- Title Pages
- Frontispiece
- Dedication
- Epigraph
- Preface
- List of Figures
- 1 Introduction
- 2 Antecedents
- 3 Mathematics and physics preliminaries: of hills and plains and other things
- 4 The Principle of Virtual Work
- 5 D’Alembert’s Principle
- 6 Lagrangian Mechanics
- 7 Hamiltonian Mechanics
- 8 The whole of physics
- 9 Final words
- Appendix A1.1 Newton’s Laws of Motion
- Appendix A2.1 Portraits of the physicists
- Appendix A3.1 Reversible displacements
- Appendix A6.1 Worked examples in Lagrangian Mechanics
- Appendix A6.2 Proof that <i>T</i> is a function of <i>v</i><sup>2</sup>
- Appendix A6.3 Energy conservation and the homogeneity of time
- Appendix A6.4 The method of Lagrange Multipliers
- Appendix A6.5 Generalized Forces
- Appendix A7.1 Hamilton’s Transformation, examples
- Appendix A7.2 Demonstration that the pi s are independent coordinates
- Appendix A7.3 Worked examples in Hamiltonian Mechanics
- Appendix A7.4 Incompressibility of the phase fluid
- Appendix A7.5 Energy conservation in extended phase space
- Appendix A7.6 Link between the action, <i>S</i>, and the ‘circulation’
- Appendix A7.7 Transformation equations linking <i>p</i> and <i>q</i> via <i>S</i>
- Appendix A7.8 Infinitesimal canonical transformations
- Appendix A7.9 Perpendicularity of wavefronts and rays
- Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation
- Appendix A7.11 Quasi refractive index in mechanics
- Appendix A7.12 Einstein’s link between Action and the de Broglie waves
- Bibliography and Further Reading
- Index

# The whole of physics

# The whole of physics

- Chapter:
- (p.183) 8 The whole of physics
- Source:
- The Lazy Universe
- Author(s):
### Jennifer Coopersmith

- Publisher:
- Oxford University Press

How the Principle of Least Action underlies all physics (all physics that can be reduced to mathematical equations) is explained at a qualitative, semi-popular level. It even applies to smartphones. The domains of classical mechanics, continuum mechanics, materials science, light and electromagnetic waves, special and general relativity (Einstein’s Theory of Gravitation), electrodynamics, quantumelectrodynamics (QED), hydrodynamics, physical chemistry, statistical mechanics, and the quantum world, are examined. It is shown that the Principles of Least Time, Least Resistance, and Maximal Ageing, and Lenz’s Law are, in fact, examples of the Principle of Least Action. It is also shown how Planck’s constant is a measure of “absolute smallness,” and its units are the units of action. Never again, post quantum mechanics, can there be any doubt about the deep significance of action in physics.

*Keywords:*
Least Resistance, Maximal Ageing, Lenz’s Law, Planck’s constant, QED, Einstein’s Gravitation, statistical mechanics, continuum mechanics, hydrodynamics, materials science

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- Title Pages
- Frontispiece
- Dedication
- Epigraph
- Preface
- List of Figures
- 1 Introduction
- 2 Antecedents
- 3 Mathematics and physics preliminaries: of hills and plains and other things
- 4 The Principle of Virtual Work
- 5 D’Alembert’s Principle
- 6 Lagrangian Mechanics
- 7 Hamiltonian Mechanics
- 8 The whole of physics
- 9 Final words
- Appendix A1.1 Newton’s Laws of Motion
- Appendix A2.1 Portraits of the physicists
- Appendix A3.1 Reversible displacements
- Appendix A6.1 Worked examples in Lagrangian Mechanics
- Appendix A6.2 Proof that <i>T</i> is a function of <i>v</i><sup>2</sup>
- Appendix A6.3 Energy conservation and the homogeneity of time
- Appendix A6.4 The method of Lagrange Multipliers
- Appendix A6.5 Generalized Forces
- Appendix A7.1 Hamilton’s Transformation, examples
- Appendix A7.2 Demonstration that the pi s are independent coordinates
- Appendix A7.3 Worked examples in Hamiltonian Mechanics
- Appendix A7.4 Incompressibility of the phase fluid
- Appendix A7.5 Energy conservation in extended phase space
- Appendix A7.6 Link between the action, <i>S</i>, and the ‘circulation’
- Appendix A7.7 Transformation equations linking <i>p</i> and <i>q</i> via <i>S</i>
- Appendix A7.8 Infinitesimal canonical transformations
- Appendix A7.9 Perpendicularity of wavefronts and rays
- Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation
- Appendix A7.11 Quasi refractive index in mechanics
- Appendix A7.12 Einstein’s link between Action and the de Broglie waves
- Bibliography and Further Reading
- Index