The End of Time: The Next Revolution in Physics

INDEX

A

aberration 128

absolute distance 74–5

absolute motion 62, 119

absolute rest 126

absolute space 20, 62–3, 83–5, 92, 119–20, 235–7

absolute time 20, 64, 83–5, 92, 119–20

action 111–13

ADM formalism 167, 253

aether 124, 126–8, 130–1, 153

Alpha 42, 46

alpha particle tracks 284–7, 290–6

angular momentum 86–90

anthropic principle 25, 342

antiparlicles 191

Arnowitt, Richard 167

arrow of time 19, 25, 27, 34, 308

Ashtekar, Abhay 351

Aspect, Alain 217

atomic time 107

atoms 24–5, 49

ionization 284–7, 290–6

number in a pea, 46–8

spectral lines 188–9

Augustine, St 11

B

Baierlein, Ralph 175–6

Baker, Dame Janet 332

Banks, Tom 258

Barbour, Julian

collaboration with Bertotti, 113–18, 167–72, 238

Discovery of Dynamics, The 239

website, 5, 7, 345

Barrow, John 341

Bell, John 220–1, 284, 287, 299–302

Bell’s inequalities 221

Berkeley, Bishop 63, 322

Bernoulli, John 110

Bertotti, Bruno 113–18, 167–72, 238

Besso, Michele 163

best matching 116–17, 170–2, 173, 175–6, 236–7

bicycle riding 88

bifurcation 55

Big Bang 12, 46, 251, 317, 320, 321

Big Crunch 263, 317, 321, 328

black holes 38, 166, 319, 320

block universe 143

body, human, as a time capsule 33

Bohm, David 218, 352

Bohr, Niels 13, 188–9, 219

Boltzmann, Ludwig 24–5, 27–8, 34, 342–3

Born, Max 198, 286, 310

Bose-Einstein statistics 191

bosons 191

bound states 234–5

boundary conditions 253

‘brachistochrone’ problem 110

brain

damage 33

motion processing 28–30, 267

organization 31–2

state 26

as a time capsule 32–3

Broderick, Damien 358

Broglie, Louis de 189–90, 352

Brout, Robert 352

Brown, Harvey 353

Bruno, Giordano 75

BSW paper 176, 253

bucket experiment 62–3

C

calculus 63

Candide 111

canonical quantization 166

Capelin, Simon 239

Carnap, Rudolf 143

Carter, Brandon 341

causality 312–13

cells 33

centre of mass 79–81

centrifugal force 62–3

Chardin, Teilhard de 328

Christian, Joy 359

chronology of the universe 313–15

Clarke, Samuel 63

Clemence, Gerald 347

Clifton, Andrew 358

clocks 93–108

defined 135

earth’s rotation 106

gravitational effects 154–5

inertial 99–104

solar 97, 98

solar system 106–7

stellar 97, 98

universe as 107–8

water-clock 95

collapse of wave function 199–200, 204, 217–18, 224, 289, 295, 297

College Farm 3, 4

complementarity 204

complex numbers 197

configuration space 43, 208–9

configurations 41, 43, 228

collinear 75

Confucius 17

consciousness 26–8, 31, 52–3

continuum spectrum 235

coordinate grid 129–32, 140–1, 206

Copenhagen interpretation 202–4

Copernicus, Nicolaus 12, 32

correlations 224, 257

cosmology see quantum cosmology

cosmos, well-ordered 322

covariance, general 160, 163–4

creation 22, 64, 110–11, 229, 232–5, 251, 254–6

Creator 326–7

curved surfaces 157–8

extrinsic/intrinsic curvature 158

shortest path on 111–12

cycling 88

D

Davies, Paul 322, 336, 337, 341, 358

Davisson, Clinton 190

Dawkins, Richard 48, 210, 324–5

De Broglie, Louis 189–90

De Chardin, Teilhard 328

degrees of freedom 79

two true 244

Descartes, René

on existence 49–50, 53

on motion 61–2

Deser, Stanley 167

Deutsch, David 333, 337, 352, 358

DeWitt, Bryce 38, 39, 221, 224, 246–7, 257, 351

on many-worlds 224–5

