Discrete or Continuous: The Quest for Fundamental Length in Modern Physics

Cover......Page 1
Half Title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 11
1 Introduction......Page 15
2.1 Outline......Page 21
2.2 Zeno\'s paradox of extension......Page 23
2.3 Topology and the argument against collision......Page 27
2.4 Geometry and the tile argument......Page 34
2.5 Richer alternatives to the real line model......Page 41
2.6 The physical Church–Turing thesis......Page 45
2.7 Pure versus applied mathematics......Page 49
3.1 Outline......Page 51
3.2 Metaphysical motivations......Page 53
3.3 Epistemology and the primacy of \"length\'\'......Page 58
3.4 Is discreteness transcendental?......Page 63
3.5 Enough with the \"isms\'\'......Page 66
4.1 Outline......Page 68
4.2 Classical electrodynamics......Page 70
4.3 From QM to QED......Page 77
4.4 The rise of renormalization......Page 97
4.5 Philosophical ramifications......Page 102
5.1 Outline......Page 111
5.2 Early steps......Page 112
5.3 Gravitons, measurability, and the Planck scale......Page 121
5.4 Non-commutative geometry......Page 126
5.5 (Re)enters gravity......Page 132
5.6 Quantizing gravity – the philosophical debate......Page 140
6.1 Outline......Page 155
6.2 Constructing the principles......Page 156
6.3 The Swann–Einstein correspondence......Page 163
6.4 Reading Einstein......Page 170
6.5 Einstein and the constructive approach to STR......Page 174
6.6 Geometry and dynamics, again......Page 184
7.1 Outline......Page 185
7.2 String theory......Page 188
7.3 Background independent strategies......Page 195
7.4 Emergent gravity......Page 207
7.5 On the \"disappearance\'\' of spacetime......Page 208
8.1 Outline......Page 215
8.2 The quest for quantum gravity phenomenology......Page 217
8.3 Consistency proofs......Page 222
8.4 The perils of innovation......Page 227
8.5 There and back again......Page 242
Questions and answers......Page 245
References......Page 253
Index......Page 278