The Enigma of Probability and Physics

I. Fundamentals of Probabilistics.- 1 / Principal Concepts.- 1.1. Concrete Objects.- 1.2. Abstract Objects.- 1.3. More about Concrete and Abstract Objects.- 1.4. Measure of a Set of Concrete Objects.- 1.5. Experimental Determination of the Measures of Sets of Concrete Objects.- 1.6. The Statistical Method.- 1.7. Probability. Preliminary Consideration.- 1.8. Mutually Adequate Sets.- 1.9. Probability. General Definition.- Problems.- Suggested References.- 2 / Main Theorems.- 2.1. Sum and Product of Events.- 2.2. Addition Theorem.- 2.3. Multiplication Theorem.- 2.4. Sequence of Random Tests.- 2.5. Law of Large Numbers.- 2.6. Limiting Cases of Binomial Law.- Problems.- Suggested References.- 3 / Random Variables.- 3.1. Definition.- 3.2. Probability Distribution.- 3.3. Joint Probability Distribution for Functions of Random Variables.- 3.4. Mathematical Expectation. Moments.- 3.5. Characteristic Function.- Problems.- Suggested References.- 4 / Some Aspects of Statistics.- 4.1. Preliminary Considerations.- 4.2. Statistical Experiment.- 4.3. Numerical Statistical Experiment.- 4.4. Concluding Remarks.- Suggested References.- 5 / States of Abstract Objects.- 5.1. Introductory Remarks.- 5.2. Description of States.- 5.3. Necessary Mathematics.- 5.4. Two Specific Modes of Description of a State.- 5.5. Additional Mathematics.- Problems.- Suggested References.- 6 / Hamiltonian Random Variables.- 6.1. Lagrangian Equations and Hamiltonian Equations.- 6.2. Hamiltonian Random Variables.- 6.3. Canonically Conjugate Operators.- 6.4. Quantum Approach.- 6.5. Standard Deviations of Canonically Conjugate Random Variables.- Problems.- Suggested References.- 7 / Random Fields.- 7.1. Definition.- 7.2. Two Types of Related Finite-Dimensional Random Variables.- 7.1. Lagrangian and Hamiltonian Partial Equations.- 7.2. Hamiltonian Random Fields.- Suggested References.- II. Fundamentals of Probabilistic Physics.- 8 / General Considerations.- 8.1. Preliminaries.- 8.2. Classification of Physical Systems.- 8.3. Two Possible Types of Problems.- 8.4. Conservation Laws.- Suggested References.- 9 / Equilibrium Classical Statistical Mechanics.- 9.1. Microcanonical Distribution.- 9.2. Canonical Distribution.- 9.3. A Separate Atom in a Thermostat.- 9.4. Thermodynamic Functions.- 9.5. The Ideal (Perfect) Gas.- 9.6. Important Notes.- Suggested Reference.- 10 / Quantum Mechanics.- 10.1. Principal Propositions.- 10.2. Operators for Physical Quantities.- 10.2.1. Coordinates and Momenta.- 10.2.2. Time and Energy.- 10.2.3. Hamiltonian.- 10.2.4. Angular Momentum.- 10.2.5. Derivatives.- 10.2.6. Quantities Having a Finite Number of Values.- 10.3. Schrodinger Equation.- 10.4. A Free Particle.- 10.5. A Particle in a One-Dimensional Potential Box.- 10.6. One-Dimensional Harmonic Oscillator.- 10.7. A Particle in a Central Field.- 10.8. Equilibrium Quantum Statistical Mechanics.- Problems.- Suggested References.- 11 / Kinetics of Physical Transformations.- 11.1. Processes in Concrete Physical Systems.- 11.2. Probabilistic Treatment of Transformations.- 11.3. Basic Principles of the Transitional Configuration Theory.- 11.4. Leaving a Potential Well Through a Potential Barrier.- 11.5. Nonexponential Decay Law.- 11.6. Intramolecular Rearrangements.- 11.7. A Criterion of the Possibility of an Intramolecular Rearrangement.- Problems.- Suggested References.- 12 / Electromagnetic Field and Photons.- 12.1. Preliminaries.- 12.2. The Four-Dimensional Space Treatment.- 12.3. Physical Consideration.- 12.4. The Emon.- 12.5. Relativistic Aberration and Doppler Effect.- Problems.- Suggested References.- III. Methodological Problems.- 13 / Problems Related to Probability.- 13.1. Basic Phenomenon of Probabilistics.- 13.2. Mises' Definition of Probability.- 13.3. Kolmogorov's Probability Theory.- 13.4. Bertrand Paradox 285 Bibliography.- 14 / Problems Related to Physics.- 14.1. Gibbs' Paradox and Indistinguishability of Particles.- 14.2. Classical Limit of Quantum Mechanics.- 14.3 Energy and Time.- 14.4. One-Particle Relativistic Equations.- 14.5. Possible States of a Conservative System.- 14.6. Conventional Decay Theories.- 14.7.Time-Energy Uncertainty Relation.- 14.8. Measurement and Related Problems.- 14.1. Wave-Corpuscle Duality and Reality of Motion.- 14.2. Reality of Motion and Potential Energy.- 14.3. Einstein-Podolsky-Rosen's Paradox.- 14.4. Bell's Theorem.- 14.5. Second Quantization.- Appendix 1. Proof of Equations (6.16") and (6.16").- Appendix 2. Derivation of Equations of Section 6.3.- Appendix 3. A General Rotation-Vibration Hamiltonian.- Answers to Problems.