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Exotic Smoothness and Physics

Author: Torsten Asselmeyer-Maluga

Publisher: World Scientific

Published: 2007

Total Pages: 339

ISBN-13: 9812706666

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."

Category Theory in Physics, Mathematics, and Philosophy

Author: Marek Kuś

Publisher: Springer Nature

Published: 2019-11-11

Total Pages: 134

ISBN-13: 3030308960

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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.

Questioning the Foundations of Physics

Author: Anthony Aguirre

Publisher: Springer

Published: 2015-01-24

Total Pages: 279

ISBN-13: 3319130455

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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.

Selected Papers from 43rd International Conference of Theoretical Physics

Author: Janusz Gluza

Publisher: MDPI

Published: 2020-03-27

Total Pages: 94

ISBN-13: 3039283707

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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).

At the Frontier of Spacetime

Author: Torsten Asselmeyer-Maluga

Publisher: Springer

Published: 2016-04-28

Total Pages: 308

ISBN-13: 3319312995

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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.

Quantum Gravity

Author: Rodrigo Sobreiro

Publisher: BoD – Books on Demand

Published: 2012-02-15

Total Pages: 114

ISBN-13: 9535100890

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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.

Number Theory and Symmetry

Author: Michel Planat

Publisher: MDPI

Published: 2021-01-20

Total Pages: 206

ISBN-13: 3039366866

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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.

Geometrodynamics of Gauge Fields

Author: Eckehard W. Mielke

Publisher: Springer

Published: 2017-01-22

Total Pages: 377

ISBN-13: 3319297341

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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.

Causality, Measurement Theory and the Differentiable Structure of Space-Time

Author: R. N. Sen

Publisher: Cambridge University Press

Published: 2010-02-11

Total Pages: 413

ISBN-13: 1139485377

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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.

Lumen Naturae

Author: Matilde Marcolli

Publisher: MIT Press

Published: 2020-05-26

Total Pages: 390

ISBN-13: 0262358328

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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.