Diana, Princess of Wales, death of 324, 360

Dido, Queen 109–10

difference

intrinsic 116–17, 172

provisional 171–2

diffraction 285

Dirac, Paul 2–3, 13, 15, 40, 167

on mental pictures 206

on self-interference 197

on space-time 2

spinor fields 191

transformation theory 206

Discovery of Dynamics, The 239, 344

discrete spectrum 234

dispersion relation 278

distance 74–5, 147, 150

absolute 74–5

in space-time 147, 150, 151

distinguished simplifier 120, 170–1

Dowker, Fay 353, 354–7, 359

duration 19, 100–3, 107, 123, 133, 136, 173

dynamics 12

E

Earth

as a clock 106

rotation 32, 87

as a time capsule 33

eclipses 98–9

Eddington, Arthur 165

eigenfunctions 234

eigenstates 201, 202

eigenvalues 234–5

eikonal equation 270

Einstein, Albert 11, 134–6, 153

equivalence principle 154

on general covariance 163–4

home in Pavia 114

on Mach 65, 66

Nobel Prize for Physics 187

on Nows 143

on quantum theory 13, 186–7, 188

on real objects 220

relativity theory 12, 15, 129–32, 151–2, 155

on rotating systems 156–7

and space-time 155–6, 159, 160, 161

Einstein-Podolsky-Rosen paradox 218–20

electromagnetism 124–6

electrons 188, 189–90, 191

Eliot, George 330–1

Eliot, T.S. 240

energy 23, 90–2 see also kinetic energy; potential energy

energy levels 188

entangled states 216–17, 222–4

entropy 23–5, 27–8, 289, 318–9

ephemeris time 107

EPR paradox 218–20

equation of time 98

equivalence principle 154, 176–7

eternity 36, 40, 328

Euler, Leonhard 111

events 139, 143

Everett, Hugh 221–7

everything, theory of 192

evolution 252, 256

excited states 234

experience 51–2, 53–4

F

faces 33

falling bodies 93–6

Faraday, Michael 15, 124

Fermat, Pierre de 110

Fermat’s principle 271, 272

Fermi-Dirac statistics 191

fermions 191

Feynman, Richard 244

on time 2

fields 124, 190–1, 222

Fischer, Arthur 344

Fitzgerald, George 128

fossils 33

Foster, Brendan 358

Fourier, Joseph 201

frames of reference 81–2

free will 324–6

Fresnel, Augustin Jean 124, 269

Friedmann, Alexander 317

G

Galileo Galilei 12, 61

falling ball experiment 93–6

odd numbers rule 93–4

parabolic motion 94, 95, 96

on relativity 81–2, 151–2

water-clock of 95

Gamow, George 284

gas 318

Gauss, Carl Friedrich 157–8

Gaussian wave packets 278

general covariance 160, 163–4

geodesics 112, 116–17, 118

geometrical optics 270–1, 288

geometrodynamics 167

geometry, non-Euclidean 157–8

Germer, Lester 190

Gill, Ann 344

Giulini, Domenico 348

God 22, 64, 110–11, 326–7

graffiti describing time 44–5

grand unified theory 192

gravitons 244

gravity 12, 15, 91

curving space-time 12, 159, 160, 161

and time 154–5

Grossman, Marcel 159, 161

ground state 234

group velocity 278

Guichardet, A. 347

Guth, Alan 359

H

haemoglobin 48

Halliwell, Jonathan 258

Hamilton, William Rowan 111, 268, 269–74

Hartle-Hawking wave function 359

Hartle, Jim 353, 354, 359

Hawking, Stephen 39, 258

on Big Bang 320

on black holes 166, 319

on end of physics 13–14

on time travel 329

no-boundary proposal 312

heaven 327–8

Heggie, Douglas 346

Heisenberg, Werner 13, 189, 284

Heisenberg cut 296

Heisenberg’s uncertainty principle 205

Heraclitus 1, 330

Hero of Alexandria 110

Hilbert space 193, 206

Hipparchus 98

history 69, 282–3, 287–92 see also records

Hofmann, Wenzel 115

