The Order of Time

INDEX

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acceleration, 17n, 216n7, 216n12

Albert, David Z., 226–27n96

Anaxandridas, 46, 47

Anaximander, 11, 14–15, 100–101

Aristotle, 63–66, 69–71, 77, 78, 84, 97, 220–21nn48–49, 221n54

astronomy, 14, 65, 102

atomism, 86

atoms, 29, 85, 99, 101–2, 210

Augustine of Hippo, 180–83, 212

Bach, Johann Sebastian: BWV 56 cantata, 206

Bede, the Venerable, 85

Beethoven, Ludwig van: Missa Solemnis, 212

Besso, Michele, 114–15

black holes, 54–55, 127

block universe, 109, 195, 222n62

Boltzmann, Ludwig, 27–36, 136, 145, 157, 225n81

Boltzmann’s constant, 217n20

brain, 153, 166, 167, 176, 179, 180, 182, 186, 189, 207, 210

and fear of death, 207–8

frontal lobes, 207, 209

neurons. See neurons/neural structures

and Proust, 188

synapses, 107, 108

Buddha, 190

Carnot, Lazare, 22–23, 216n10

Carnot, (Nicolas Léonard) Sadi, 23, 28

cause and effect, 20, 21, 33, 168–69, 176

change

and complexity, 109–10

relations, events and world dynamics without a time variable, 117–28, 195–96

time as measurement of change, and Aristotle’s space, 63–79, 97

time when nothing changes, 63–4, 72

and world as network of events, 95–104, 195

Clausius, Rudolf, 23–25, 157

equation of entropy, 27, 157, 188–89

Cleomenes I, 45–46, 47

clocks, 15, 59–63, 67, 74, 96–97, 197, 216n8

and effect of speed on time, 40n, 197

slowed by a mass/gravitational field, 9–13, 75–77

synchronization of, 61–62

Connes, Alain, 138–42, 225n85

consciousness, 63, 173, 182–87, 199–203

internal consciousness of time, 183, 186

continuity, 84, 96

Copernicus, Nicolaus, 11, 201, 218n26

death, 206

fear of, 206, 207–8

delirium, collective, 211

Democritus, 85, 101, 221n54

Descartes, René, 176–77, 220–21n48

DeWitt, Bryce, 119, 121–22, 124

diurnal rhythms, 62–63

Dorato, Mauro, 215n3

Duino, 36

Durkheim, Émile, 229n122

Earman, J., 226n90

Ecclesiastes, 131, 198

Einstein, Albert, 10–12, 37–40, 44, 52–53, 197, 218n26, 223n66

and Besso, 114–15

general theory of relativity, 16

and the gravitational field, 74–79, 195

on illusion of time, 108–9, 114

simultaneity, 218n27, 222n62

special relativity theory, 48, 218n26

at Swiss Patent Office, 61

electrons, 85, 87, 89–90, 124, 138

Ellis, George, 219n34

energy, 159–60

conservation of, 27, 135–36, 159

thermal. See heat

and thermal time, 134–37. See also thermal time

entropy, 25–36, 136, 143, 145–51, 155–57, 159–66, 196–97, 198, 217n15, 217n20, 226n94

and blurring, 21–36, 135–37, 144–51, 154, 155–57, 199

Clausius’s equation, 25–27, 157, 188–89

and coarse graining, 217n18

in distant past, 143, 146–51, 161, 163–64, 167, 169

increase, 161–66, 189, 196, 217n15

low, 31–32, 143, 146–51, 156–57, 160–63, 167, 169, 196

and perspective, 147–50

second law of thermodynamics, 23–28, 149, 160, 165

eternalism, 108–9. See also block universe

events

relations, events and loop theory without a time variable, 117–28

world as network of, 95–104, 195

evolution, 207–10

fear of death, 206, 207–8

flow of time, 1, 2–3, 193–97

and cause and effect, 20, 21, 33, 168–69

Durkheim, religion and, 229n122

heat, entropy, and our blurred vision of, 25–36, 135–37, 145–51, 154, 156–57, 199

in Hindu mythology, 2

internal consciousness of, 183, 186

and particularity, 16, 30–34, 91, 146–51, 162, 170, 188–89, 194, 196, 198

past, future, and the arrow of time, 19–36, 146–51, 194, 195, 196

and relativity, 138. See also relativity

slowed by a mass, 9–13, 76–77, 194, 197, 198

slowed by speed, 37–40, 194, 197, 198

source of Rilke’s eternal current, 20–36

and the structure of spacetime, 48–56, 73–79, 106–7, 109, 184

and subjectivity/identity/consciousness, 3, 5, 20–21, 57–58, 63, 171–92, 199–202. See also perspective

