The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.
Author(s): Amit Hagar
Publisher: Cambridge University Press
Year: 2014
Language: English
Pages: 282
Tags: Физика;История физики;
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
