Scientific Uncertainty, and Information

DedicationIntroductionPart I - Information and Imagination in Science Chapter I - Thermodynamics, Statistics, and Information 1 Sadi Carnot—A Pioneer 2 Two Principles of Thermodynamics 3 Thermal Engines 4 Entropy and Value, Negentropy, and Energy Degradation 5 Entropy and Probability 6 Thermodynamics and Information Theory 7 A Precise Definition of "Information" 8 Information and Negentropy References Chapter II - The Importance of Scientific Laws 1 The Role of Scientific Laws 2 Scientific Laws and Negentropy 3 Quanta and Uncertainty Principle 4 Criticisms and Suggestions 5 The Information Content of an Empirical Law 6 Examples and Discussion 7 How Is Science Actually Being Built? The Meaning of an Experiment 8 Empirical and Theoretical Laws 9 The Conditions for an Ideal Theory 10 Importance and Value of Theories References Chapter III - Mathematical Theorems and Physical Theories 1 Necessary Distinction Between Mathematics and the Physical Sciences 2 Basic Formulations in Mathematics 3 The Viewpoint of Experimental Scientists 4 The Opinion of Max Born 5 The Experimental Customer is Always Right References Chapter IV - Imagination and Invention in a Theory 1 The Birth of a Scientific Law 2 A Scientific Law Is an Interpretation of Nature by Human Thought 3 Bridgman's Operational Method 4 Scientific Theories are Born in Our Imagination 5 Connections or Overlapping: Conditions Relating to Different Theoretical Models References Chapter V - The Opinions of Planck, Bohr, and Schrödinger 1 Beware of "isms 2 Max Planck's Criticism of Positivism 3 Science Based on Experience 4 The Outside World and Physical Representation of the World 5 Schrödinger and the Greek Inheritance 6 Bohr's Complementarity 7 Incomplete Models, Complementarity and Uncertainty References Chapter VI - The Arrow of Time 1 Is Time Reversible or Not? 2 The Role Played by Time in Problems of Wave Propagation 3 General Remarks About Retarded Waves 4 Short Historical Survey; the Ritz-Einstein Discussion 5 Past, Future and Relativity 6 Recent Discussions About Time Irreversibility 7 Causality or Finality: Bergson, Fantappié, Arcidiacono, and Elsasser 8 Time Arrow and Causality References Chapter VII - Causality and Determinism; Empirical Limitations 1 Strict Determinism or Loose Causality? 2 A Very Simple Example: Radioactivity 3 Emission of Light by Atoms 4 Philosophical Significance of Einstein's Formulas 5 Quantized Waves Do Not Support Determinism 6 Born's Statistical Interpretation of Waves 7 Superquantization 8 Transformations and Metamorphosis of the Idea of Fields 9 Some Examples of Overlapping Theoretical Models ReferencesPart II - Uncertainty in Classical Mechanics Chapter VIII - Weaknesses and Limitations of Mechanics 1 The Need to Scrutinize Classical Mechanics. What is Space? 2 Errors and Information in Mechanics 3 The Objective World and the Problem of Determinism 4 A Simple Example for Discussion of Uncertainties in Mechanics 5 Some More Examples: Anharmonic Oscillators, and a Rectifier 6 The Anomaly of the Harmonic Oscillator 7 The Problem of Determinism 8 Information Theory and Our Preceding Examples 9 Observations and Interpretation 10 Conclusions References Chapter IX - Poincaré and the Shortcomings of the Hamilton-Jacobi Method for Classical or Quantized Mechanics 1 Poincaré's "Science and Hypothesis 2 Poincaré's Great Theorem on Celestial Mechanics 3 The Methods of Analytical Dynamics for Separated Variables 4 NonSeparable Variables. Hamilton-Jacobi Procedure 5 Successive Approximations 6 Approximations for NonDegenerate Systems 7 Poincaré's Great Theorem Again 8 The Role of Degeneracy Conditions in Poincaré's Theorem 9 Degeneracy Conditions and the Possibility of Finding a Hamilton-Jacobi Transformation Function 10 Sketch of a Discussion of the Possibilities of Convergence for NonSeparated Variables 11 Discussion of a Simple Example with Two Variables; Degeneracy Means Instability or Resonance 12 Some General Conclusions. Determinism versus Statistical Mechanics References Chapter X - Examples of Uncertainty in Classical Mechanics 1 Introduction 2 The Hamilton-Jacobi Method 3 Conditions of Discontinuity and Cases of Resonance 4 One Degree of Freedom and A Single Frequency Equal to Zero 5 Motions in Space 6 Coupled Oscillators 7 Some Examples in Astronomy 8 Problems of Applied Mechanics 9 Negative Resistances in Oscillators 10 Wheel Shimmy in Cars; Wing Flutter in Airplanes 11 Transition from Classical Mechanics to Wave Mechanics 12 Wave Scattering 13 Conclusion ReferencesBooks Published by L. BrillouinSubject Index