French Revolution, 22, 216n10

Gödel, Kurt, 53, 218–19n29, 222–23n63

Gorgo, queen of Sparta, 45–46, 47–48

grammar

of change, 97–104

inadequacy of, 105–15, 132–34

granularity, quantum mechanics, 83–85, 124–25

spin networks, 126, 127, 224–25n75

gravitational field, 74–79, 90, 124, 195, 197, 198–99

and granularity, 83, 124–25

Hamiltonian H, 223–24n67, 224n72, 225nn81–82

heat, 22–26, 160, 165

and entropy. See entropy

thermal time, 134–38, 139–40, 142, 196, 225n87

thermodynamics. See thermodynamics

Hegel, Georg Wilhelm Friedrich, 200

Heidegger, Martin, 84, 186, 200n

helium, 163

Hilbert space, 224n72, 224n74

Hildegard of Bingen, 154–55

Hindu mythology, 1, 17, 166, 205, 208

Hofmannstahl, Hugo von: Der Rosenkavalier, 191–92

Hume, David, 176

Husserl, Edmund, 183, 184–86, 228n114

hydrogen, 163

identity, 171–92, 199

impermanence, 97. See also change

indeterminacy, quantum mechanics, 87–89, 124–28, 140, 196

and blurring, 140–42, 170

indexicality, 151–55

Isham, Chris, 121–22

Isidore of Seville, 85

Ismael, Jenann T., 226n95

Job, 206

Kant, Immanuel, 184

Kepler, Johannes, 101–3

Kuchar, Karel, 121–22

Lagrange, Joseph-Louis, 216n10

Lavoisier, Antoine, 216n10

Leibniz, Gottfried Wilhelm, 68, 220–21n48

Leonidas I, 45–46, 47

light, 41, 50, 74

cones, 50–55, 77, 88

granularity of, 85, 124

and indeterminacy in quantum mechanics, 88

photons, 85, 124, 160–61

loop theory/loop quantum gravity, 82, 85, 124–28

Lorentz, Hendrik, 218n25

Louis XVI, 22

Mahābhārata, 205, 208

Maimonides, 85

Marat, Jean-Paul, 216n10

Maroun, Samy, 219n34

mass, time slowed by, 9–13, 76–77, 194, 197, 198

Matthew, Gospel of, 58

Maxwell’s equations, 14, 39–40, 103, 216n11

McTaggart, John, 221–22n60

memory/memories, 21, 121, 149, 166, 169–70, 196

identity, time and, 178–92

Milinda Pañha, 172–73

music, 182, 184, 191–92, 212

nervous system, 175, 179–80, 187

neurons/neural structures, 62, 175–76, 180, 188, 202, 228n14

Newton, Isaac, 64–69, 69–76, 77–78, 117

equations, 14, 67, 216–17n12

mechanics, 14, 103

Philosophiae Naturalis Principia Mathematica, 183

Newtonian gravity, 215n5

noncommutativity

quantum, 138–40, 199

Von Neumann algebra, 139, 225n85, 225n87

nostalgia, 120, 123, 202

nuclear fission, 163

Ockham, William of, 183

Parmenides, 200

partial order, 46–48, 139, 219n31

particularity, 16, 30–34, 91, 146–51, 162, 170, 188–89, 194, 196, 198

past traces, 166–67, 181, 183, 187, 196–97. See also memory/memories

Penrose, Roger, 137–38

perspective, 4, 5, 122, 143–57, 196–97

blurring, 21–36, 135–37, 140–41, 144–51, 154, 170, 196, 199

and entropy, 146–57. See also entropy: and blurring

and indexicality, 151–55

and particularity. See particularity

subjectivity/identity/consciousness and time, 3, 5, 20–21, 57–58, 63, 171–92, 199–202

