Scientific Uncertainty, and Information

Scientific Uncertainty and Information focuses on the validation of theories developed in physics, chemistry, biology, and other fields of science.

The book first elaborates on thermodynamics, statistics, and information and the importance of scientific laws. Discussions focus on the importance and value of theories, empirical and theoretical laws, scientific laws and negentropy, principles of thermodynamics, entropy and value, negentropy, and energy degradation, and thermodynamics and information theory. The text then ponders on mathematical theorems and physical theories, imagination and invention in a theory, and causality and determinism.

The manuscript underscores the weaknesses and limitations of mechanics and Poincare and the shortcomings of the Hamilton-Jacobi method for classical or quantized mechanics. Topics include the discussion of a simple example with two variables; degeneracy conditions and the possibility of finding a Hamilton-Jacobi transformation function; approximations for nondegenerate systems; methods of analytical dynamics for separated variables; and the objective world and the problem of determinism.

The publication is a dependable reference for researchers interested in the validation of theories in science.

Dedication

Introduction

Part 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

References

Part 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

References

Books Published by L. Brillouin

Subject Index