Holland, Peter 352

Hopkins, Gerard Manley 75, 323

Hoyle, Fred 359

human body as a time capsule 33

Hut, Piet 346

hyperplanes 143–4

I

identity of indiscernibles 85–6

inertia 62, 65, 93

inertial clock 99–104

inertial frame of reference 82

inflation 359

initial conditions 22, 253

instants of time 16, 18, 247, 265–6

interactions 104–5

interference 124, 125, 195–6

self- 197

fringes 196

intrinsic difference 116–17, 172

intrinsic time 245

invariable plane 88

ionization 284–7, 290–6

Isham, Christopher 351

J

James, William 28

K

Kant, Immanuel 207

Kaon decay 342

Keats, John 326, 331

Kepler, Johannes 2, 12, 98, 164, 269

Kiefer, Claus 352, 353

kinematic relativity 152

kinetic energy 90, 108, 112

Klein-Gordon equation 351

Kretschmann, Erich 164

Kubasiak, Gretchen Mills 334, 338–40

Kuchař, Karel 172–3, 238–9, 246, 349, 351

Kuhn, Thomas 115

L

LaFlamme, Raymond 358

Lagrange, Joseph-Louis de 111

Lanczos, Cornelius 268–9

Lange, Ludwig 346

Lapchinskii, V. 258

Laplace, Pierre 71, 76, 88

Laplacian determinism, perfect 83, 156, 177

Laue, Max von 190

least action, principle of 111–3

least-time theory 110

Leibniz, Willhelm Gottfried 16, 63–4, 74, 110, 119, 240, 322

on creation 63–4, 110–11

identity of indiscernibles 85–6

principle of sufficient reason 64, 86

satirized as Dr Pangloss 111

Leibniz-Clarke Correspondence 63–4

length of time 19, 100–2, 107, 123, 133, 173

Liebscher, Dierck 6, 73, 346

light

cone 148

diffraction 285

interference 124, 125

polarization 244

quanta (photons) 187, 188, 191, 243–4

rays 269–73

refraction 110

wave theory 124, 125, 269–71

‘line of time’ 27–8

linearity

in quantum mechanics 225, 231, 275

of time 19, 27–8

Littlejohn, Robert 347

Lorentz, Hendrik Anton 128

Lorentz frames 141

Lorentz transformation 141

lottery, cosmic 52–3

Lovelock, James 4

M

Mach, Ernst 65, 153, 334

on inertia 65–6

on time 67

Machian distinguished simplifier 120, 170–1

Mach’s principle 65–6, 113–5

magnetism 124, 126

Makino, Jun 346

many-instants 302–5

many-worlds 53, 221–7, 229–302, 323–4

mass

centre of 79–81

of particles 243–4

matrix mechanics 13, 189, 280

Maupertuis, Pierre 111

Maxwell, James Clerk 15, 124–5

McMillan, Steve 346

McTaggart, John 343

measurement problem 200, 224

measurements 200, 222–4

mechanics 12

Megamolecule Land 43

memory 19, 28, 32–3, 53, 55–6, 300

mental pictures 206–7

Mercury 161

Michelson-Morley experiment 128

Middlemarch 330–1

Midsummer Night’s Dream, A 276

Minkowski, Hermann 12, 138–42, 144, 147, 150–1

Minkowski space-time 141–2, 143, 145, 146, 174

Misner, Charles 167

mist(s) 51, 197

molecules 210, 235

momentum 200

angular 86–90

eigenstates 201

Monadology 111, 240

Moon 98–9, 205, 298

motion 61–70

absolute 62, 119

brain processing 28–30, 267

Descartes on 61–2

as an illusion 39, 46–9, 266–7, 329–35

Newtonian concepts 12, 20–1, 22, 62–3

‘philosophical’ 61

relative 61–2, 63, 119

Mott, Nevill 284, 307, 310, 354

movement see motion

music of the spheres 75, 325–6

N

Neumann, Carl 99–100

Newton, Isaac 11, 12, 20–2, 119

on absolute motion 62

on absolute space 20, 62–3

on absolute time 20

on creation 22

on Descartes 62

laws of 12, 20–1, 22, 64

on making his discoveries 74

on motion 12, 20–1, 22, 62–3