photons, 85, 124, 160– 61

photosynthesis, 164

Planck constant, 221nn51–52

Planck length, 85–86

Planck scale, 83, 125–26

Planck time, 83

Plato, 101, 102, 200

Pleistarchus, 45–46, 47

prediction, 175, 179–80, 189, 207

and loop theory, 85, 128

present, 33, 43–44, 193–94

meaninglessness of “now,” and loss of the present, 37–56, 107–8, 194

temporal structure of universe without the present, 45–56, 106–7, 109–10

presentism, 106, 108, 222–23n63

probability, quantum mechanics. See indeterminacy, quantum mechanics

proper time, 16, 40, 216n8

Proust, Marcel, 188

Putnam, Hilary, 222n62

quantum field theory, 15

quantum gravity, 4, 81, 91, 119–20

loop quantum gravity, 82, 85, 124–28

quantum mechanics, 14, 79, 81–92, 103, 195

and granularity, 83–85, 124–25

and indeterminacy. See indeterminacy, quantum mechanics

and loop quantum gravity, 82, 85, 124–28

noncommutativity, 138–40

and quanta of time, 81–92. See also quantum time

quantum superpositions of times, 87–88

relationality, 89–90

and relativity, 81–83, 138

quantum time, 138–42

spinfoam and “quantum spacetime,” 126

reality, 1–2, 74, 78, 99

and the block universe, 109, 222n62

collective delirium and our vision of, 211

and inadequacy of grammar, 105–15

and memory, 178–92. See also memory/memories

relations, events and world dynamics without a time variable, 117–28, 195–96

reason, 208–9

Reichenbach, Hans, 200, 227nn99–100

relationality

quantum mechanics, 89–90

relations, events and world dynamics without a time variable, 117–28, 195–96

relativity, 14–17, 46, 145

and experience of flow of time, 138

general theory of, 15–16

and quantum mechanics, 81–83, 138. See also quantum mechanics

special, 48, 218n16

Rilke, Rainer Maria: Duino Elegies, 20, 36

Russell, Bertrand, 169

Saadi Shirazi, 22–23

Schrödinger equations, 14–15, 102, 224n72

Shiva, 1, 17, 166

simultaneity, 218n27, 222n62

slowing of time, 9–13, 37–40, 76, 194, 197, 198

Smolin, Lee, 219n34

Sophocles: Oedipus Rex, 5

spacetime

and Aristotle, 63–79, 97

curved, 77, 210

“empty space,” 70–71

and eternalism, 108–9. See also block universe

fluctuations, 88–90

granularity, 83–85, 124–25

gravitational field. See gravitational field

loss of, 95–128, 195

and quantum mechanics. See quantum mechanics

spinfoam and “quantum spacetime,” 126. See also loop theory/loop quantum gravity

structure of, 48–56, 73–79, 106–7, 109, 184, 197–98

“true” time and Newton’s space, 65–79

special relativity theory, 48, 218n26

speed, 145

acceleration, 17n, 216n7, 216–17n12

time slowed by, 37–40, 194, 197

spin networks, 126, 127, 224–25n75

spinfoam, 126

Strasburg Cathedral, 59

Strauss, Richard: Der Rosenkavalier, 191–92

string theory, 82

suffering, 115, 190–91, 206

sundials, 59–61

synapses, 107–8

Tempier, Étienne, 182

temporal precedence, 48

thermal time, 134–38, 139–40, 142, 196, 222n87

thermodynamics

second law of, 21–28, 149, 160, 165

and thermal time, 137, 142. See also thermal time

variables, 226n93

time

absence, and equations without a time variable, 96, 117–28, 195, 199, 220n47

Anaximander and the order of, 14–15, 100–101

arrow of, 19–36, 147–50, 194, 195, 196

Augustine on, 180–83

clock-regulated, 59–63. See also clocks

closed lines, 53n

and diurnal rhythms, 62–63

dividing and measuring, 58–64

Einstein on illusion of, 108–9, 114

and emotion, 141, 200–201, 211–12

and eternalism, 108–9. See also block universe

flow of. See flow of time

and grammar. See grammar

granularity of, 85–86

and the gravitational field, 74–79, 90, 124, 195,

197, 198–99. See also gravitational field

and heat. See heat

internal consciousness of, 183–86

loss of direction, 19–36, 194, 195

loss of independence, 57–79

loss of the present, 37–56, 107–8, 194

loss of unity, 9–17

as measurement of change, and Aristotle’s space, 63–79, 97

and memory. See memory/memories

modification of structure of, 9–13

multilayered aspect of, 3, 198

multiple meanings of, 17n

mystery of, 1–5, 199–202

and network of relations, 89–91. See also relationality

when nothing changes, 63–64, 72

Planck time, 83

proper time, 16, 40, 216n8

quantum superpositions of times, 87–88. See also quantum mechanics

quantum time. See quantum time

and relativity. See relativity

sources of, 193–203

spacetime. See spacetime

standardized, 61–62

as suffering, 190–91

temporal structure of universe without the present, 46–56, 106–7, 109

thermal, 134–38, 139–40, 142, 196, 222n87

traces of the past, 166–67, 181, 183, 187, 196–97. See also memory/memories

“true” time and Newton’s space, 65–79

Tomita–Takesaki theorem, 225n85

universal man, 154–55

Wheeler, John, 119–21, 122, 124

Wheeler–DeWitt equation, 119, 224n72