Book contents
- Frontmatter
- Contents
- List of Illustrations
- Acknowledgments
- 1 Introduction
- 2 Prehistory of Variational Principles
- 3 An Excursion to Newton's Principia
- 4 The Optical-Mechanical Analogy, Part I
- 5 D'Alembert, Lagrange, and the Statics-Dynamics Analogy
- 6 The Optical-Mechanical Analogy, Part II: The Hamilton-Jacobi Equation
- 7 Relativity and Least Action
- 8 The Road to Quantum Mechanics
- Appendix A Newton's Solid of Least Resistance, Using Calculus
- Appendix B Original Statement of d'Alembert's Principle
- Appendix C Equations of Motion of McCullagh's Ether
- Appendix D Characteristic Function for a Parabolic Keplerian Orbit
- Appendix E Saddle Paths for Reflections on a Mirror
- Appendix F Kinetic Caustics from Quantum Motion in One Dimension
- Appendix G Einstein's Proof of the Covariance of Maxwell's Equations
- Appendix H Relativistic Four-Vector Potential
- Appendix I Ehrenfest's Proof of the Adiabatic Theorem
- References
- Index
7 - Relativity and Least Action
Published online by Cambridge University Press: 26 March 2018
- Frontmatter
- Contents
- List of Illustrations
- Acknowledgments
- 1 Introduction
- 2 Prehistory of Variational Principles
- 3 An Excursion to Newton's Principia
- 4 The Optical-Mechanical Analogy, Part I
- 5 D'Alembert, Lagrange, and the Statics-Dynamics Analogy
- 6 The Optical-Mechanical Analogy, Part II: The Hamilton-Jacobi Equation
- 7 Relativity and Least Action
- 8 The Road to Quantum Mechanics
- Appendix A Newton's Solid of Least Resistance, Using Calculus
- Appendix B Original Statement of d'Alembert's Principle
- Appendix C Equations of Motion of McCullagh's Ether
- Appendix D Characteristic Function for a Parabolic Keplerian Orbit
- Appendix E Saddle Paths for Reflections on a Mirror
- Appendix F Kinetic Caustics from Quantum Motion in One Dimension
- Appendix G Einstein's Proof of the Covariance of Maxwell's Equations
- Appendix H Relativistic Four-Vector Potential
- Appendix I Ehrenfest's Proof of the Adiabatic Theorem
- References
- Index
Summary
In 1905, Albert Einstein published a series of papers that constitute an unprecedented display of creativity. The paper Einstein (1905) published in June of this annus mirabilis deals with the theory of relativity, a work that eventually brought Einstein rock-star fame. The first sentence of the essay makes an aesthetic observation: “It is known that Maxwell's electrodynamics, as usually understood at the present time, when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena” (italics added). Einstein discusses the meaning of this asymmetry with an example from the theory of electromagnetism. He observes that a magnet in motion relative to a wire loop produces an electrical current in the wire. According to Maxwell's theory, different equations apply when the magnet moves and the wire is stationary and vice versa. In one case, the magnet is moving with respect to the ether (a universal static substance that acts as the medium for transmission of light) and in the other, the magnet is at rest with respect to the ether. This asymmetry was unacceptable to Einstein. If the current is the same in both cases, then one is looking at the same phenomenon from different perspectives, or from different reference frames, thus making the idea of an ether superfluous. McCullagh's prediction (see the quotation on page 110) of an unexpected, simple and beautiful ether is perhaps fulfilled; non-existence is the ultimate simplicity. The new theory is based on two simple postulates:
The laws of physics take the same form for “all reference frames for which the equations of mechanics hold good” (inertial frames).
Light always propagates in empty space with a velocity c which is independent of the state of motion of the emitting body.
From this starting point, as simple as it is audacious, Einstein leads us through a path of impeccable logic that culminates in the notion that time, represented by the ticking of a wristwatch, is not an absolute phenomenon.
It is remarkable that the equations that Einstein derives existed before his work. In 1895, the Dutch physicist Hendrik A. Lorentz, in order to explain some experiments by Michelson and Morley wrote a set of equations (identical to Einstein's) in which time appeared as a mathematical variable that depended on velocity and position.
- Type
- Chapter
- Information
- The Principle of Least ActionHistory and Physics, pp. 162 - 188Publisher: Cambridge University PressPrint publication year: 2018