Einstein introduced quantum entanglement in 1935 and referred to it as “spooky actions at a distance” because it seemed to conflict with his theory of special relativity. Today, some refer to it as "the greatest mystery in physics" and the 2022 Nobel Prize in Physics was even awarded for experimental confirmation of the "spookiness." While the mystery is experimentally well-established, its solution remains elusive because it is commonly believed that quantum entanglement entails that quantum mechanics is incomplete, that the world works according to "spooky actions at a distance," that causes from the future create effects in the present, that there is "superdeterministic" causal control of experimental procedures, that people can correctly disagree on the outcome of one and the same experiment, and that a single experimental measurement can produce all possible outcomes. In this book, a rigorous solution to the mystery of quantum entanglement is provided that entails none of those things. The key to this seemingly impossible feat is - to use Einstein's own language - a "principle" explanation that foregoes the need for any "constructive" explanation of quantum entanglement, such as those listed above. Ironically, the proposed principle explanation is Einstein's own relativity principle as grounded in quantum information theory. So contrary to popular belief, quantum mechanics and special relativity are far from inconsistent, as both are a consequence of the exact same relativity principle.
Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
This text explores medical imaging, one of the most significant areas of recent mathematical applications, in a concise manner accessible to undergraduate students. The author emphasizes the mathematical aspects of medical imaging, including not only the theoretical background, but also the role of approximation methods and the computer implementation of the inversion algorithms. In twenty-first century health care, CAT scans, ultrasounds, and MRIs are commonplace. Significant computational advances, along with the development, design, and improvement of the machines themselves, can only occur in conjunction with a proper understanding of the mathematics. This book is inherently interdisciplinary in nature, and therefore is appropriate for students of engineering, physics, and computer science, in addition to mathematics.
This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Provides fully updated coverage of new experiments in quantum optics This fully revised and expanded edition of a well-established textbook on experiments on quantum optics covers new concepts, results, procedures, and developments in state-of-the-art experiments. It starts with the basic building blocks and ideas of quantum optics, then moves on to detailed procedures and new techniques for each experiment. Focusing on metrology, communications, and quantum logic, this new edition also places more emphasis on single photon technology and hybrid detection. In addition, it offers end-of-chapter summaries and full problem sets throughout. Beginning with an introduction to the subject, A Guide to Experiments in Quantum Optics, 3rd Edition presents readers with chapters on classical models of light, photons, quantum models of light, as well as basic optical components. It goes on to give readers full coverage of lasers and amplifiers, and examines numerous photodetection techniques being used today. Other chapters examine quantum noise, squeezing experiments, the application of squeezed light, and fundamental tests of quantum mechanics. The book finishes with a section on quantum information before summarizing of the contents and offering an outlook on the future of the field. -Provides all new updates to the field of quantum optics, covering the building blocks, models and concepts, latest results, detailed procedures, and modern experiments -Places emphasis on three major goals: metrology, communications, and quantum logic -Presents fundamental tests of quantum mechanics (Schrodinger Kitten, multimode entanglement, photon systems as quantum emulators), and introduces the density function -Includes new trends and technologies in quantum optics and photodetection, new results in sensing and metrology, and more coverage of quantum gates and logic, cluster states, waveguides for multimodes, discord and other quantum measures, and quantum control -Offers end of chapter summaries and problem sets as new features A Guide to Experiments in Quantum Optics, 3rd Edition is an ideal book for professionals, and graduate and upper level students in physics and engineering science.
Highlighting the new aspects of MATLAB 7.10 and expanding on many existing features, this eighth edition continues to offer a hands-on, step-by-step introduction to using the powerful tools of MATLAB. It includes a new chapter on object-oriented programming, a new discussion of the MATLAB File Exchange window, major changes to the MATLAB Editor, and an explanation of more powerful Help tools. It also presents a synopsis of the most frequently used functions, operators, and special characters-providing quick and easy access to frequently used information. M-files and MEX-files for large examples are available at www.crcpress.com
Liquid crystals had a controversial discovery at the end of the 19th century but were later accepted as a 'fourth state' of matter, and finally used throughout the world in modern displays and new materials. This book explains the fascinating science in accessible terms, and puts it into social, political, and historical perspectives.
