The Lazy Universe
An Introduction to the Principle of Least Action
(Sprache: Englisch)
The Principle of Least Action underlies all physics and leads into quantum mechanics and Einstein's Relativity. There are some textbooks that do the calculations, and one book with nice pictures, but no book (before this one) that explains what 'action' is, and why nature follows this principle.
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Produktinformationen zu „The Lazy Universe “
The Principle of Least Action underlies all physics and leads into quantum mechanics and Einstein's Relativity. There are some textbooks that do the calculations, and one book with nice pictures, but no book (before this one) that explains what 'action' is, and why nature follows this principle.
Klappentext zu „The Lazy Universe “
This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.
Inhaltsverzeichnis zu „The Lazy Universe “
- 1: Introduction
- 2: Antecedents
- 3: Mathematics and physics preliminaries
- 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
- Appendices
- A1.1: Newton's Laws of Motion
- A3.1: Reversible Displacements
- A2.1: Portraits of the physicists
- A6.1: Worked examples in Lagrangian Mechanics
- A6.2: Proof that T is a function of v²
- A6.3: Energy conservation and the homogeneity of time
- A6.4: The method of Lagrange Multipliers
- A6.5: Generalized Forces
- A7.1: Hamilton's Transformation, Examples
- A7.2: Demonstration that the p_s are independent coordinates
- A7.3: Worked examples in Hamiltonian Mechanics
- A7.4: Incompressibility of the phase fluid
- A7.5: Energy conservation in extended phase space
- A7.6: Link between the action, S, and the 'circulation'
- A7.7: Transformation equations linking p and q via S
- A7.8: Infinitesimal canonical transformations
- A7.9: Perpendicularity of wavefronts and rays
- A7.10: Problems solved using the Hamilton-Jacobi Equation
- A7.11: Quasi refractive index in mechanics
- A7.12: Einstein's link between Action and the de Broglie waves
Autoren-Porträt von Jennifer Coopersmith
Jennifer Coopersmith took her PhD in nuclear physics from the University of London, and was later a research fellow at TRIUMF, University of British Columbia. She was for many years an associate lecturer for the Open University (London and Oxford), and was then a tutor on astrophysics courses at Swinburne University of Technology in Melbourne while based at La Trobe University in Bendigo, Victoria. She now lives in France.Bibliographische Angaben
- Autor: Jennifer Coopersmith
- 2017, 288 Seiten, 52 Abbildungen, Maße: 14,9 x 22,5 cm, Gebunden, Englisch
- Verlag: Oxford University Press
- ISBN-10: 0198743041
- ISBN-13: 9780198743040
- Erscheinungsdatum: 19.05.2017
Sprache:
Englisch
Pressezitat
Jennifer Coopersmith has written a most welcome book, the first historically and philosophically motivated full study since two classics written nearly a half-century ago... [She] has attempted and succeeded admirably I believe in her aim to write a modern book on the history and philosophy of the action principles, as well as to give the technical details. Chris Gray, American Journal of Physics
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