The Cellular Automaton Interpretation of Quantum Mechanics.

• Superior document: Fundamental Theories of Physics Series ; v.185
• Author: 't Hooft, Gerard.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2016.; ©2016.
• Year of Publication: 2016
• Edition: 1st ed.
• Language: English
• Series: Fundamental Theories of Physics Series
• Physical Description: 1 online resource (296 pages)

Table of Contents

• Intro
• The Cellular Automaton Interpretation of Quantum Mechanics
• Foreword
• Preface
• Acknowledgements
• Contents
• List of Figures
• Part I: The Cellular Automaton Interpretation as a General Doctrine
• Chapter 1: Motivation for This Work
• 1.1 Why an Interpretation Is Needed
• 1.2 Outline of the Ideas Exposed in Part I
• 1.3 A 19th Century Philosophy
• 1.4 Brief History of the Cellular Automaton
• 1.5 Modern Thoughts About Quantum Mechanics
• 1.6 Notation
• Chapter 2: Deterministic Models in Quantum Notation
• 2.1 The Basic Structure of Deterministic Models
• 2.1.1 Operators: Beables, Changeables and Superimposables
• 2.2 The Cogwheel Model
• 2.2.1 Generalizations of the Cogwheel Model: Cogwheels with N Teeth
• 2.2.2 The Most General Deterministic, Time Reversible, Finite Model
• Chapter 3: Interpreting Quantum Mechanics
• 3.1 The Copenhagen Doctrine
• 3.2 The Einsteinian View
• 3.3 Notions Not Admitted in the CAI
• 3.4 The Collapsing Wave Function and Schrödinger's Cat
• 3.5 Decoherence and Born's Probability Axiom
• 3.6 Bell's Theorem, Bell's Inequalities and the CHSH Inequality
• 3.7 The Mouse Dropping Function
• 3.7.1 Ontology Conservation and Hidden Information
• 3.8 Free Will and Time Inversion
• Chapter 4: Deterministic Quantum Mechanics
• 4.1 Introduction
• 4.2 The Classical Limit Revisited
• 4.3 Born's Probability Rule
• 4.3.1 The Use of Templates
• 4.3.2 Probabilities
• Chapter 5: Concise Description of the CA Interpretation
• 5.1 Time Reversible Cellular Automata
• 5.2 The CAT and the CAI
• 5.3 Motivation
• 5.3.1 The Wave Function of the Universe
• 5.4 The Rules
• 5.5 Features of the Cellular Automaton Interpretation (CAI)
• 5.5.1 Beables, Changeables and Superimposables
• 5.5.2 Observers and the Observed
• 5.5.3 Inner Products of Template States
• 5.5.4 Density Matrices.
• 5.6 The Hamiltonian
• 5.6.1 Locality
• 5.6.2 The Double Role of the Hamiltonian
• 5.6.3 The Energy Basis
• 5.7 Miscellaneous
• 5.7.1 The Earth-Mars Interchange Operator
• 5.7.2 Rejecting Local Counterfactual De niteness and Free Will
• 5.7.3 Entanglement and Superdeterminism
• 5.7.4 The Superposition Principle in Quantum Mechanics
• 5.7.5 The Vacuum State
• 5.7.6 A Remark About Scales
• 5.7.7 Exponential Decay
• 5.7.8 A Single Photon Passing Through a Sequence of Polarizers
• 5.7.9 The Double Slit Experiment
• 5.8 The Quantum Computer
• Chapter 6: Quantum Gravity
• Chapter 7: Information Loss
• 7.1 Cogwheels with Information Loss
• 7.2 Time Reversibility of Theories with Information Loss
• 7.3 The Arrow of Time
• 7.4 Information Loss and Thermodynamics
• Chapter 8: More Problems
• 8.1 What Will Be the CA for the SM?
• 8.2 The Hierarchy Problem
• Chapter 9: Alleys to Be Further Investigated and Open Questions
• 9.1 Positivity of the Hamiltonian
• 9.2 Second Quantization in a Deterministic Theory
• 9.3 Information Loss and Time Inversion
• 9.4 Holography and Hawking Radiation
• Chapter 10: Conclusions
• 10.1 The CAI
• 10.2 Counterfactual De niteness
• 10.3 Superdeterminism and Conspiracy
• 10.3.1 The Role of Entanglement
• 10.3.2 Choosing a Basis
• 10.3.3 Correlations and Hidden Information
• 10.4 The Importance of Second Quantization
• Part II: Calculation Techniques
• Chapter 11: Introduction to Part II
• 11.1 Outline of Part II
• 11.2 Notation
• 11.3 More on Dirac's Notation for Quantum Mechanics
• Chapter 12: More on Cogwheels
• 12.1 The Group SU(2), and the Harmonic Rotator
• 12.2 In nite, Discrete Cogwheels
• 12.3 Automata that Are Continuous in Time
