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.