*Jennifer Coopersmith*

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198716747
- eISBN:
- 9780191800955
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716747.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Energy is explained through its history. Newton missed ‘energy’, Leibniz defined kinetic energy, and potential energy emerged from ideas about stored ‘live force’, the concept of ‘work’, analyses of ...
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Energy is explained through its history. Newton missed ‘energy’, Leibniz defined kinetic energy, and potential energy emerged from ideas about stored ‘live force’, the concept of ‘work’, analyses of vibrating strings, the figure of the Earth, and so forth. The Principles of Virtual Work, Least Action, and D’Alembert underpinned Lagrange’s Analytical Mechanics. Daniel Bernoulli appreciated energy-in-the-round, and quantified the ‘live force’ in coal. Rumford’s experiments on canon-boring showed an ‘inexhaustible’ source of frictional heating, but didn’t immediately topple caloric theory. Clairaut, Laplace, and Green founded potential function theory. Hamilton brought in the ‘Hamiltonian’, and his approach led into Schrödinger’s wave mechanics. Carnot defined an ideal heat-engine (Carnot cycle) and realized temperature was the parameter. Watt’s steam engine started the Industrial Revolution, but why was it discovered in just one place, at one time? Mayer and Joule crossed the ‘category error’, merging mechanics and heat. Helmholtz invoked Kantian ‘cause equals effect’ to justify conservation of ‘energy’. Maxwell was the first to use probability theory in physics; Boltzmann posited discrete energy levels. The Maxwell–Boltzmann kinetic theory brought in a deeper understanding of energy. Clausius and Thomson (Kelvin) discovered the First and Second Laws of Thermodynamics. Einstein’s Principle of Relativity led to the famous E = mc2. The force and energy views are compared, and difficult questions are examined: why are there two forms of energy–kinetic and potential–and is one more fundamental? Why does kinetic energy have the form 1/2mv2? What are action, temperature, and the Hamiltonian? What is energy?Less

Energy is explained through its history. Newton missed ‘energy’, Leibniz defined kinetic energy, and potential energy emerged from ideas about stored ‘live force’, the concept of ‘work’, analyses of vibrating strings, the figure of the Earth, and so forth. The Principles of Virtual Work, Least Action, and D’Alembert underpinned Lagrange’s *Analytical Mechanics.* Daniel Bernoulli appreciated energy-in-the-round, and quantified the ‘live force’ in coal. Rumford’s experiments on canon-boring showed an ‘inexhaustible’ source of frictional heating, but didn’t immediately topple caloric theory. Clairaut, Laplace, and Green founded potential function theory. Hamilton brought in the ‘Hamiltonian’, and his approach led into Schrödinger’s wave mechanics. Carnot defined an ideal heat-engine (Carnot cycle) and realized temperature was *the* parameter. Watt’s steam engine started the Industrial Revolution, but why was it discovered in just one place, at one time? Mayer and Joule crossed the ‘category error’, merging mechanics and heat. Helmholtz invoked Kantian ‘cause equals effect’ to justify conservation of ‘energy’. Maxwell was the first to use probability theory in physics; Boltzmann posited discrete energy levels. The Maxwell–Boltzmann kinetic theory brought in a deeper understanding of energy. Clausius and Thomson (Kelvin) discovered the First and Second Laws of Thermodynamics. Einstein’s Principle of Relativity led to the famous *E = mc*^{2}. The force and energy views are compared, and difficult questions are examined: why are there two forms of energy–kinetic and potential–and is one more fundamental? Why does kinetic energy have the form 1/2*mv*^{2}? What are action, temperature, and the Hamiltonian? What is energy?

*Jennifer Coopersmith*

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198743040
- eISBN:
- 9780191802966
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198743040.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and ...
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Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton’s Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While there is still some mathematics in the main text, the reader may select whether to work through, skim-read, or skip over it: the “story-line” will just about be maintained whatever route is chosen. The work is a much-reduced and simplified version of the outstanding text, “The Variational Principles of Mechanics” written by Cornelius Lanczos in 1949. That work is barely known today, and the present work may be considered as a tiny stepping-stone toward it. A principle that underlies all of physics will have wider repercussions; it is also to be appreciated in an aesthetic sense. It is hoped that this book will lead the reader to the widest possible understanding of the Principle of Least Action. Ideas such as Variational Mechanics, phase space, Fermat’s Principle, and Noether’s Theorem are explained.Less

Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton’s Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While there is still some mathematics in the main text, the reader may select whether to work through, skim-read, or skip over it: the “story-line” will just about be maintained whatever route is chosen. The work is a much-reduced and simplified version of the outstanding text, “The Variational Principles of Mechanics” written by Cornelius Lanczos in 1949. That work is barely known today, and the present work may be considered as a tiny stepping-stone toward it. A principle that underlies all of physics will have wider repercussions; it is also to be appreciated in an aesthetic sense. It is hoped that this book will lead the reader to the widest possible understanding of the Principle of Least Action. Ideas such as Variational Mechanics, phase space, Fermat’s Principle, and Noether’s Theorem are explained.

