Physical (a)Causality : : Determinism, Randomness and Uncaused Events.

• Superior document: Fundamental Theories of Physics Series ; v.192
• Author: Svozil, Karl.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2018.; ©2018.
• Year of Publication: 2018
• Edition: 1st ed.
• Language: English
• Series: Fundamental Theories of Physics Series
• Physical Description: 1 online resource (215 pages)

Table of Contents

• Intro
• Preface
• Contents
• Part I Embedded Observers, Reflexive Perception and Representation
• 1 Intrinsic and Extrinsic Observation Mode
• 1.1 Pragmatism by ``Fappness''
• 1.2 Level of Description
• 1.3 Arguments for and Against Measurement
• 1.3.1 Distinction Between Observer and Object
• 1.3.2 Conventionality of the Cut Between Observer and Object
• 1.3.3 Relational Encoding
• 1.4 Inset: How to Cope with Perplexities
• 1.5 Extrinsic Observers
• 1.6 Intrinsic Observers
• 1.7 Nesting
• 1.8 Reflexive (Self-)nesting
• 1.8.1 Russian Doll Nesting
• 1.8.2 Droste Effect
• 1.9 Chaining
• 2 Embedded Observers and Self-expression
• 3 Reflexive Measurement
• 3.1 General Framework
• 3.2 Earlier and More Recent Attempts
• 4 Intrinsic Self-representation
• Part II Provable Unknowns
• 5 On What Is Entirely Hopeless
• 6 Forecasting and Unpredictability
• 6.1 Reduction from Logical Incompleteness
• 6.2 Determinism Does Not Imply Predictability
• 6.2.1 Unsolvability of the Halting Problem
• 6.2.2 Determinism Does Not Imply Predictability
• 6.3 Quantitative Estimates in Terms of the Busy Beaver Function
• 7 Induction by Rule Inference
• 8 Other Types of Recursion Theoretic Unknowables
• 9 What if There Are No Laws? Emergence of Laws
• 9.1 Mythological Roots
• 9.2 Physical Indeterminism in Vienna at the Dawn of Quantum Mechanics
• 9.3 Contemporary Representations
• 9.4 Provable Impossibility to Prove (In)Determinism
• 9.5 Potential Misperceptions by Over-interpretation
• Part III Quantum Unknowns
• 10 ``Shut Up and Calculate''
• 11 Evolution by Permutation
• 11.1 Representation Entities by Vectors and Matrices
• 11.2 Reversibility by Permutation
• 11.2.1 Representation as a Sum of Dyadic Products
• 11.2.2 No Coherent Superposition and Entanglement
• 11.2.3 Universality with Respect to Boolean Functions.
• 11.2.4 Universal Turing Computability from Boolean Functions
• 11.2.5 d-Ary Information Beyond Bits
• 11.2.6 Roadmap to Quantum Computing
• 12 Quantum Mechanics in a Nutshell
• 12.1 The Quantum Canon
• 12.2 Assumptions of Quantum Mechanics
• 12.3 Representation of States
• 12.4 Representation of Observables
• 12.5 Dynamical Laws by Isometric State Permutations
• 12.6 Disallowed Irreversible Processes
• 12.6.1 Disallowed State Reduction
• 12.6.2 Disallowed Partial Traces
• 12.7 Superposition of States - Quantum Parallelism
• 12.8 Composition Rules and Entanglement
• 12.8.1 Relation Properties About Versus Individual Properties of Parts
• 12.8.2 ``Breathing'' In and Out of Entanglement and Individuality
• 12.9 Quantum Probabilities
• 12.9.1 Boole's Conditions of Possible Experience
• 12.9.2 Classical Strategies: Probabilities from Convex Sum of Truth Assignments and the Convex Polytope Method
• 12.9.3 Context and Greechie Orthogonality Diagrams
• 12.9.4 Two-Valued Measures, Frame Functions and Admissibility of Probabilities and Truth Assignments
