THE STRUCTURAL FOUNDATIONS OF QUANTUM GRAVITY
CONTENTS 1 QUANTUM GRAVITY MEETS STRUCTURALISM: INTERWEAVING RELATIONS IN THE FOUNDATIONS OF PHYSICS 1 1 QUANTUM GRAVITY: BACKGROUND, CONCEPTS, AND METHODS 1 1 1 THE HOLE ARGUMENT AND SPACETIME ONTOLOGY 1 1 2 GAUGING THE HOLE ARGUMENT 1 1 3 ENTER QUANTUM GRAVITY 1 1 4 CATEGORIZING THE MANIFOLD METHODS 1 1 5 WHAT’S WRONG WITH BACKGROUND-DEPENDENT METHODS? 1 1 6 WHAT’S RIGHT ABOUT BACKGROUND-INDEPENDENT METHODS? 1 1 7 BACKGROUND INDEPENDENCE AND STRUCTURALISM 1 2 STRUCTURALISM AND STRUCTURAL REALISM 1 2 1 MOTIVATING STRUCTURALISM 1 2 2 WHAT IS STRUCTURALISM? 1 2 3 … AND WHERE DOES IT COME FROM? 1 2 4 STRUCTURAL REALISM 2 STRUCTURAL REALISM AND QUANTUM GRAVITY 2 1 STRUCTURAL REALISM 2 2 PHYSICAL REALITY OF SPACETIME AND QUANTUM FIELDS 2 3 QUANTUM GRAVITY 3 STRUCTURE, INDIVIDUALITY, AND QUANTUM GRAVITY 3 1 WHAT IS STRUCTURAL REALISM? 3 2 STRUCTURE AND INDIVIDUALITY 3 3 EFFECTIVE FIELD THEORY AND ASYMPTOTIC QUANTIZATION 3 4 STRING THEORY 3 5 QUANTUM GENERAL RELATIVITY: SOME PRELIMINARY PROBLEMS 3 5 1 STATES OR PROCESSES: WHICH IS PRIMARY? 3 5 2 FORMALISM AND MEASURABILITY 3 6 CANONICAL QUANTIZATION (LOOP QUANTUM GRAVITY) 3 7 THE CAUSAL SET (CAUSET) APPROACH 3 8 WHAT STRUCTURES TO QUANTIZE? 4 POINTS, PARTICLES, AND STRUCTURAL REALISM 4 1 WHAT IS STRUCTURAL REALISM? 4 2 UNDERDETERMINATION 4 3 WHAT IS ONTIC STRUCTURAL REALISM? 4 4 OBJECTS 4 5 SOPHISTICATED SUBSTANTIVALISM 4 6 STACHEL’S GENERALIZED HOLE ARGUMENT FOR SETS 4 7 STACHEL ON IDENTICAL PARTICLES 4 8 IDENTICAL PARTICLES AND IDENTITY OVER TIME 4 9 TWO MORALS FOR QUANTUM GRAVITY 5 HOLISM AND STRUCTURALISM IN CLASSICAL AND QUANTUM GENERAL RELATIVITY 5 1 INTRODUCTION: TWO STRANDS OF PHILOSOPHY OF PHYSICS THAT OUGHT TO BE BROUGHT TOGETHER 5 2 MANY ‘REALISMS’ OR ONE? 5 2 1 WHAT, EXACTLY, IS A PHYSICAL STRUCTURE? 5 3 A CASE STUDY: THE HOLISTIC AND STRUCTURAL NATURE OF GENERAL-RELATIVISTIC SPACETIME IN A CLASS OF MODELS OF GR 5 3 1 THE HOLE ARGUMENT AND ITS CONSEQUENCES 5 3 2 THE DYNAMICAL INDIVIDUATION OF POINT-EVENTS 5 4 DEVELOPING HINTS FOR THE QUANTUM GRAVITY PROGRAMME 5 5 STRUCTURAL SPACETIME REALISM 5 5 1 THE NATURE OF POINT-EVENTS AND OVERCOMING THE SUBSTANTIVALISM/RELATIONISM DEBATE 6 TIME AND STRUCTURE IN CANONICAL GRAVITY 6 1 INTRODUCTION 6 2 CONSTRAINTS, GAUGE, AND HOLES 6 2 1 HAMILTONIAN SYSTEMS: CONSTRAINTS AND GAUGE 6 2 2 CONSTRAINTS AND GAUGE IN GENERAL RELATIVITY 6 2 3 INTERPRETING GAUGE THEORIES 6 3 WHAT IS THE PROBLEM OF TIME? 6 4 A SNAPSHOT OF THE PHILOSOPHICAL DEBATE 6 4 1 TIME SERIES FROM A TO D 6 4 2 MAUDLIN VERSUS EARMAN 6 5 CATALOGUE OF RESPONSES 6 5 1 TIMEFULL STRATAGEMS 6 5 2 TIMELESS STRATAGEMS 6 6 ENTER STRUCTURALISM 6 7 CONCLUSION 7 THE CASE FOR BACKGROUND INDEPENDENCE 7 1 INTRODUCTION 7 2 A BRIEF HISTORY OF RELATIONAL TIME 7 3 WHAT PHYSICISTS MEAN WHEN WE TALK ABOUT RELATIONAL SPACE AND TIME 7 4 GENERAL RELATIVITY AS A PARTLY RELATIONAL THEORY 7 4 1 THE PROBLEM OF TIME AND RELATED ISSUES 7 5 RELATIONALISM AND THE SEARCH FOR THE QUANTUM THEORY OF GRAVITY 7 5 1 THE CAUSAL SET THEORY 7 5 2 LOOP QUANTUM GRAVITY 7 5 3 CAUSAL DYNAMICAL TRIANGULATION MODELS 7 5 4 BACKGROUND-INDEPENDENT APPROACHES TO STRING AND M THEORY 7 6 RELATIONALISM AND REDUCTIONISM 7 6 1 THE CHALLENGE OF THE STRING THEORY LANDSCAPE 7 7 A RELATIONAL APPROACH TO THE PROBLEMS OF UNI?CATION AND DETERMINATION OF THE STANDARD MODEL PARAMETERS 7 8 RELATIONALISM AND NATURAL SELECTION 7 9 WHAT ABOUT THE COSMOLOGICAL CONSTANT PROBLEM? 7 10 THE ISSUE OF EXTENDING QUANTUM THEORY TO COSMOLOGY 7 10 1 RELATIONAL APPROACHES TO QUANTUM COSMOLOGY 7 10 2 RELATIONAL APPROACHES TO GOING BEYOND QUANTUM THEORY 7 11 CONCLUSIONS 8 QUANTUM QUANDARIES: A CATEGORY-THEORETIC PERSPECTIVE 8 1 INTRODUCTION 8 2 LESSONS FROM TOPOLOGICAL QUANTUM FIELD THEORY 8 3 THE ?-CATEGORY OF HILBERT SPACES 8 4 THE MONOIDAL CATEGORY OF HILBERT SPACES 8 5 CONCLUSIONS