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Author: James Read
Publisher: Cambridge University Press
ISBN: 1108786812
Category : Science
Languages : en
Pages : 388
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Book Description
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.
Author: James Read
Publisher: Cambridge University Press
ISBN: 1108786812
Category : Science
Languages : en
Pages : 388
Get Book Here
Book Description
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.
Author: Dwight E. Neuenschwander
Publisher: JHU Press
ISBN: 1421422689
Category : Science
Languages : en
Pages : 338
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Book Description
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.
Author: Yvette Kosmann-Schwarzbach
Publisher: Springer Science & Business Media
ISBN: 0387878688
Category : Mathematics
Languages : en
Pages : 211
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Book Description
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.
Author: Katherine Brading
Publisher: Cambridge University Press
ISBN: 1139442023
Category : Science
Languages : en
Pages : 459
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Book Description
This book brings together philosophical discussions of symmetry in physics, highlighting the main issues and controversies. It covers all the fundamental symmetries of modern physics, as well as discussing symmetry-breaking and general interpretational issues. For each topic, classic texts are followed by review articles and short commentaries.
Author: Antonio Vassallo
Publisher: Taylor & Francis
ISBN: 1000688003
Category : Science
Languages : en
Pages : 298
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Book Description
This book provides an up-to-date overview of the foundations of spacetime physics. It features original essays written by world-class experts in the physics and philosophy of spacetime. The foundational questions regarding the origin and nature of spacetime are branching into new and exciting directions. These questions are not restricted to the quantum gravity program but also arise in the context of a well-established theory like general relativity. Against the background of these quick and diverse developments, this volume features a broad range of perspectives on spacetime. Part I focuses on the nature of spacetime in non-quantum theories, such as Newtonian mechanics and relativity. Part II explores some intriguing conceptual implications of developing a quantum theory of spacetime. The Foundations of Spacetime Physics is an essential resource for scholars and advanced students working in philosophy of physics, philosophy of science, and scientific metaphysics.
Author: Philipp Berghofer
Publisher: Cambridge University Press
ISBN: 1009197312
Category : Science
Languages : en
Pages : 124
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Book Description
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.
Author: James Read
Publisher: Oxford University Press
ISBN: 0192889117
Category : Philosophy
Languages : en
Pages : 159
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Book Description
It is often claimed that Einstein's magnum opus---his 1915 theory of General Relativity---is distinguished from other theories of space and time in virtue of its background independence. It's also often claimed that background independence is an essential feature of any quantum theory of gravity. But are these claims true? This book aspires to offer definitive answers to both of these questions, by (a) charting the space of possible definitions of background independence, and (b) applying said definitions to various classical and quantum theories of gravity. The outcome, in brief, is as follows: General Relativity is not unique by virtue of its background independence (and, indeed, fails to be background independent on some popular definitions); moreover, the situation in the case of quantum theories of gravity is delicate, because (i) there are viable such theories which (by some accounts, at least) fail to be background independent, but also (ii) theories (e.g. perturbative string theory) which have often been dismissed for (allegedly) being background dependent in fact, on many accounts, are better classified as background independent. In giving these answers in rigorous detail, this book seeks to elevate the standards and generality of future discussions of background independence in the foundations of spacetime theories.
Author: Klaas Landsman
Publisher: Radboud University Press
ISBN: 9083178927
Category : Science
Languages : en
Pages : 394
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Book Description
This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.
Author: Yemima Ben-Menahem
Publisher: Springer Nature
ISBN: 3030967751
Category : Science
Languages : en
Pages : 390
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Book Description
This book subjects the traditional concept of law of nature to critical examination. There are two kinds of reasons that invite this reexamination, one deriving from philosophical concerns over the traditional concept, the other motivated by theoretical and practical changes in science. One of the philosophical worries is that the idiom of law of nature, especially when combined with the notion of laws 'governing' individual events and processes, is no longer as intelligible as it used to be in the theistic context in which the formulation of laws became central to science. The traditional concept is also challenged in various ways by contemporary scientific theories such as quantum mechanics, chaos theory and the general theory of relativity. It is no longer clear that there are any universal laws, laws do not always guarantee predictability, and the border between physical and mathematical considerations is constantly shifting. The most difficult challenge, perhaps, is to come up with a scientific explanation of the origin of laws. Wrestling with these intriguing problems, the papers in this volume broaden both our understanding of the natural order and our desiderata of scientific explanation.
Author: Conor Husbands
Publisher: Springer Nature
ISBN: 3030865304
Category : Philosophy
Languages : en
Pages : 306
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Book Description
Metaphysics has often held that laws of nature, if legitimate, must be time-independent. Yet mounting evidence from the foundations of science suggests that this constraint may be obsolete. This book provides arguments against this atemporality conjecture, which it locates both in metaphysics and in the philosophy of science, drawing on developments in a range of fields, from the foundations of physics to the philosophy of finance. It then seeks to excavate an alternative philosophical lineage which reconciles time-dependent laws with determinism, converging in the thought of Immanuel Kant.
