The economist John K. Galbraith writes17 of the psychological shock induced by these huge numbers with their strings of zeros:
“‘Zero stroke’ or ‘cipher stroke’ is the name created by German physicians for a prevalent nervous malady brought about by the present fantastic currency figures. Scores of cases of the ‘stroke’ are reported among men and women of all classes, who have been prostrated by their efforts to figure in thousands of millions. Many of these persons apparently are normal, except for a desire to write endless rows of ciphers.”
Pockets of hyperinflation persist around the globe; indeed there are more zeros around today than at any other time in history. The introduction of binary arithmetic for computer calculation, together with the profusion of computer codes for the control of just about everything, has filled machines with 0s and 1s. Once you had a ten per cent chance of happening upon a zero, now it’s evens. But there are huge numbers that are now almost commonplace. Everyone knows there are billions and billions of stars, and national debts conjure up similar astronomical numbers. Yet we have found a way to hide the zeros: 109 doesn’t look as bad as 1,000,000,000.
The sheer number of synonyms for ‘nothing’ is in itself evidence of the subtlety of the idea that the words try to capture. Greek, Judaeo-Christian, Indian and Oriental traditions all confronted the idea in different ways which produced different historical threads. We will find that the concept of nothingness that developed in each arena merely to fill some sort of gap then took on a life of its own and found itself describing a something that had great importance. The most topical example is the physicists’ concept of nothing – the vacuum. It began as empty space – the void, survived Augustine’s dilution to ‘almost nothing’,18 turned into a stagnant ether through which all the motions in the Universe swam, vanished in Einstein’s hands, then re-emerged in the twentieth-century quantum picture of how Nature works. This perspective has revealed that the vacuum is a complex structure that can change its character in sudden or gradual ways. Those changes can have cosmic effects and may well have been responsible for endowing the Universe with many of its characteristic features. They may have made life a possibility in the Universe and one day they may bring it to an end.
When we read of the difficulties that the ancients had in coming to terms with the concept of nothing, or the numeral for zero, it is difficult to put oneself in their shoes. The idea now seems commonplace. But mathematicians and philosophers had to undergo an extraordinary feat of mental gymnastics to accommodate this everyday notion. Artists took rather longer to explore the concepts of Nothing that emerged. But, in modern times, it is the artist who continues to explore the paradoxes of Nothing in ways that are calculated to shock, surprise or amuse.
“Now, is art about drawing or is it about colouring in?”
Ali G
“Nothing is closer to the supreme commonplace of our commonplace age than its preoccupation with Nothing . . . Actually, Nothing lends itself very poorly indeed to fantastic adornment.”
Robert M. Adams19
In the 1950s artists began to explore the limiting process of going from polychrome to monochrome to nullichrome. The American abstract artist Ad Reinhardt produced canvases coloured entirely red or blue, before graduating to a series of five-foot square all-black productions that toured the leading galleries in America, London and Paris in 1963. Not surprisingly, some critics condemned him as a charlatan20 but others admired his art noir: ‘an ultimate statement of esthetic purity’, according to American art commentator Hilton Kramer.21 Reinhardt went on to run separate exhibitions of his all-red, all-blue and all-black canvases and writes extensively about the raison d’être for his work.22 It is a challenge to purists to decide whether Reinhardt’s all-black canvases capture the representation of Nothing more completely than the all-white canvases of Robert Rauschenberg. Personally, I prefer the spectacular splash of colours in Jasper Johns’ The Number Zero.23
The visual zero did not need to be explicitly represented by paint or obliquely signalled by its absence. The artists of the Renaissance discovered the visual zero for themselves in the fifteenth century and it became the centrepiece of a new representation of the world that allowed an infinite number of manifestations. The ‘vanishing point’ is a device to create a realistic picture of a three-dimensional scene on a flat surface. The painter fools the eye of the viewer by imagining lines which connect the objects being represented to the viewer’s eye. The canvas is just a screen that intervenes between the real scene and the eye. Where the imaginary lines intersect that screen, the artist places his marks. Lines running parallel to the screen are represented by parallel lines which recede to the line of the distant horizon, but those seen as perpendicular to the screen are represented by a cone of lines that converge towards a single point – the vanishing point – which creates the perspective of the spectator.
Musicians have also followed the piper down the road to nothing-town. John Cage’s musical composition 4′ 33″ – enthusiastically encored in some halls – consists of 4 minutes and 33 seconds of unbroken silence, rendered by a skilled pianist wearing evening dress and seated motionless on the piano stool in front of an operational Steinway. Cage explains that his idea is to create the musical analogue of absolute zero of temperature24 where all thermal motion stops. A nice idea, but would you pay anything other than nothing to see it? Martin Gardner tells us that ‘I have not heard 4′ 33″ performed but friends who have tell me that it is Cage’s finest composition’.25
Writers have embraced the theme with equal enthusiasm. Elbert Hubbard’s elegantly bound Essay on Silence contains only blank pages, as does a chapter in the autobiography of the English footballer Len Shackleton which bears the title ‘What the average director knows about football’. An empty volume, entitled The Nothing Book, was published in 1974 and appeared in several editions and even withstood a breach of copyright action by the author of another book of blank pages.
