Space, Time and Einstein

SPACE , TIME AND EINSTEIN

Bohm, D. 181 intervals
boundary conditions 167–8 Dobbs, B. J. 104
Bruno, G. 108 Drake, F. 194
B-series 133–8 durations see time or spacetime
bucket 112–14
intervals
and equivalence 147
and Mach 160–62 Earman, J. 162, 169, 191
in orbit 169–71 eclipse expedition 8, 142–3
Eddington 8, 142–3
calculus 115–16, 124–5 Edinburgh School 203
Cambridge change 101 Einstein
Caroline, Princess 116–17
causality biography 7–9
black holes 189–90
common cause 179 block universe 55–6, 59–60
in Leibniz’s monadology 123 cosmology 200
order 66–7, 215 Lorentz 26–7
slower than light 67 quantum theory 182–4
celestial speed limit 42–3 telegraphing into the past 67
chain reactions 44–7 embedding space 155
change see problem of change empiricism 111, 162
Clarke, S. 116–17, 119 energy 41
co-existence 62–5, 220–21 energy-mass see mass-energy
common cause 179 endurance 51
conservation Epicurus see atomists
and change 79–81 epistemology 5
of energy in Newton 107 equivalence
constructive theories 9 gravity 145
continuum 92, 98 bucket 147
contradiction 12 ether 27–30, 73
contradictory opposites 82 ethics 5
contrary opposites 82 Euclid 8, 149–58
correlation 178 events 50–3
cosmic microwave background and block universe 54
ontology 51–3
radiation 186 evolution, Darwinian 193
cosmological constant 200–201 existence, tenseless 55
counterparts 126–32
creation from nothing 81 faster-than-light 177–84
creation myths 185 fatalism 55
curvature 168, 190 Fermi, E. 194
Cushing, J. 181 Fine, A. 181, 204
force 107
Democritus see atomists four-dimensions 50–65, 165
Descartes, R. 101, 105–6, 108, 202 frame-dragging 170
determinism 55 van Fraassen, B. 181, 204
dimensions 56 Friedman, M. 169
dispositions see potentials
distances see lengths or spacetime

240

INDEX

Galileo, G. 108 see also minority, mainstream
gamma-ray bursts 195–6 intrinsic description 155
Gauss, K. F. 152–4 invariance
garage 33–5, 213–15
garbage-in garbage-out 181 property of appearances 109
general relativity see relativity theory spacetime intervals 56–7
geometrization of space 105 versus relative 22
geometry isomers 131

Euclidean 149–51 Kant, I. 112, 126–32
fall of 149–58 Kuhn, T. 26, 182, 203, 205
intrinsic 155
Non-Euclidean 151–8 Latour, B. 203
global vs. local 168 Lauden, L. 203
Gödel, K. 61 law
gravity
acceleration 145 of inertia 107–8
geometrized away 141 of non-contradiction 12
waves 141 of conservation of mass-energy 44
Grunbaum, A. 169 laws
Guth, A. 198–201 brute facts 52–3
determinism and 55
harmony, pre-established 123 of motion, Newton’s 107
Hawkings, S. 190 physical 16–7
heat death 198 Lee, T. 131
Hegel, G. W. F. 98 left and right 126–32
Heisenberg uncertainty principle 203 Leibniz, W. G. 115–25
Hiroshima 4, 41, 47 why question 185
horizon problem 197 Leibniz–Clarke correspondence 117–
Hubble, E. 186, 200
21
incongruency 126–32 length contraction 18–19, 27, 213–
Indo-European 77
inertia 107, 140; see also law of 15, 225
ether causes 27–9
inertia illusion 37
inertial motion 15 symmetry of 31–5
inference to best explanation 108 lengths
infinity 41–2, 92–103, 125 real relations 38, 58
symmetry 31–8
Aristotle’s denial 94–5 variable properties 27
black holes 190–91 lensing, gravitational 143
potential 95 Leucippus see atomists
vicious 138 Lewis, D. 69–70
inflation 198–201 light cone 216–18
interpretation 9, 20, 24 light speed
block universe 60 celestial speed limit 42, 177
mass-energy 47–9 depends on medium 28
space-time interval 55–9 faster-than-light 177–84
symmetry 35–9 relative speed constant 10
relative speed not constant 28