Newtonian space-time 139–40, 146, 174

Newtonian time 107

no-boundary proposal of Hawking 312

Nobel Prize for Physics 187, 235

Nows 16, 18, 34, 40–1, 43, 44–5, 55–6, 174, 177, 333

Einstein on 143

and experiences 51–2, 53–4

and memories 55–6

in relativity 142–6

self-awareness 52–3

O

observables 204

odd numbers rule 93–4

Olivieri, Claudio 333

Omego 328

Ó Murchadha, Niall 35, 349, 352, 358

ontology 138, 301

optics 269–71

optimization 109–13

ovens, heating 185

P

Page, Don 257, 358

Pais, Abraham 123

Pangloss, Dr 111

parabolic motion 94, 95, 96

paradigms 115

Parmenides 1

particles 185–92

mass of 243–4

‘past’ 299, 300 see also history

paths 43–4, 69, 111–3, 118

Pavia 114

pea, number of atoms in 46–8

Penrose, Roger 7, 31, 166, 319, 320, 360

perihelion, advance of 161

persistence of objects 252

phase locking 259

‘philosophical’ motion 61

photons 187, 188, 191, 243–4

physics 38

end of 13–14

quantum versus classical 13, 15–16

Pied Beauty 75, 323

Pinker, Steven 342–3

Planck, Max 13, 185–6

Planck length 311

Planck mass 311

Planck time 311

Planck’s constant 186

planets see solar system

Plato 44, 45

Platonia 44, 45–6, 47, 344

asymmetry of 55, 307–9

for Minkowski space-time 145

for general relativity 167–9

geodesics in 116–17, 118

‘mist’ over 51–6, 197–8

Platonic forms 44, 251

Podolsky, Boris 218

Poincaré, Henri 71, 76, 128, 135–6, 152–3, 156, 180, 346

on duration 123

Point Omega 328

polarized light 244

pond argument 127

position eigenstates 202

potential energy 90–1, 108, 112, 117

preferred-basis problem 226–7, 301

Price, Huw 341

principal function 272

principle theories 134

probability 24, 198–9, 203–4, 356

proper time 150–1, 175

psychophysical parallelism 226, 301–2

Ptolemy, Claudius 99

pulsars 166

Purser, John 325–6

Purser, Michael 5, 325, 336

Pythagoras’ theorem 150

Q

Q space 209

quanta 13 see also photons

quantization 15, 166

quantum cosmology 16, 197, 247, 251, 284, 311–21

quantum gravity 15–16, 240, 242–8

quantum inseparability 216–17

quantum mechanics 183–245

discovery of 12–13, 185–92

good measurement in 223

measurement problem 200, 224

measurements in 200–4, 212–24

quantum of action 185–6

R

radioactive decay 284

realism 252

real objects 220, 227, 228

records 30–1, 32–3, 284–7, 292–6, 300

refraction 110

Reinsch, M 347

Reissner, Hans 115

relative motion 61–2, 63, 119

relativity 12, 121–81

Einstein on 12, 15, 129–32, 151–2, 155

Galilean 81–2, 151–2

general 12, 155

kinematic 152

special 12, 152

rest 126–7

Ricci tensor 161

Riemann, Bernhard 158–9

Riemannian spaces 159, 169

Rosen, Nathan 218

rotation 86–90, 157

Rovelli, Carlo 351

Rubakov, V. 258

Rutherford, Ernest 188

S

Saturn 89, 90

scalar fields 191

Schrödinger, Erwin 13, 115, 189–90, 207, 208–9

on ‘I’ 331–2

Nobel Prize for Physics 235

stationary equation 230, 231, 232–5, 253

time-dependent Schrödinger equation 230, 231, 258

wave-packets 275–80

self-awareness 52–3

self-interference 197

semiclassical approach 258, 259–64, 273

semiclassical solution 258, 288, 296

Shape Space 73, 74–7

Shapere, A. 348

Sharp, David 175–6

Shimony, Abner 329, 343, 360

shortest paths 111–13, 117–18

shortest-time theory 110

sidereal time 97, 98

simultaneity 12, 123, 129–32