• 12.9.5 Why Classical Correlation Polytopes?
• 12.9.6 What Terms May Enter Classical Correlation Polytopes?
• 12.9.7 General Framework for Computing Boole's Conditions of Possible Experience
• 12.9.8 Some Examples
• 12.9.9 Quantum Probabilities and Expectations
• 12.9.10 Min-Max Principle
• 12.9.11 What Can Be Learned from These Brain Teasers?
• 12.10 Quantum Mechanical Observer-Object Theory
• 12.11 Observer-Objects ``Riding'' on the Same State Vector
• 12.12 Metaphysical Status of Quantum Value Indefiniteness
• 13 Quantum Oracles
• 14 Vacuum Fluctuations
• 15 Radioactivive Decay
• Part IV Exotic Unknowns
• 16 Classical Continua and Infinities
• 17 Classical (In)Determinism
• 17.1 Principle of Sufficient Reason and the Law of Continuity.
• 17.2 Possible Definition of Indeterminism by Negation
• 17.3 Unique State Evolution
• 17.4 Nonunique Evolution Without Lipschitz Continuity
• 18 Deterministic Chaos
• 18.1 Sensitivity to Changes of Initial Value
• 18.2 Symbolic Dynamics of the Logistic Shift Map
• 18.3 Algorithmic Incomputability of Series Solutions of the n-Body Problem
• Part V Transcendence
• 19 Partition Logics, Finite Automata and Generalized Urn Models
• 19.1 Modelling Complementarity by Finite Partitions
• 19.2 Generalized Urn and Automata Models
• 19.2.1 Automaton Models
• 19.2.2 Generalized Urn Models
• 19.2.3 Logical Equivalence for Concrete Partition Logics
• 19.3 Some Examples
• 19.3.1 Logics of the ``Chinese Lantern Type''
• 19.3.2 (Counter-)Examples of Triangular Logics
• 19.3.3 Generalized Urn Model of the Kochen-Specker ``Bug'' Logic
• 19.3.4 Kochen-Specker Type Logics
• 20 Miracles, Gaps and Oracles
• 21 Dualistic Interfaces
• 21.1 Gaming Metaphor
• 21.2 How to Acknowledge Intentionality?
• Part VI Executive Summary
• 22 (De)briefing
• 22.1 Provable Unknowables
• 22.2 Quantum (In)Determinism
• 22.3 Classical (In)Determinism
• 22.4 Comparison with Pseudo-randomness
• 22.5 Perception and Forward Tactics Toward Unknowns
• Appendix A Formal (In)Computability and Randomness
• A.1 Abundance of Incomputable Reals
• A.2 Random Reals
• A.3 Algorithmic Information
• A.3.1 Definition
• A.3.2 Algorithmic Information of a Single Random Sequence
• A.3.3 Bounds from Above
• A.3.4 Abundance of Random Reals
• A.4 Information-Theoretic Limitations of Formal Systems
• A.5 Abundance of True Yet Unprovable Statements
• A.6 Halting Probability Ω
• A.7 Busy Beaver Function and Maximal Execution and Recurrence Time
• A.8 Some Speculations on Primordial Chaos and Unlimited Information Content.
• Appendix B Two Particle Correlations and Expectations
• B.1 Two Two-State Particle Correlations and Expectations
• B.1.1 Classical Correlations with Dichotomic Observables in a ``Singlet'' State
• B.1.2 Quantum Dichotomic Case
• B.1.2.1 Single Particle Observables and Projection Operators
• B.1.2.2 Substitution Rules for Probabilities and Correlations
• B.1.2.3 Quantum Correlations for the Singlet State
• B.1.2.4 Quantum Predictions
• B.2 Two Three-State Particles
• B.2.1 Observables
• B.2.2 Singlet State
• B.3 Two Four-State Particles
• B.3.1 Observables
• B.3.2 Singlet State
• B.4 General Case of Two Spin j Particles in a Singlet State
• References
• Index.