Lost Causes in and beyond Physics (eBook)

Preface 5
Contents 7
1 Introduction 9
2 Munchausen’s Syndrome by Proxy 14
2.1 Munchausen’s Syndrome by Proxy 14
2.2 Statistics in Human Affairs 15
2.3 Meadow’s Logical Error 18
3 Elementary Probability 26
3.1 Basics 26
3.2 Probability Distributions 29
3.3 Moments 34
3.4 Probability with Two Observers 36
3.5 Statistical Models 37
3.6 The Algebraic Theory of Gelfand 39
4 Quantum Probability 42
4.1 Algebras 42
4.2 The Schrödinger Picture 45
4.3 State Space 47
4.4 The Spectral Theorem 48
4.5 Tensor Products 50
4.6 Superselection Rules 52
4.7 Measurement and Events 61
4.8 The Quantum Game with Two Observers 67
5 Bayesians 71
5.1 Classical Bayesianism 71
5.2 Physics from Fisher Information 75
5.3 Quantum Bayesianism 76
6 EPR and the Dangers of Cannabis 79
6.1 Cannabis 79
6.2 The EPR Experiment 84
6.3 Counterfactuals 90
7 Stapp’s Theory of the Brain 94
7.1 The Speed at Which Concepts are Formed 94
7.2 The Claimed Absence of Correlations in Classical Field Theory 95
7.3 Supposed nonlocalities of Quantum Theory 96
7.4 Conclusion 97
8 Hidden Variables 99
8.1 Bell’s Theorem 103
9 Bohmian Mechanics 107
10 The Analytic S-matrix Bootstrap 117
10.1 Scattering 117
10.2 Dispersion Relations 119
10.3 Mandelstam’s Formula 121
10.4 Bootstrap 122
11 Nelson and Wiener 127
11.1 Wiener 127
11.2 Nelson 128
12 Other Lost Causes 133
12.1 Bondi’s Solution to the Twin Paradox 133
12.2 Quantum Logic 134
12.3 Trivalent Logic 135
12.4 Jordan Algebras 135
12.5 Non-self-adjoint Observables 136
12.6 Critique of Geometro-Stochastic Theory 141
12.7 Dirac’s Programme of Quantisation 144
12.8 DiffM as a Gauge Group 146
12.9 Dirac Notation 147
13 Some Good Ideas 149
13.1 Euclidean Quantum Field Theory 149
13.2 The Most General Quantum Theory 150
13.3 Cohomology 152
References 158
Index 165