Exotic Smoothness And Physics
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Exotic Smoothness And Physics Differential Topology And Spacetime Models
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Author : Torsten Asselmeyer-maluga
language : en
Publisher: World Scientific
Release Date : 2007-01-23
Exotic Smoothness And Physics Differential Topology And Spacetime Models written by Torsten Asselmeyer-maluga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-23 with Science categories.
The recent revolution in differential topology related to the discovery of non-standard (”exotic”) 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 — but now shown to be incorrect — assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's 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.
Exotic Smoothness And Physics
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Author : Torsten Asselmeyer-Maluga
language : en
Publisher: World Scientific
Release Date : 2007
Exotic Smoothness And Physics written by Torsten Asselmeyer-Maluga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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."
Wild Fractal Nature Of Spacetime The Smooth Quantum Gravity And Cosmology
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Author : Torsten Asselmeyer-maluga
language : en
Publisher: World Scientific
Release Date : 2025-06-13
Wild Fractal Nature Of Spacetime The Smooth Quantum Gravity And Cosmology written by Torsten Asselmeyer-maluga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-13 with Science categories.
Covering 20 years of Dr Torsten Asselmeyer-Maluga's research, this book shall be viewed as a second volume to Exotic Smoothness and Physics (written in collaboration with Prof. Carl Brans).A prominent question that the author tries to find an answer to is, how does specific physics emerge from the abstract mathematics of 4-manifolds? The key idea to that question is Smooth Quantum Gravity, a theory based on very few principles and therefore easily understood. Through the application of this theory, a connection between geometry/topology and quantum physics is created.In The Wild Fractal Nature of Spacetime, Dr Torsten Asselmeyer-Maluga explains Smooth Quantum Gravity and applies it to the standard cosmological model. Through that, the inflationary expansion of the cosmos is introduced, the cosmological constant is calculated, dark matter is shown as a direct consequence and the Big Bang is described as well. The entire concept of the cosmos is based on a model of spacetime, which is based on 4 simple axioms and thus uniquely defines it. As a result, measurable quantities such as the inflation rate and the cosmological constant can be calculated and compared with the measurement results of the PLANCK mission, for instance.However, the results on inflation theory, the cosmological constant and dimensional reduction can be understood and used independently from an exotic smoothness structure — no prior knowledge on the topic is required.The author recommends his book to scientists and interested students who see the world through the lens of geometry and physics.
Quantum Gravity
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Author : Rodrigo Sobreiro
language : en
Publisher: BoD – Books on Demand
Release Date : 2012-02-15
Quantum Gravity written by Rodrigo Sobreiro and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-15 with Science categories.
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.
At The Frontier Of Spacetime
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Author : Torsten Asselmeyer-Maluga
language : en
Publisher: Springer
Release Date : 2016-04-28
At The Frontier Of Spacetime written by Torsten Asselmeyer-Maluga and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Science categories.
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.
Number Theory And Symmetry
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Author : Michel Planat
language : en
Publisher: MDPI
Release Date : 2021-01-20
Number Theory And Symmetry written by Michel Planat and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Computers categories.
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.
Causality Measurement Theory And The Differentiable Structure Of Space Time
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Author : R. N. Sen
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11
Causality Measurement Theory And The Differentiable Structure Of Space Time written by R. N. Sen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-11 with Science categories.
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.
Selected Papers From 43rd International Conference Of Theoretical Physics
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Author : Janusz Gluza
language : en
Publisher: MDPI
Release Date : 2020-03-27
Selected Papers From 43rd International Conference Of Theoretical Physics written by Janusz Gluza and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-27 with Science categories.
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).
Lumen Naturae
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Author : Matilde Marcolli
language : en
Publisher: MIT Press
Release Date : 2020-05-26
Lumen Naturae written by Matilde Marcolli and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-26 with Mathematics categories.
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.
Relativity And Scientific Computing
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Author : Friedrich W Hehl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Relativity And Scientific Computing written by Friedrich W Hehl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.