The Lazy Universe

An Introduction to the Principle of Least Action
Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0191060720
Category: Science
Page: 272
View: 8976

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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.

The Lazy Universe

An Introduction to the Principle of Least Action
Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0191060739
Category: Science
Page: 272
View: 8059

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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.

The Lazy Universe

An Introduction to the Principle of Least Action
Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0198743041
Category:
Page: 272
View: 1929

Continue Reading →

This book is about 'action' and the Principle of Least Action. 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). The present book is no mere copy with the difficult bits left out. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

Energy, the Subtle Concept

The discovery of Feynman's blocks from Leibniz to Einstein
Author: Jennifer Coopersmith
Publisher: OUP Oxford
ISBN: 0191057509
Category: Science
Page: 432
View: 5569

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Energy is at the heart of physics and of huge importance to society and yet no book exists specifically to explain it, and in simple terms. In tracking the history of energy, this book is filled with the thrill of the chase, the mystery of smoke and mirrors, and presents a fascinating human-interest story. Moreover, following the history provides a crucial aid to understanding: this book explains the intellectual revolutions required to comprehend energy, revolutions as profound as those stemming from Relativity and Quantum Theory. Texts by Descartes, Leibniz, Bernoulli, d'Alembert, Lagrange, Hamilton, Boltzmann, Clausius, Carnot and others are made accessible, and the engines of Watt and Joule are explained. Many fascinating questions are covered, including: - Why just kinetic and potential energies - is one more fundamental than the other? - What are heat, temperature and action? - What is the Hamiltonian? - What have engines to do with physics? - Why did the steam-engine evolve only in England? - Why S=klogW works and why temperature is IT. Using only a minimum of mathematics, this book explains the emergence of the modern concept of energy, in all its forms: Hamilton's mechanics and how it shaped twentieth-century physics, and the meaning of kinetic energy, potential energy, temperature, action, and entropy. It is as much an explanation of fundamental physics as a history of the fascinating discoveries that lie behind our knowledge today.

The Principle of Least Action

History and Physics
Author: Alberto Rojo,Anthony Bloch
Publisher: Cambridge University Press
ISBN: 0521869021
Category: Mathematics
Page: 278
View: 9708

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This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.

The Variational Principles of Mechanics


Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486134709
Category: Science
Page: 464
View: 9977

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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Lagrangian Interaction

An Introduction To Relativistic Symmetry In Electrodynamics And Gravitation
Author: Noel Doughty
Publisher: CRC Press
ISBN: 0429973160
Category: Science
Page: 592
View: 1487

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This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

Algebraic Equations

An Introduction to the Theories of Lagrange and Galois
Author: Edgar Dehn
Publisher: Courier Corporation
ISBN: 0486155102
Category: Mathematics
Page: 224
View: 9269

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Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.

Noise Theory and Application to Physics

From Fluctuations to Information
Author: Philippe Réfrégier
Publisher: Springer Science & Business Media
ISBN: 0387225269
Category: Science
Page: 288
View: 1943

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This is a unique approach to noise theory and its application to physical measurements that will find its place among the graduate course books. In a very systematic way, the foundations are laid and applied in a way that the book will also be useful to those not focusing on optics. Exercises and solutions help students to deepen their knowledge.

The Principle of Least Action in Geometry and Dynamics


Author: Karl Friedrich Siburg
Publisher: Springer
ISBN: 3540409858
Category: Mathematics
Page: 132
View: 4068

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New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.

Perfect Form

Variational Principles, Methods, and Applications in Elementary Physics
Author: Don Stephen Lemons
Publisher: Princeton University Press
ISBN: 9780691026633
Category: Science
Page: 117
View: 7238

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What does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes, and many artificial ones, manifest such "perfect form" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary. Perfect Form introduces the basic "variational" principles of classical physics (least time, least potential energy, least action, and Hamilton's principle), develops the mathematical language most suited to their application (the calculus of variations), and presents applications from the physics usually encountered in introductory course sequences. The text gradually unfolds the physics and mathematics. While other treatments postulate Hamilton's principle and deduce all results from it, Perfect Form begins with the most plausible and restricted variational principles and develops more powerful ones through generalization. One selection of text and problems even constitutes a non-calculus of variations introduction to variational methods, while the mathematics more generally employed extends only to solving simple ordinary differential equations. Perfect Form is designed to supplement existing classical mechanics texts and to present variational principles and methods to students who approach the subject for the first time.

