The Cellular Automaton Interpretation of Quantum Mechanics.
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing AG,
2016.
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| Edition: | 1st ed. |
| Series: | Fundamental Theories of Physics Series
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| Subjects: | |
| Online Access: | Click to View |
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>
- 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>
- 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.