The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.
Theoretical physics and foundations of physics have not made much progress in the last few decades. Whether we are talking about unifying general relativity and quantum field theory (quantum gravity), explaining so-called dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity, there is no consensus in sight. In addition, both enterprises are deeply puzzled about various facets of time including above all, time as experienced. The authors argue that, across the board, this impasse is the result of the "dynamical universe paradigm," the idea that reality is fundamentally made up of physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. This book offers a completely new paradigm (called Relational Blockworld), whereby the past, present and future co-determine each other via "adynamical global constraints," such as the least action principle. Accordingly, the future is just as important for explaining the present as is the past. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
There is ample evidence that children and adolescents in large numbers are actively using integrative (complementary and alternative) therapies. Various studies now indicate that over 50% of pediatricians surveyed would refer a patient for integrative therapy, and they would welcome more natural therapies for children provided they were safe and effective. However, there has been little training for pediatricians in this area. Integrative Pediatrics addresses these issues and provides guidelines for pediatricians, parents, and general audiences in a balanced, evidence-based manner. In this volume in the Weil Integrative Medicine Library series, the authors describe a rational and evidence-based approach to the integrative therapy of childhood disorders and well-child care, integrating the principles of alternative and complementary therapies into the principles and practice of conventional pediatrics. The authors examine what works and what doesn't and offer practical guidelines for physicians to incorporate integrative medicine into their practice and how to advise patients and their parents on reasonable and effective therapies. The text also covers areas of controversy and identifies areas of uncertainty where future research is needed. Chapters also cite the best available evidence for both safety and efficacy of all therapies discussed. The series editor is Andrew Weil, MD, Professor and Director of the Program of Integrative Medicine at the University of Arizon. Dr. Weil's program was the first academic program in the US and he is the major name in integrative medicine in the US, and well-known around the world. His program's stated goal is "to combine the best ideas and practices of conventional and alternative medicine into cost effective treatments without embracing alternative practices uncritically.
With the spread of the powerhouse MATLAB software into nearly every area of math, science, and engineering, it is important to have a strong introduction to using the software. Updated for version 7.0, MATLAB Primer, Seventh Edition offers such an introduction as well as a "pocketbook" reference for everyday users of the software. It offers an intu
This insightful book introduces the most important trends, people, events, and products of popular culture in Latin America and the Caribbean. In recent times, Latin American influences have permeated American culture through music, movies, television, and literature. This sweeping volume serves as a ready-reference guide to pop culture in Central America, South America, and the Caribbean, focusing on Mexico, Brazil, Venezuela, Argentina, Haiti, Cuba, the Dominican Republic, Jamaica, and Costa Rica, among other areas. The work encourages hands-on engagement with the popular culture in these places, making such suggestions as Brazilian films to rent or where to find Venezuelan music on the Internet. To start, the book covers various perspectives and issues of these regions, including the influence of the United States, how the idea of machismo reflects on the portrayal of women in these societies, and the representation of Latino-Caribo cultures in film and other mediums. Entries cover key trends, people, events, and products from the beginning of the 20th century to the present day. Each section gives detailed information and profound insights into some of the more academic—and often controversial—debates on the subject, while the inclusion of the Internet, social media, and video games make the book timely and relevant.
Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as "infinity,” "curved space,” and "imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.
It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).
In this global introduction to philosophy of religion you begin not with a single tradition, but with religious philosophies from East Asia, South Asia, West Africa, and Native North America, alongside the classical Abrahamic and modern European traditions. Matching this diversity of traditions, chapters are organized around questions that acknowledge there is no single understanding of any god or ultimate reality. Instead you approach six different traditions of philosophizing about religion by asking questions about the journeys of both the self and the cosmos such as “What is my path?” and “Where did the cosmos come from?” Accompanied by introductory materials and an extensive glossary, each chapter includes learning objectives, questions for discussion, and suggested primary and secondary sources. The categories of religion and philosophy are interrogated throughout. Equipped with study tools and universal questions about the self and the cosmos, Philosophies of Religion: A Global and Critical Introduction shows you how to philosophize about religions around the world.