• Chapter 13: The Continuum Limit of Cogwheels, Harmonic Rotators and Oscillators
• 13.1 The Operator phiop in the Harmonic Rotator.
• 13.2 The Harmonic Rotator in the x Frame
• Chapter 14: Locality
• Chapter 15: Fermions
• 15.1 The Jordan-Wigner Transformation
• 15.2 `Neutrinos' in Three Space Dimensions
• 15.2.1 Algebra of the Beable `Neutrino' Operators
• 15.2.2 Orthonormality and Transformations of the `Neutrino' Beable States
• 15.2.3 Second Quantization of the `Neutrinos'
• 15.3 The `Neutrino' Vacuum Correlations
• Chapter 16: PQ Theory
• 16.1 The Algebra of Finite Displacements
• 16.1.1 From the One-Dimensional In nite Line to the Two-Dimensional Torus
• 16.1.2 The States |Q,P&gt
• in the q Basis
• 16.2 Transformations in the PQ Theory
• 16.3 Resume of the Quasi-periodic Phase Function phi(xi,kappa)
• 16.4 The Wave Function of the State |0,0&gt
• Chapter 17: Models in Two Space-Time Dimensions Without Interactions
• 17.1 Two Dimensional Model of Massless Bosons
• 17.1.1 Second-Quantized Massless Bosons in Two Dimensions
• 17.1.2 The Cellular Automaton with Integers in 2 Dimensions
• 17.1.3 The Mapping Between the Boson Theory and the Automaton
• 17.1.4 An Alternative Ontological Basis: The Compacti ed Model
• 17.1.5 The Quantum Ground State
• 17.2 Bosonic Theories in Higher Dimensions?
• 17.2.1 Instability
• 17.2.2 Abstract Formalism for the Multidimensional Harmonic Oscillator
• 17.3 (Super)strings
• 17.3.1 String Basics
• 17.3.2 Strings on a Lattice
• 17.3.3 The Lowest String Excitations
• 17.3.4 The Superstring
• 17.3.5 Deterministic Strings and the Longitudinal Modes
• 17.3.6 Some Brief Remarks on (Super)string Interactions
• Chapter 18: Symmetries
• 18.1 Classical and Quantum Symmetries
• 18.2 Continuous Transformations on a Lattice
• 18.2.1 Continuous Translations
• 18.2.2 Continuous Rotations 1: Covering the Brillouin Zone with Circular Regions
• 18.2.3 Continuous Rotations 2: Using Noether Charges and a Discrete Subgroup.
• 18.2.4 Continuous Rotations 3: Using the Real Number Operators p and q Constructed Out of P and Q
• 18.2.5 Quantum Symmetries and Classical Evolution
• 18.2.6 Quantum Symmetries and Classical Evolution 2
• 18.3 Large Symmetry Groups in the CAI
• Chapter 19: The Discretized Hamiltonian Formalism in PQ Theory
• 19.1 The Vacuum State, and the Double Role of the Hamiltonian (Cont'd)
• 19.2 The Hamilton Problem for Discrete Deterministic Systems
• 19.3 Conserved Classical Energy in PQ Theory
• 19.3.1 Multi-dimensional Harmonic Oscillator
• 19.4 More General, Integer-Valued Hamiltonian Models with Interactions
• 19.4.1 One-Dimensional System: A Single Q, P Pair
• 19.4.2 The Multi-dimensional Case
• 19.4.3 The Lagrangian
• 19.4.4 Discrete Field Theories
• 19.4.5 From the Integer Valued to the Quantum Hamiltonian
• Chapter 20: Quantum Field Theory
• 20.1 General Continuum Theories-The Bosonic Case
• 20.2 Fermionic Field Theories
• 20.3 Standard Second Quantization
• 20.4 Perturbation Theory
• 20.4.1 Non-convergence of the Coupling Constant Expansion
• 20.5 The Algebraic Structure of the General, Renormalizable, Relativistic Quantum Field Theory
• 20.6 Vacuum Fluctuations, Correlations and Commutators
• 20.7 Commutators and Signals
• 20.8 The Renormalization Group
• Chapter 21: The Cellular Automaton
• 21.1 Local Time Reversibility by Switching from Even to Odd Sites and Back
• 21.1.1 The Time Reversible Cellular Automaton
• 21.1.2 The Discrete Classical Hamiltonian Model
• 21.2 The Baker Campbell Hausdorff Expansion
• 21.3 Conjugacy Classes
• Chapter 22: The Problem of Quantum Locality
• 22.1 Second Quantization in Cellular Automata
• 22.2 More About Edge States
• 22.3 Invisible Hidden Variables
• 22.4 How Essential Is the Role of Gravity?
• Chapter 23: Conclusions of Part II.
• Appendix A: Some Remarks on Gravity in 2+1 Dimensions
• A.1 Discreteness of Time
• Appendix B: A Summary of Our Views on Conformal Gravity
• Appendix C: Abbreviations
• References.