simultaneity hyperplanes 143–4

Smolin, Lee 239–41, 322, 327, 337, 351

snapshots 18–19, 20

solar system 12, 88–9

as a clock 106–7

solar time 97, 98

solipsism 50, 252, 300

space 138

absolute 20, 62–3, 83–5, 92, 119–20, 235–7

space-like 149

space-time 12, 138–42, 145–6, 155–6

curvature 12, 159, 160, 161

distance in 147, 150, 151

Minkowski 141–2, 143, 145, 146, 174

Newtonian 139–40, 146, 174

past, present and future 147–50

spatiotemporal framework 136

specious present 28

spectral lines 188–9

speed 96, 97

group 278

spin 86–90, 157, 218

spinor fields 191

spiral galaxies 88

St Augustine 11

stars as clocks 97, 98

‘state’ 26

stationary points 172

stationary Schrödinger equation 230, 231, 232–5, 253

stationary states 230, 231

statistical behaviour 191

stellar clocks 97, 98

strata 345

stratified manifold 344

sufficient reason, principle of 64, 86, 156

Sun 12, 316–17

as a clock 97, 98

superposition 201–2, 210–12, 225

superspace 169, 348

superstring theory 39, 166, 192, 359

supersymmetry 192

syzgies 78

T

Tait, Peter 100–1

Tail’s problem 100–4, 135, 139, 144, 347

tensors 161, 191

Tetrahedron Land 43, 168

theory of everything 192

thermodynamics 23

Thomson, George 190

Thomson, James 123, 135

Thorne, Kip 166, 319, 336–7

3-spaces 171

time 17–19

absolute 20, 64, 83–5, 92, 119–20

arrow of 19, 25, 27, 34, 308

atomic 107

directionality of 19

ephemeris 107

equation of 98

experiencing 19–20

graffiti describing 44–5

and gravity 154–5

instants of 16, 18, 247, 265–6

intrinsic 245

length of 19, 100–2, 107, 123, 133, 173

‘line of 27–8

linearity of 19, 27–8

Newtonian 107

non-existence of 14–15, 35–8, 39, 247, 251, 309–11

proper 150, 175

sidereal 97, 98

solar 97, 98

time capsules 30–4, 251, 261, 264–7, 299, 300, 308

defined 31

time-dependent Schrödinger equation 230, 231, 258

time-independent (stationary)

Schrödinger equation 230, 231, 232–5, 253

time-like 148

time travel 328–9

timelessness 14–15, 35–8, 39, 247, 251, 309–11

Tipler, Frank 328, 341

transformation theory 206

trial pairing 171

Triangle Land 40, 41, 42, 45–6, 116–17, 344

Twain, Mark 338

two-and-a-bit puzzle 109

two-slit experiment 194–6

two-snapshots problem 92, 103

U

unbound states 235

unity of unities 75

universal equation 254

universe 22

chronology of 313–15

as a clock 107–8

expansion 262–4

modelling 40–6

order of 23

wave function of 242

V

Vaughan, Henry 328

vector fields 191

velocity 96, 97

group 278

Vilenkin, Alexander 352, 359

Voltaire 111

von Laue, Max 190

Vonnegut, Kurt 359

W

Walsch, Neale Donald 344

water-clock 95

wave function 194–205, 241–2

collapse 199–200, 204, 217–18, 224, 297

of the universe 242

wave mechanics 13, 189–90, 194–205

wave optics 270

wave packets 201, 205, 262, 275–81

wave theory of light 124, 125, 269–71

website 5, 7, 344

Weinberg, Steven 244

well behaved, conditions of being 254

Wheeler, John Archibald 38, 44, 136, 167, 169, 175–6, 246–7

Wheeler-DeWitt equation 38–9, 242, 247, 256, 351, 359

Whitehead, Alfred North 329

Wilczek, Frank 347

Williams, Tennessee 331, 332

Wootters, William 257

World, The 328

world line 140

X

X-rays 190

Y

Yeats, W.B. 322

Young, Thomas 124, 125

Z

Zeh, Dieter 264, 307, 338, 354

Zeilinger, Anton 360

Zeno’s paradox 49