An expansive, yet succinct, analysis of the Philosophy of Religion – from metaphysics through theology. Organized into two sections, the text first examines truths concerning what is possible and what is necessary. These chapters lay the foundation for the book’s second part – the search for a metaphysical framework that permits the possibility of an ultimate explanation that is correct and complete. A cutting-edge scholarly work which engages with the traditional metaphysician’s quest for a true ultimate explanation of the most general features of the world we inhabit Develops an original view concerning the epistemology and metaphysics of modality, or truths concerning what is possible or necessary Applies this framework to a re-examination of the cosmological argument for theism Defends a novel version of the Leibnizian cosmological argument
Metaphors of inscription and writing figure prominently in all levels of discourse in and about science. The description of nature as a book written in the language of mathematics has been a common trope since at least the time of Galileo, a metaphor supplemented in our own day by the characterization of DNA sequences as the code for the book of life, decipherable in terms of protein semantic units. An important recent direction in the fields of science and literature studies is to consider such descriptions as more than metaphoric, as revelatory of the processes of signification in science more generally. Nearly everywhere we look, the "semiotic turn” is upon us. Recent science and technology studies have been characterized by a rich diversity of research directions, manifesting several trends apparently counter to one another. On the one hand stands the rich tradition of detailed microstudies of experiments, instruments, and scientific practice; on the other hand are grouped studies grander in scope, aimed at examining science within the framework of cultural production. This volume of sixteen essays seeks common ground among these different approaches by juxtaposing work from historically focused science and literature studies with work inspired by poststructuralist philosophy and semiotics. The contributors are Gillian Beer, Lisa Bloom, Robert Brain, Lorraine Daston, Richard M. Doyle, David Gugerli, Hans Ulrich Gumbrecht, Friedrich Kittler, Timothy Lenoir, Alex Pang, Philip Prodger, Hans-Jörg Rheinberger, Robin Rider, Brian Rotman, Simon Schaffer, and Bernhard Siegert.
Explores computer-intensive probability and statistics for ecosystem management decision making Simulation is an accessible way to explain probability and stochastic model behavior to beginners. This book introduces probability and statistics to future and practicing ecosystem managers by providing a comprehensive treatment of these two areas. The author presents a self-contained introduction for individuals involved in monitoring, assessing, and managing ecosystems and features intuitive, simulation-based explanations of probabilistic and statistical concepts. Mathematical programming details are provided for estimating ecosystem model parameters with Minimum Distance, a robust and computer-intensive method. The majority of examples illustrate how probability and statistics can be applied to ecosystem management challenges. There are over 50 exercises – making this book suitable for a lecture course in a natural resource and/or wildlife management department, or as the main text in a program of self-study. Key features: Reviews different approaches to wildlife and ecosystem management and inference. Uses simulation as an accessible way to explain probability and stochastic model behavior to beginners. Covers material from basic probability through to hierarchical Bayesian models and spatial/ spatio-temporal statistical inference. Provides detailed instructions for using R, along with complete R programs to recreate the output of the many examples presented. Provides an introduction to Geographic Information Systems (GIS) along with examples from Quantum GIS, a free GIS software package. A companion website featuring all R code and data used throughout the book. Solutions to all exercises are presented along with an online intelligent tutoring system that supports readers who are using the book for self-study.
This book presents an ethical theory for financial transactions that underpins the stability of modern economies. It combines elements from history, ethics, economics and mathematics to show how these combined can be used to develop a pragmatic theory of financial markets. Written in three sections; section one examines the co-evolution of finance and mathematics in an ethical context by focusing on three periods: pre-Socratic Greece, Western Europe in the thirteenth century and North-western Europe in the seventeenth century to demonstrate how the historical development of markets and finance were critical in the development of European ideas of science and democracy. Section two interprets the evidence presented in section one to provide examples of the norms reciprocity, sincerity and charity and introduce the pragmatic theory. Section three uses the pragmatic theory to interpret recent financial crises, address emergent phenomena and relate the theory to alternative contemporary theories of markets. Presenting a unique synthesis of mathematical and behavioural approaches to finance this book provides explicit ethical guidance that will be of interest to academics and practitioners alike.
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