241

SPACE , TIME AND EINSTEIN

role in atomic bomb 44 symmetry in 35–9, 222–4
local vs. global 168 Möbius strip 130
Lorentz monism 84, 97
motion
biography 26
conflict with Einstein 73 absolute vs. relative 110–12, 163
quantum theory and 182–4 inertial 140, 163
Lorentz–Fitzgerald contraction see
National Space and Aeronautics
length-contraction Administration (NASA) 112, 169–
Lyceum 87 71
Lucretius 148
necessary vs. sufficient 118
Mach, E. 115, 160–64 negative energy 201
mainstream interpretation 23–5, 27– Neo-Newtonian Spacetime 164–7
Newton, I. 8, 92, 104–5
30, 221
quantum theory and 182–4 emblem of empiricism 111
spacetime interval 57–9 reputation shifts 104–5
summary 72 sea shore 109
symmetry in 35–9 nominalists 159
mass non-standard models 167–9
effective 48 nothing see void
electromagnetic 48 nothing comes from nothing 80, 88
increase, relativistic 41–2
rest 43 ontology
mass–energy conversion 40, 44, 225–6 constructive theories and 9
mathematics 92, 102, 115 event 51
change and 124
combined with physics 106 opposites 81
Greek 149–51 contradictories 82
McMullin, E. 204 contraries 82
McTaggart, J. 133–8 mutually exclusive 81
measurements
inertial 15 orientation 128
of lengths in time 32–3, 214–15
metaphysics 5, 85, 87 paradoxes and problems
Aristotle’s 87–9 arrow 93, 98
atomist 85 change 78–84
geometry and 150 change from conservation 78–84,
Leibniz’s 121–4 88–91, 125
positivism and 160 change from contradiction 81–83
Miller, S. 193 dichotomy, Zeno’s 94
Minkovski, H. 50, 207 Fermi 194, 196
diagrams 207–21 fine-tuning 198
minority interpretation 26–30 flat universe 198–9
block universe 65 garage 33–5, 213–15
mass-energy in 48 horizon 197
quantum theory favours 182–4 infinity 92–103
summary 73 killing grandmothers 67–70, 182
motion, Zeno’s 92–103
plurality, Zeno’s 96–9

242

INDEX

set theoretic 102–3 contiguity 90–91
stopping and starting 81–83 inherency 91
twin 31–9, 215–16 laws as 17
void 85–6 Leibniz and 121–4
Zeno’s 92–103 length as 25, 58
Parmenides 83–4, 86, 90, 92, 96 occupancy 89–90
past, existence 134–8 real 100, 121, 123, 173
Penrose, R. 190 realism about 100–102
persistence through time 51–3 reductionism about 100
block universe and 60 relative 22
change and 79 motion 163
Pickering, A. 204 speeds 11
Plato 86–7, 96–7, 121, 150–51 versus invariant 22
Platonic solids 150 relativism 22
plenum 87, 107, 122 relativity theory, general 139–48
pluralism 97 absolutes in 167–9
positivism 160 black holes 188–92
potentials 87–9, 95 central idea 140
pragmatist 125 cosmological constant 200
principle of sufficient reason 118–19, eclipse expedition 8
eliminates absolute acceleration
121
principle theories 9 164
presentism 53–5 introduced 8
relation to special relativity 8, 10
block universe and 62–5 relativity theory, special 7–76
problems see paradoxes inertial measurements 15
properties 25, 87, 100 introduced 7
summary 71
monadic 100 religion 116
in substances 122 right and left 126–32
Putnam, H. 60 rotation see also bucket
analogy 58
quantum theory 177–84, 203 rubber sheet analogy 140–43
and block universe 55 Russell, B. 60, 96, 99, 100–102, 157

rationalism 117 Scholium, Newton’s 108–14
realism about relations 100–102 scientific realism 204
reality versus appearances 22–3 scientism 204
reason Simplicius 98
simultaneity
fall of geometry 149–58
Parmenides’ defence 84 block universe and 60–65
sufficient 118 length measurements and 32–3
reductio ad absurdum 67 plane of 211
reductionism about relations 100 relativity of 19–20, 210–13
reference frame 170 singularity 190–91
Reichenbach, H. 157 social constructivists 203–204
relationalism 160–62, 165, 169 Socrates 86–7
relations 25, 99–102
co-existence 62–5

243

SPACE , TIME AND EINSTEIN

solipsism 62, 64, 221 absolute 109–12
space dilation 12–4, 16, 66, 225
flow of 3–4, 109, 135–8
absolute 109–15 travel 66–70, 218–20
absolute, Leibniz’s attack 116–21 unreality of 133–8
change and 87–9, 139–48 time-like separation 218
curved 152–8 topology 131–2
invention 77–91 truthmaker principle 89, 122,
relationalism 160–2
relative 109–11 133–4
space-like separation 218 twin paradox 31–9, 215–16
spacetime 50–65, 216
diagrams 207–21 universals 159
intervals 56–7 universe
Neo-Newtonian 162–4
special relativity see relativity accelerating 197–201
beginning 185–7
theory expanding 186
speed flat 198
inflationary 197–201
faster-than-light 177–84 shape and size 147–8, 168
light see light speed uranium 46
relative 11 Urey, H. 193
Stein, H. 64
substance 87 void 85–6, 105
and Leibniz 115, 121
ontology 121, 124 websites 227–8
substantivalism 162, 165, 169, 171, Weyl, H. 60
Westfall, R. 105
173 wheel, spinning 144–6
sufficient reason 118–21 worldlines 70
sufficient vs. necessary 118 wormholes 70
supernova 187, 196 worms, spacetime 51
symmetry 31–9
Wu, C. (Madam) 131
Leibniz’s argument 119–20
Lorentz’s explanation 222–4 Yang, C. N. 131

tachyons 42 Zeno of Elea 77, 92–103, 124, 190
teleology 185 on plurality 96–9
Thorne, K. 70 calculus and 124–5
thought experiments 143, 147
time

244