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Exotic Smoothness And Physics
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Book Synopsis Exotic Smoothness and Physics by : Torsten Asselmeyer-Maluga
Download or read book Exotic Smoothness and Physics written by Torsten Asselmeyer-Maluga and published by World Scientific. This book was released on 2007 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent revolution in differential topology related to the discovery of non-standard (OC exoticOCO) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit OCo but now shown to be incorrect OCo assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, EinsteinOCOs relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models."
Book Synopsis Category Theory in Physics, Mathematics, and Philosophy by : Marek Kuś
Download or read book Category Theory in Physics, Mathematics, and Philosophy written by Marek Kuś and published by Springer Nature. This book was released on 2019-11-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.
Book Synopsis Questioning the Foundations of Physics by : Anthony Aguirre
Download or read book Questioning the Foundations of Physics written by Anthony Aguirre and published by Springer. This book was released on 2015-01-24 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays in this book look at way in which the fundaments of physics might need to be changed in order to make progress towards a unified theory. They are based on the prize-winning essays submitted to the FQXi essay competition “Which of Our Basic Physical Assumptions Are Wrong?”, which drew over 270 entries. As Nobel Laureate physicist Philip W. Anderson realized, the key to understanding nature’s reality is not anything “magical”, but the right attitude, “the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions.” The authors of the eighteen prize-winning essays have, where necessary, adapted their essays for the present volume so as to (a) incorporate the community feedback generated in the online discussion of the essays, (b) add new material that has come to light since their completion and (c) to ensure accessibility to a broad audience of readers with a basic grounding in physics. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.
Book Synopsis Selected Papers from 43rd International Conference of Theoretical Physics by : Janusz Gluza
Download or read book Selected Papers from 43rd International Conference of Theoretical Physics written by Janusz Gluza and published by MDPI. This book was released on 2020-03-27 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the origins of the Universe and how it works and evolves is the present mission of a large community of physicists. It calls for a large scale vision, involving general relativity, astrophysics, and cosmology. Theoretical physics is presently at an important moment in its history. As predicted by Einstein, gravitational waves have been experimentally proven to exist. With the discovery of the Higgs boson, the set of interactions and elementary particles that is called the "standard model" (SM), is complete. Yet the Higgs boson itself, and how it breaks the electroweak symmetry, remains a fascinating subject requiring further studies and verification. Furthermore, several experimental facts are not accounted for by the SM: (i) the baryon asymmetry of the Universe, (ii) the nature and origin of dark matter, and (iii) the origin of neutrino masses; these have no unique, if any, explanation in the SM and yet will require answers from particle physics. We need to explore further both SM and its extensions. This is a subject of papers included in this book, which gives representation to the topics discussed during the Matter to the Deepest conference in 2019 in Poland (http://indico.if.us.edu.pl/event/5).
Book Synopsis At the Frontier of Spacetime by : Torsten Asselmeyer-Maluga
Download or read book At the Frontier of Spacetime written by Torsten Asselmeyer-Maluga and published by Springer. This book was released on 2016-04-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and historical aspects round off the collection.
Book Synopsis Quantum Gravity by : Rodrigo Sobreiro
Download or read book Quantum Gravity written by Rodrigo Sobreiro and published by BoD – Books on Demand. This book was released on 2012-02-15 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unification between gravity and quantum field theory is one of the major problems in contemporary fundamental Physics. It exists for almost one century, but a final answer is yet to be found. Although string theory and loop quantum gravity have brought many answers to the quantum gravity problem, they also came with a large set of extra questions. In addition to these last two techniques, many other alternative theories have emerged along the decades. This book presents a series of selected chapters written by renowned authors. Each chapter treats gravity and its quantization through known and alternative techniques, aiming a deeper understanding on the quantum nature of gravity. Quantum Gravity is a book where the reader will find a fine collection of physical and mathematical concepts, an up to date research, about the challenging puzzle of quantum gravity.
Book Synopsis Number Theory and Symmetry by : Michel Planat
Download or read book Number Theory and Symmetry written by Michel Planat and published by MDPI. This book was released on 2021-01-20 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.
Book Synopsis Geometrodynamics of Gauge Fields by : Eckehard W. Mielke
Download or read book Geometrodynamics of Gauge Fields written by Eckehard W. Mielke and published by Springer. This book was released on 2017-01-22 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.
Book Synopsis Causality, Measurement Theory and the Differentiable Structure of Space-Time by : R. N. Sen
Download or read book Causality, Measurement Theory and the Differentiable Structure of Space-Time written by R. N. Sen and published by Cambridge University Press. This book was released on 2010-02-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.
Download or read book Lumen Naturae written by Matilde Marcolli and published by MIT Press. This book was released on 2020-05-26 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.
Book Synopsis Brazilian Studies in Philosophy and History of Science by : Décio Krause
Download or read book Brazilian Studies in Philosophy and History of Science written by Décio Krause and published by Springer Science & Business Media. This book was released on 2011-01-27 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context.
Book Synopsis On Hilbert's Sixth Problem by : Newton C. A. da Costa
Download or read book On Hilbert's Sixth Problem written by Newton C. A. da Costa and published by Springer Nature. This book was released on 2022-01-25 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico–canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism. The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler–Lagrange equations. The theory of Suppes predicates as the main tool in the axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences. This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set–theoretically generic spacetimes.
Book Synopsis Relativity and Scientific Computing by : Friedrich W Hehl
Download or read book Relativity and Scientific Computing written by Friedrich W Hehl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.
Book Synopsis Quantum Interaction by : Peter Bruza
Download or read book Quantum Interaction written by Peter Bruza and published by Springer. This book was released on 2009-03-18 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Symposium on Quantum Interaction, QI 2009, held in Saarbrücken, Germany, in March 2009. The 21 revised full papers presented together with the 3 position papers were carefully reviewed and selected from numerous submissions. The papers show the cross-disciplinary nature of quantum interaction covering topics such as computation, cognition, decision theory, information retrieval, information systems, social interaction, computational linguistics and finance.
Download or read book Goedel's Way written by Gregory Chaitin and published by CRC Press. This book was released on 2011-10-14 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8
Book Synopsis Gravitation And Cosmology - Proceedings Of The Pacific Conference by : Yongmin Cho
Download or read book Gravitation And Cosmology - Proceedings Of The Pacific Conference written by Yongmin Cho and published by World Scientific. This book was released on 1998-12-08 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry and Mathematical Physics by : Gerd Rudolph
Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
