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The Philosophy and Physics of Noether's Theorems by James Read,Nicholas J. Teh Pdf
In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be generalised, and the physical applications of her results continue to diversify. This centenary volume brings together world-leading historians, philosophers, physicists, and mathematicians in order to clarify the historical context of this work, its foundational and philosophical consequences, and its myriad physical applications. Suitable for advanced undergraduate and graduate students and professional researchers, this is a go-to resource for those wishing to understand Noether's work on variational problems and the profound applications which it finds in contemporary physics.
The Noether Theorems by Yvette Kosmann-Schwarzbach Pdf
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.
Emmy Noether's Wonderful Theorem by Dwight E. Neuenschwander Pdf
One of the most important—and beautiful—mathematical solutions ever devised, Noether’s theorem touches on every aspect of physics. "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."—Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. Noether’s “first” and “second” theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s “first” theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the “second” theorem, including Noether’s resolution of concerns about general relativity. Other refinements in the new edition include an enlarged biography of Emmy Noether’s life and work, parallels drawn between the present approach and Noether’s original 1918 paper, and a summary of the logic behind Noether’s theorem.
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
Noether's Theorem and Symmetry by P.G.L. Leach,Andronikos Paliathanasis Pdf
In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.
The Philosophy of Symmetry by Nicholas Joshua Yii Wye Teh Pdf
This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.
The Noether Theorems by Yvette Kosmann-Schwarzbach Pdf
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the vario.
Philosophy of Physics by Jeremy Butterfield,John Earman Pdf
The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers
Problems in the Foundations of Physics by M. Bunge Pdf
This is a collection of technical papers in the foundations and the philoso It takes both "foundations" phy of physics with emphasis on the former. and "philosophy" in their narrow technical senses but it construes "physics" lato sensu, as including all the sciences of nonliving systems. All eleven papers constituting this volume were written for it. The problems tackled in this book concern certain basic concepts, hypotheses, theories, and research programmes in physical science. Some of these problems are topical, others new, but they are all fundamental and the subject of research and controversy. Consequently this volume is expected to serve those students, teachers and researchers who enjoy learning, teaching, discussing or doing theoretical physics. It is addressed to the nine to niners rather than to the nine to fivers. It is expected to attract the theoretician in search for new basic ideas, the teacher eager to perfect his understanding of physical theory and transmit his own zeal and his own doubts, as well as the student anxious to get down to essentials. This book may also interest the mathematician for whom physics offers a challenge (or a good pretext). Finally, it should get the attention of the philosopher of science aware of the advantages of philosophizing on foundations research problems rather than on the popularization of some results of research. There are at least two reasons for valuing foundations research.
The Brauer-Hasse-Noether Theorem in Historical Perspective by Peter Roquette Pdf
The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept at the Handschriftenabteilung of the University Library at Göttingen. Hasse had an extensive correspondence; he liked to exchange mathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical interest, searching through this treasure can help us to assess the development of Number Theory through the 1920s and 1930s. The present volume is largely based on the letters and other documents its author has found concerning the Brauer-Hasse-Noether Theorem in the theory of algebras; this covers the years around 1931. In addition to the documents from the literary estates of Hasse and Brauer in Göttingen, the author also makes use of some letters from Emmy Noether to Richard Brauer that are preserved at the Bryn Mawr College Library (Pennsylvania, USA).
Named for the noted mathematician, the Emmy Noether Research Institute for Mathematics held a two-day conference dedicated to her heritage and her influence on mathematics and physics in the 20th and 21st centuries. This volume presents the proceedings of that conference. It includes a comprehensive description of Noether's contributions to commutative and noncommutative algebra, algebraic geometry, topology, and physics given by world experts in these fields. Also included is a profile of her life. The volume is a comprehensive collection of Noether's valuable contributions to mathematics and physics.
Bridging the Gap: Philosophy, Mathematics, and Physics by G. Corsi,Maria Luisa Dalla Chiara,Giancarlo Ghirardi Pdf
Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general `malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.
Polish Essays in the Philosophy of the Natural Sciences by W. Krajewski Pdf
Modern philosophy has benefited immensely from the intelligence and sensitivity, the creative and critical energies, and the lucidity of Polish scholars. Their investigations into the logical and methodological founda tions of mathematics, the physical and biological sciences, ethics and esthetics, psychology, linguistics, economics and jurisprudence, and the social sciences - all are marked by profound and imaginative work. To the centers of empiricist philosophy of science in Vienna, Berlin and Cambridge during the first half of this century, one always added the great school of analytic and methodological studies in Warsaw and Lw6w. To the world centers of Marxist theoretical practice in Berlin, Moscow, Paris, Rome and elsewhere, one must add the Poland of the same era, from Ludwig Krzywicki (1859-1941) onward. (From our preface to Wiatr [1979p. Other movements also have been distinctive in Poland. Phenomenology was developed in the impressive school of Roman Ingarden at Cracow, semiotics from the early work of the philosopher and psychologist Kazimierz Twardowski at Lw6w in the 1890's, with masterful develop ment by his disciples Kotarbinski and Ajdukiewicz onward, conceptual foundations of physics in the incisive methodological reflections of Marian Smoluchowski, and mathematical logic from Jan I:.ukasiewicz and Stanislaw Lesniewski to Tarski, Mostowski, and many others.