Quantum concepts in space and time


Author: Roger Penrose,C. J. Isham
Publisher: Oxford University Press, USA
ISBN: N.A
Category: Philosophy
Page: 358
View: 4960

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Recent developments in quantum theory have focused attention on fundamental questions, in particular on whether it might be necessary to modify quantum mechanics to reconcile quantum gravity and general relativity. This book is based on a conference held in Oxford in the spring of 1984 to discuss quantum gravity. It brings together contributors who examine different aspects of the problem, including the experimental support for quantum mechanics, its strange and apparently paradoxical features, its underlying philosophy, and possible modifications to the theory.

The Physics of Quantum Mechanics


Author: James Binney,David Skinner
Publisher: Oxford University Press
ISBN: 0199688575
Category: Science
Page: 392
View: 2758

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"First published by Cappella Archive in 2008."

The Physical World

An Inspirational Tour of Fundamental Physics
Author: Nicholas Manton,Nicholas Mee
Publisher: Oxford University Press
ISBN: 0198795939
Category: Science
Page: 608
View: 3029

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"It is over half a century since The Feynman lectures on physics were published. A new authoritative account of fundamental physics covering all branches of the subject is now well overdue. The physical world has been written to satisfy this need."--Back cover.

The Origin of Mass

Elementary Particles and Fundamental Symmetries
Author: John Iliopoulos
Publisher: Oxford University Press
ISBN: 0192527533
Category: Science
Page: 176
View: 3037

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The discovery of a new elementary particle at the Large Hadron Collider at CERN in 2012 made headlines in world media. Since we already know of a large number of elementary particles, why did this latest discovery generate so much excitement? This small book reveals that this particle provides the key to understanding one of the most extraordinary phenomena which occurred in the early Universe. It introduces the mechanism that made possible, within tiny fractions of a second after the Big Bang, the generation of massive particles. The Origin of Mass is a guided tour of cosmic evolution, from the Big Bang to the elementary particles we study in our accelerators today. The guiding principle of this book is a concept of symmetry which, in a profound and fascinating way, seems to determine the structure of the Universe.

Space, Time, and Stuff


Author: Frank Arntzenius,Cian Dorr
Publisher: Oxford University Press (UK)
ISBN: 0198705913
Category: Philosophy
Page: 288
View: 6305

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Frank Arntzenius presents a series of radical new ideas about the structure of space and time. Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one's peril!

Introduction to the Theory of Distributions


Author: Friedrich Gerard Friedlander,Mark Suresh Joshi
Publisher: Cambridge University Press
ISBN: 9780521649711
Category: Mathematics
Page: 175
View: 3151

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The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.

Conjuring the Universe

The Origins of the Laws of Nature
Author: Peter Atkins
Publisher: Oxford University Press
ISBN: 0198813376
Category: Science
Page: 208
View: 3494

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The marvellous complexity of the Universe emerges from several deep laws and a handful of fundamental constants that fix its shape, scale, and destiny. There is a deep structure to the world which at the same time is simple, elegant, and beautiful. Where did these laws and these constants come from? And why are the laws so fruitful when written in the language of mathematics? Peter Atkins considers the minimum effort needed to equip the Universe with its laws and its constants. He explores the origin of the conservation of energy, of electromagnetism, of classical and quantum mechanics, and of thermodynamics, showing how all these laws spring from deep symmetries. The revolutionary result is a short but immensely rich weaving together of the fundamental ideas of physics. With his characteristic wit, erudition, and economy, Atkins sketches out how the laws of Nature can spring from very little. Or arguably from nothing at all.

Before Time Began

The Big Bang and the Emerging Universe
Author: Helmut Satz
Publisher: Oxford University Press
ISBN: 0198792425
Category: Science
Page: 192
View: 1486

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What is the origin of the universe? What was there before the universe appeared? We are currently witnessing a second Copernican revolution: neither our Earth and Sun, nor our galaxy, nor even our universe, are the end of all things. Beyond our world, in an endless multiverse, are innumerable other universes, coming and going, like ours or different. Fourteen billion years ago, one of the many bubbles constantly appearing and vanishing in the multiverse exploded to form our universe. The energy liberated in the explosion provided the basis for all the matter our universe now contains. But how could this hot, primordial plasma eventually produce the complex structure of our present world? Does not order eventually always lead to disorder, to an increase of entropy? Modern cosmology is beginning to find out how it all came about and where it all might lead. Before Time Began tells that story.