Space, time, & stuff / Frank Arntzenius ; with a contribution by Cian Dorr.

Format:

Book

Author/Creator:

Arntzenius, Frank.

Contributor:

Dorr, Cian Seán, 1972-

Language:

English

Subjects (All):

Ontology.

Space and time.

Geometry in nature.

Physical Description:

vii, 288 pages : illustrations ; 25 cm

Edition:

First edition.

Other Title:

Space, time, and stuff

Place of Publication:

Oxford, U.K. ; New York : Oxford Univ. Press, 2012.

Summary:

"Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover.

Contents:

1 It's just one damn thing after another 5

1.1 Introduction 5

1.2 The structure of time and space in Newtonian physics 7

1.3 The structure of time and space in relativistic physics 12

1.4 The idea that time has no structure 19

1.5 Ridding time of structure in Newtonian particle physics 21

1.6 Ridding time of structure in Special Relativity 33

1.7 Ridding time of structure in General Relativity 36

2 There goes the neighbourhood... 39

2.1 Introduction 39

2.2 How separable is the geometric structure of spacetime? 43

2.3 How separable is classical particle structure? 49

2.4 Are velocities intrinsic to spacetime points? 59

2.5 How separable are the properties of classical fields? 69

2.6 Separability, dynamical locality, and relativity 74

3 The world according to quantum mechanics 79

3.1 Introduction 79

3.2 An argument that the world is not separable according to quantum mechanics 80

3.3 Configuration space realism 87

3.4 Configuration space realism in Newtonian particle mechanics 88

3.5 Configuration space realism in non-relativistic quantum particle mechanics 93

3.6 Relativistic quantum mechanics and narratibility failure 94

3.7 Can one use dynamics to rescue narratability? 97

3.8 There is no configuration spacetime 99

3.9 Multi-time configuration space wave-functions 100

3.10 Indeterministic relativistic theories in general 103

3.11 Amplitude realism 107

3.12 Liberal amplitude realism 113

3.13 Density-operator realism 113

3.14 Heisenberg-operator realism 116

3.15 Flash realism 120

3.16 Tentative conclusions 123

4 Pointlessness 125

4.1 Introduction 125

4.2 The possibility of motion and determinism 126

4.3 Cutting things in half 127

4.4 Paradoxes of size 128

4.5 Quantum mechanics and points 132

4.6 Contact between objects 133

4.7 The topological approach to pointless spaces 134

4.8 Objects in a pointless topology 138

4.9 Fields in a pointless topology 139

4.10 Problems for the topological approach to gunk 140

4.11 Measure theoretic gunk 145

4.12 Problems for measure theoretic gunk 149

4.13 Conclusions 150

5 Do space and time exist? 153

5.1 Introduction 153

5.2 Leibniz's shifts; an argument against the existence of space 153

5.3 Newton's buckets; an argument for the existence of space 154

5.4 Leibnizean relationism and Newtonian particle theories 155

5.5 Relationism and Newtonian field theories 163

5.6 Relationism about time in Newtonian physics 166

5.7 Piggy-back relationism 169

5.8 Rich relationism and Newtonian physics 170

5.9 Relationism and Special Relativity 171

5.10 The 'hole' argument 172

5.11 General Relativity and relationism 173

5.12 Substantivalism 176

5.13 Supersubstantivalism 181

6 Gauge theories and fibre-bundle spaces 183

6.1 Introduction 183

6.2 Are velocities properties? 184

6.3 Fibre-bundle substantivalism 185

6.4 Gauge relationism 193

6.5 Conclusions 198

7 Directions, hands, and charges 199

7.1 Introduction 199

7.2 How do quantities transform under PT? 200

7.3 PT in classical field theories 202

7.4 PT in quantum field theories when one takes wave-functions as the fundamental quantities 207

7.5 PT in quantum field theories when one takes field operators as the fundamental quantities 211

7.6 Conclusions 212

8 Calculus as geometry (co-authored with Cian Dorr) 213

8.1 Introduction 213

8.2 Nominalizing Newtonian gravitation 218

8.3 Richness and the existence of property spaces 223

8.4 Differentiable manifolds 230

8.5 Nominalizing differential geometry 233

8.6 Can we make do with points and regions? 234

8.7 Differentiable structure via scalar-value space 243

8.8 Physical fields in scalar-value space 248

8.9 Differential structure via vector bundles 255

8.10 Tangent-bundle substantivalism 264

8.11 Further possible simplifications 267

8.12 Conclusions 268.

Notes:

Includes bibliographical references (pages [279]-283) and index.

ISBN:

9780199696604

0199696608

OCLC:

742512006