Another style of writing uses Nothing as a fulcrum around which to spin opposites that cancel. Gogol’s Dead Souls begins with a description of a gentleman with no characteristics arriving at a town known only as N.:
“The gentleman in their carriage was not handsome but neither was he particularly bad-looking; he was neither too fat nor too thin; he could not be said to be too old, but he was not too young either.”
A classic example of this adversarial descriptive style, in which attributes and counter-attributes cancel out to zero, is to be found on a woman’s tomb in Northumberland. The family inscribed the words
“She was temperate, chaste, and charitable, but she was proud, peevish, and passionate. She was an affectionate wife and tender mother but her husband and child seldom saw her countenance without a disgusting frown . . .”26
Not to be forgotten, of course, are those commercial geniuses who are able to make more out of nothing than most of us can earn from anything. ‘Polo, the mint with the hole’ is one of the best-known British advertising pitches for a sweet that evolved independently as a ‘Lifesaver’ in the United States. More than forty years of successful marketing have promoted the hole in the mint rather than the mint itself. Nobody seems to notice that they are buying a toroidal confection that contains a good chunk of empty space, but then he wouldn’t.
“Nothing is real.”
The Beatles, “Strawberry Fields Forever”
So much for these snippets of nothing. They show us nothing more than that there is a considerable depth and breadth to the contemplation of Nothing. In the chapters to come, we shall explore some of these unexpected paths. We shall see that, far from being a quirky sideshow, Nothing is never far from the central plots in the history of ideas. In every field we shall explore, we shall find that there is a central issue which involves a right conception of Nothing, and an appropriate representation of it. Philosophical overviews of key ideas in the history of human thought have always made much of concepts like infinity,27 but little of Nothing. Theology was greatly entwined with the complexities of Nothing, to decide whether we were created out of it and whether we risked heading back into its Godless oblivion. Religious practices could readily make contact with the reality of Nothingness through death. Death as personal annihilation is an ancient and available variety of Nothing, with traditional functions in artistic representation. It is a terminus, a distancing, suggesting an ultimate perspective or perhaps a last judgement; and its cold reality can be used to spook the complacent acceptance of a here-and-now to which listeners are inevitably committed.
One of our aims is to right this neglect of nothing and show a little of the curious way in which Nothing in all its guises has proved to be a key concept in many human inquiries, whose right conception has opened up new ways of thinking about the world. We will begin our nullophilia by investigating the history of the concept and symbol for the mathematicians’ zero. Here, nothing turns out to be quite as one expected. The logic of the Greeks prevents them having the idea at all and it is to the Indian cultures that we must look to find thinkers who are comfortable with the idea that Nothing might be something. Next, we shall follow what happened after the Greeks caught up. Their battle with zero focused upon its manifestation as a physical zero, the zero of empty space, the vacuum and the void. The struggle to make sense of these concepts, to incorporate them into a cosmological framework that impinged upon everyday experiences with real materials, formed the starting point for an argument that would continue unabated, becoming ever more sophisticated, for nearly two thousand years. Medieval science and theology grappled constantly with the idea of the vacuum, trying to decide questions about its physical reality, its logical possibility and its theological desirability.
Part of the problem with zero, as with the complementary concept of infinity, was the way in which it seemed to invite paradox and confusing self-reference. This was why so many careful thinkers had given it such a wide berth. But what was heresy to the logician was a godsend to the writer. Countless authors avoided trouble with Nothing by turning over its paradoxes and puns, again and again, in new guises, to entertain and perplex. Whereas the philosopher might face the brunt of theological criticism for daring to take such a sacrilegious concept seriously, the humorist trying to tell his readers that ‘Nothing really matters’ could have his cake and eat it, just as easily as Freddie Mercury. If others disapproved of Nothing, then the writer’s puns and paradoxes just provided more ammunition to undermine the coherence of Nothing as a sensible concept. But when it came back into fashion amongst serious thinkers, then were not his word games profound explorations of the bottomless philosophical concept that Nothingness presented?
Hand-in-hand with the searches for the meaning of Nothing and the void in the Middle Ages, there grew up a serious experimental philosophy of the vacuum. Playing with words to decide whether or not a vacuum could truly exist was not enough. There was another route to knowledge. See if you could make a vacuum. Gradually, theological disputes about the reality of a vacuum became bound up with a host of simple experiments designed to decide whether or not it was possible to evacuate a region of space completely. This line of inquiry eventually stimulated scientists like Torricelli, Galileo, Pascal and Boyle to use pumps to remove air from glass containers and demonstrate the reality of the pressure and weight of the air above our heads. The vacuum had become part of experimental science. It was also very useful.