Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics

Contents
Preface and Acknowledgements
Origins
Acknowledgements
Figure Credits
1 Introduction
	1.1 Pedagogical and Real Physics
	1.2 Reflections on What Every Student Should Know
	1.3 The Nature of Physics and Theoretical Physics
	1.4 Environmental Influences
	1.5 Final Disclaimer
	Notes
	Case Study I The Origins of Newton’s Laws of Motion and of Gravity
2 From Ptolemy to Kepler: The Copernican Revolution
	2.1 Ancient History
	2.2 The Copernican Revolution
	2.3 Tycho Brahe: The Lord of Uraniborg
	2.4 Johannes Kepler and Heavenly Harmonies
	Notes
3 Galileo and the Nature of the Physical Sciences
	3.1 Introduction
	3.2 Galileo as an Experimental Physicist
	3.3 Galileo’s Telescopic Discoveries
	3.4 Aristotelian versus Galilean Physics: The Heart of the Matter
	3.5 The Trial of Galileo
	3.6 Galilean Relativity
	3.7 Reflections
	Notes
4 Newton and the Law of Gravity
	4.1 Introduction
	4.2 Lincolnshire 1642–61
	4.3 Cambridge 1661–65
	4.4 Lincolnshire 1665–67
	4.5 Cambridge 1667–96
	4.6 Newton the Alchemist
	4.7 The Interpretation of Ancient Texts and the Scriptures
	4.8 London 1696–1727
	Appendix to Chapter 4: Notes on Conic Sections and Central Orbits
	Notes
	Case Study II Maxwell’s Equations
5 The Origin of Maxwell’s Equations
	5.1 How It All Began
	5.2 Michael Faraday: Mathematics without Mathematics
	5.3 Maxwell’s Route to the Equations for the Electromagnetic Field
	Appendix to Chapter 5: Notes on Vector Fields
	Notes
6 Maxwell(1865): A Dynamical Theory of the Electromagnetic Field
	6.1 PART I – Introductory
	6.2 PART II – On Electromagnetic Induction
	6.3 PART III – General Equations of the Electromagnetic Field
	6.4 PART IV – Mechanical Actions in the Field
	6.5 PART V – Theory of Condensers
	6.6 PART VI – Electromagnetic Theory of Light
	6.7 PART VII – Calculation of the Coefficients of Electromagnetic Induction
	6.8 The Aftermath
	Notes
7 How to Rewrite the History of Electromagnetism
	7.1 Introduction
	7.2 Maxwell’s Equations as a Set of Vector Equations
	7.3 Gauss’s Theorem in Electromagnetism
	7.4 Time-Independent Fields as Conservative Fields of Force
	7.5 Boundary Conditions in Electromagnetism
	7.6 Amp ` ere’s Law
	7.7 Faraday’s Law
	7.8 Coulomb’s Law
	7.9 The Biot–Savart Law
	7.10 The Interpretation of Maxwell’s Equations in Material Media
	7.11 The Energy Densities of Electromagnetic Fields
	7.12 Concluding Remarks
	Notes
	CaseStudy III Mechanics and Dynamics: Linear and Non-linear
8 Approaches to Mechanics and Dynamics
	8.1 Newton’s Laws of Motion
	8.2 Principles of ‘Least Action’
	8.3 The Euler–Lagrange Equations
	8.4 Lagrangians, Conservation Laws and Symmetry
	8.5 Lagrangians, Small Oscillations and Normal Modes
	8.6 Hamilton’s Equations
	8.7 Hamilton’s Equations and Poisson Brackets
	8.8 The Hamilton–Jacobi Equations and Action–Angle Variables
	8.9 A Warning
	Notes
9 The Motion of Fluids
	9.1 The Equation of Continuity
	9.2 The Equations of Motion for an Incompressible Fluid in the Absence of Viscosity
	9.3 Some Applications of Bernoulli’s Theorem
	9.4 Gravity Waves in Shallow and Deep Water
	9.5 The Equation of Motion of an Incompressible Fluid Including Viscous Forces
	9.6 Stokes’ Formula for Highly Viscous Flow
	9.7 Vorticity, Circulation and Kelvin’s Circulation Theorem
	9.8 Concluding Remarks
	Notes
10 Dimensional Analysis,Chaos and Self-Organised Criticality
	10.1 Introduction
	10.2 Dimensional Analysis
	10.3 Introduction to Chaos
	10.4 Scaling Laws and Self-Organised Criticality
	10.5 Beyond Computation
	Notes
	Case Study IV Thermodynamics and Statistical Physics
11 Basic Thermodynamics
	11.1 Heat and Temperature
	11.2 Heat as Motion versus the Caloric Theory of Heat
	11.3 The First Law of Thermodynamics
	11.4 The Origin of the Second Law of Thermodynamics
	11.5 The Second Law of Thermodynamics
	11.6 Entropy
	11.7 The Law of Increase of Entropy
	11.8 The Differential Form of the Combined First and Second Laws of Thermodynamics
	Appendix to Chapter 11: Maxwell’s Relations and Jacobians
	Notes
12 Kinetic Theory and the Origin of Statistical Mechanics
	12.1 The Kinetic Theory of Gases