*Helge Kragh*

- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198722892
- eISBN:
- 9780191789564
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722892.001.0001
- Subject:
- Physics, History of Physics, Particle Physics / Astrophysics / Cosmology

This book is a different way of telling the story about how our modern picture of the universe came into being. From about 1910 to 1970 cosmology underwent a revolutionary change from a somewhat ...
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This book is a different way of telling the story about how our modern picture of the universe came into being. From about 1910 to 1970 cosmology underwent a revolutionary change from a somewhat speculative theory of the classical, static universe to an observationally based science of the expanding universe starting in a big bang. The book tells the fascinating story of how modern cosmology developed, and it does so in an unusual format that blends factual and fictional elements. It is based on a series of recently unearthed interviews that an imagined person (CCN) conducted over a long period of time with distinguished astronomers and physicists. Among the interviewed scientists are giants such as Albert Einstein, Edwin Hubble, and George Gamow, but also scientists who are less well known today or not primarily known as cosmologists. They include Karl Schwarzschild, Paul Dirac, and Svante Arrhenius. The last of the interviews is from the summer of 1965, shortly after the discovery of the cosmic microwave background. By following the interviews the reader gets a lively and “almost authentic” impression of the problems that faced the early generation of cosmologists–and that even before cosmology became recognized as a proper science. Although the interviews are purely fictional, a product of the author’s imagination, they could have taken place just as reported. They are solidly based on historical facts and are supplemented with careful annotations and references to the literature. In this way the book bridges the gap between scholarly and popular history of science.Less

This book is a different way of telling the story about how our modern picture of the universe came into being. From about 1910 to 1970 cosmology underwent a revolutionary change from a somewhat speculative theory of the classical, static universe to an observationally based science of the expanding universe starting in a big bang. The book tells the fascinating story of how modern cosmology developed, and it does so in an unusual format that blends factual and fictional elements. It is based on a series of recently unearthed interviews that an imagined person (CCN) conducted over a long period of time with distinguished astronomers and physicists. Among the interviewed scientists are giants such as Albert Einstein, Edwin Hubble, and George Gamow, but also scientists who are less well known today or not primarily known as cosmologists. They include Karl Schwarzschild, Paul Dirac, and Svante Arrhenius. The last of the interviews is from the summer of 1965, shortly after the discovery of the cosmic microwave background. By following the interviews the reader gets a lively and “almost authentic” impression of the problems that faced the early generation of cosmologists–and that even before cosmology became recognized as a proper science. Although the interviews are purely fictional, a product of the author’s imagination, they could have taken place just as reported. They are solidly based on historical facts and are supplemented with careful annotations and references to the literature. In this way the book bridges the gap between scholarly and popular history of science.

*John Iliopoulos*

- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198805175
- eISBN:
- 9780191843259
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805175.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Why do most ‘elementary particles’ which form the constituents of all matter have a non-zero mass? Strange question, apparently in contradiction with our physical intuition. In this little book we ...
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Why do most ‘elementary particles’ which form the constituents of all matter have a non-zero mass? Strange question, apparently in contradiction with our physical intuition. In this little book we attempt to explain that the question is far from being trivial and that the answer can be found in the recent discovery of a new particle in the Large Hadron Collider (LHC) at CERN near Geneva. We offer the reader a guided tour, starting from the tiny fractions of a second after the Big Bang, when all particles have been created, to the present experiments we perform in our laboratories. We show that the Universe follows a profound symmetry principle which seems to determine the structure of the world.Less

Why do most ‘elementary particles’ which form the constituents of all matter have a non-zero mass? Strange question, apparently in contradiction with our physical intuition. In this little book we attempt to explain that the question is far from being trivial and that the answer can be found in the recent discovery of a new particle in the Large Hadron Collider (LHC) at CERN near Geneva. We offer the reader a guided tour, starting from the tiny fractions of a second after the Big Bang, when all particles have been created, to the present experiments we perform in our laboratories. We show that the Universe follows a profound symmetry principle which seems to determine the structure of the world.