	12.2 Kinetic Theory of Gases: First Version
	12.3 Kinetic Theory of Gases: Second Version
	12.4 Maxwell’s Velocity Distribution
	12.5 The Viscosity of Gases
	12.6 Pedagogical Digression (1): A Numerical Approach to the Boltzmann and Maxwell Distributions
	12.7 The Statistical Nature of the Second Law of Thermodynamics
	12.8 Entropy and Probability
	12.9 Entropy and the Density of States
	12.10 Pedagogical Digression (2): A Numerical Approach to the Law of Increase of Entropy
	12.11 Gibbs Entropy and Information
	12.12 Concluding Remarks
	Notes
	Case StudyV The Origins of the Concepts of Quantisation and Quanta
13 Black-Body Radiation up to 1895
	13.1 Physics and Theoretical Physics in 1890
	13.2 Kirchhoff’s Law of Emission and Absorption of Radiation
	13.3 The Stefan–Boltzmann Law
	13.4 Wien’s Displacement Law and the Spectrum of Black-Body Radiation
	Notes
14 1895–1900: Planck and the Spectrum of Black-Body Radiation
	14.1 Planck’s Early Career
	14.2 Oscillators and Their Radiation in Thermal Equilibrium
	14.3 The Equilibrium Radiation Spectrum of a Harmonic Oscillator
	14.4 Towards the Spectrum of Black-Body Radiation
	14.5 The Primitive Form of Planck’s Radiation Law
	14.6 Rayleigh and the Spectrum of Black-Body Radiation
	14.7 Comparison of the Laws for Black-Body Radiation with Experiment
	Appendix to Chapter 14: Rayleigh’s Paper of 1900
	Notes
15 Planck’s Theory of Black-Body Radiation
	15.1 Introduction
	15.2 Boltzmann’s Procedure in Statistical Mechanics
	15.3 Planck’s Analysis
	15.4 Planck and ‘Natural Units’
	15.5 Planck and the Physical Significance of h
	15.6 Why Planck Found the Right Answer
	Notes
16 Einstein and the Quantisation of Light
	16.1 1905: Einstein’s Annus Mirabilis
	16.2 Einstein (1905) On a Heuristic Viewpoint Concerning the Production and Transformation of Light
	16.3 The Quantum Theory of Solids
	16.4 Debye’s Theory of Specific Heat Capacities
	16.5 The Specific Heat Capacities of Gases Revisited
	16.6 Conclusion
	Notes
17 The Triumph of the Light Quantum Hypothesis
	17.1 The Situation in 1909
	17.2 Fluctuations of Particles and Waves
	17.3 Fluctuations of Randomly Superposed Waves
	17.4 Fluctuations in Black-Body Radiation
	17.5 The First Solvay Conference
	17.6 Experimental and Theoretical Advances 1911 to 1925
	17.7 Einstein (1916) ‘On the Quantum Theory of Radiation’
	17.8 Compton Scattering
	17.9 The Threshold of Quantum Mechanics
	17.10 The Story Concluded
	Notes
	Case StudyVI Special and General Relativity
18 Special Relativity: A Study in Invariance
	18.1 Introduction
	18.2 Geometry and the Lorentz Transformation
	18.3 Three-Vectors and Four-Vectors
	18.4 Relativistic Dynamics: The Momentum and Force Four-Vectors
	18.5 The Relativistic Equations of Motion
	18.6 The Frequency Four-Vector
	18.7 Lorentz Contraction and the Origin of Magnetic Fields
	18.8 Reflections
	Notes
19 An Introduction to General Relativity
	19.1 Introduction
	19.2 Essential Features of the Relativistic Theory of Gravity
	19.3 Isotropic Curved Spaces
	19.4 The Route to General Relativity
	19.5 The Schwarzschild Metric
	19.6 Particle Orbits about a Point Mass
	19.7 Advance of the Perihelia of Planetary Orbits
	19.8 Light Rays in Schwarzschild Space-Time
	19.9 Particles and Light Rays near Black Holes
	19.10 Circular Orbits about Schwarzschild Black Holes
	19.11 Gravitational Waves
	Notes
	Case Study VII Cosmology and Physics
20 Cosmology
	20.1 Cosmology and Physics
	20.2 Basic Cosmological Data
	20.3 The Robertson–Walker Metric
	20.4 Observations in Cosmology
	20.5 The Standard World Models
	20.6 Historical Interlude: Steady State Theory
	20.7 The Thermal History of the Universe
	20.8 Nucleosynthesis in the Early Universe
	20.9 The Values of the Cosmological Parameters
	Notes
21 Dark Matter, Dark Energy and the Inflationary Paradigm
	21.1 Introduction
	21.2 Dark Matter and Dark Energy
	21.3 The Big Problems
	21.4 A Pedagogical Interlude: Distances and Times in Cosmology
	21.5 The Inflationary Universe: Historical Background
	21.6 The Origin of the Spectrum of Primordial Perturbations
	21.7 Baryogenesis
	21.8 The Planck Era
	Notes
Author Index
Subject Index