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Quantum Untangling: An Intuitive Approach to Quantum Mechanics from Einstein to Higgs
by Simon SherwoodQuantum Untangling Non-technical and accessible primer providing key foundational knowledge on quantum mechanics and quantum field theory Quantum Untangling introduces the readers to the fascinating and strange realm of quantum mechanics and quantum field theory, written in an accessible manner while not shying away from using mathematics where necessary. The book goes into sufficient depth and conveys basic and more intricate concepts such as wave-particle duality, wave functions, the superposition principle, quantum tunneling, the quantum harmonic oscillator, the Dirac equation, and Feynman diagrams. It also covers the physics of the Higgs boson and provides a glimpse into string theory and loop quantum gravity. Overall, the author introduces complex concepts of quantum mechanics in an accessible and fun-to-read manner while laying the groundwork for mastering an advanced level of treatment in standard quantum mechanics textbooks and university courses. Quantum Untangling includes information on: Special relativity, time and length distortion, Einstein’s famous equation, how Einstein figured it out, and the implications for energy, mass and momentum Wave particle duality, discussing what classical physics cannot explain, quanta of light and the photoelectric effect, De Broglie’s crazy idea, and the double-slit experiment Making sense of Schrödinger’s equation, angular momentum and the wave function, angular rotational energy, atomic structure and molecular bonds Spin, Quantum Electrodynamics, gauge invariance, the strong and weak forces, plus a step-by-step description of the Higgs mechanism With Quantum Untangling, any reader with a good grasp of and an above-average interest in mathematics at advanced high-school level can follow the presentation and acquaint themselves with the fundamental and advanced topics of quantum mechanics and quantum field theory, making it a helpful resource for many different students.
Quantum Variational Calculus
by Agnieszka B. Malinowska Delfim F. M. TorresThis Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.
Quantum versus Classical Mechanics and Integrability Problems: towards a unification of approaches and tools
by Maciej BłaszakThis accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Quantum Walks and Search Algorithms (Quantum Science and Technology)
by Renato PortugalThe revised edition of this book offers an extended overview of quantum walks and explains their role in building quantum algorithms, in particular search algorithms.Updated throughout, the book focuses on core topics including Grover's algorithm and the most important quantum walk models, such as the coined, continuous-time, and Szedgedy's quantum walk models. There is a new chapter describing the staggered quantum walk model. The chapter on spatial search algorithms has been rewritten to offer a more comprehensive approach and a new chapter describing the element distinctness algorithm has been added. There is a new appendix on graph theory highlighting the importance of graph theory to quantum walks.As before, the reader will benefit from the pedagogical elements of the book, which include exercises and references to deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks.Review of the first edition:“The book is nicely written, the concepts are introduced naturally, and many meaningful connections between them are highlighted. The author proposes a series of exercises that help the reader get some working experience with the presented concepts, facilitating a better understanding. Each chapter ends with a discussion of further references, pointing the reader to major results on the topics presented in the respective chapter.” - Florin Manea, zbMATH.
Quantum Walks and Search Algorithms
by Renato PortugalThis book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operatorAnalytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transformsQuantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing timeSpatial search algorithms, with emphasis on the abstract search algorithm (the two-dimensional lattice is used as an example)Szedgedy's quantum-walk model and a natural definition of quantum hitting time (the complete graph is used as an example)The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature. Exercises and references further deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks are also provided.
Quantum Waveguides
by Pavel Exner Hynek KovaříkThis monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
Quantum Wells, Wires and Dots
by Paul HarrisonQuantum Wells, Wires and Dots, 3rd Edition is aimed at providing all the essential information, both theoretical and computational, in order that the reader can, starting from essentially nothing, understand how the electronic, optical and transport properties of semiconductor heterostructures are calculated. Completely revised and updated, this text is designed to lead the reader through a series of simple theoretical and computational implementations, and slowly build from solid foundations, to a level where the reader can begin to initiate theoretical investigations or explanations of their own.
Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures
by Paul Harrison Alex ValavanisQuantum Wells, Wires and Dots provides all the essential information, both theoretical and computational, to develop an understanding of the electronic, optical and transport properties of these semiconductor nanostructures. The book will lead the reader through comprehensive explanations and mathematical derivations to the point where they can design semiconductor nanostructures with the required electronic and optical properties for exploitation in these technologies. This fully revised and updated 4th edition features new sections that incorporate modern techniques and extensive new material including: - Properties of non-parabolic energy bands - Matrix solutions of the Poisson and Schrödinger equations - Critical thickness of strained materials - Carrier scattering by interface roughness, alloy disorder and impurities - Density matrix transport modelling -Thermal modelling Written by well-known authors in the field of semiconductor nanostructures and quantum optoelectronics, this user-friendly guide is presented in a lucid style with easy to follow steps, illustrative examples and questions and computational problems in each chapter to help the reader build solid foundations of understanding to a level where they can initiate their own theoretical investigations. Suitable for postgraduate students of semiconductor and condensed matter physics, the book is essential to all those researching in academic and industrial laboratories worldwide.
The Quantum World: Quantum Physics for Everyone
by Kenneth W. FordAs Kenneth W. Ford shows us in The Quantum World, the laws governing the very small and the very swift defy common sense and stretch our minds to the limit. Drawing on a deep familiarity with the discoveries of the twentieth century, Ford gives an appealing account of quantum physics that will help the serious reader make sense of a science that, for all its successes, remains mysterious. In order to make the book even more suitable for classroom use, the author, assisted by Diane Goldstein, has included a new section of Quantum Questions at the back of the book. A separate answer manual to these 300+ questions is available; visit The Quantum World website for ordering information. There is also a cloth edition of this book, which does not include the "Quantum Questions" included in this paperback edition.
The Quantum World: The disturbing theory at the heart of reality
by New ScientistForget everything you thought you knew about reality.The world is a seriously bizarre place. Things can exist in two places at once and travel backwards and forwards in time. Waves and particles are one and the same, and objects change their behaviour according to whether they are being watched. This is not some alternative universe but the realm of the very small, where quantum mechanics rules. In this weird world of atoms and their constituents, our common sense understanding of reality breaks down - yet quantum mechanics has never failed an experimental test. What does it all mean? For all its weirdness, quantum mechanics has given us many practical technologies including lasers and the transistors that underlie computers and all digital technology. In the future, it promises computers more powerful than any built before, the ability to communicate with absolute privacy, and even quantum teleportation. The Quantum World explores the past, present and future of quantum science, its applications and mind-bending implications. Discover how ideas from quantum mechanics are percolating out into the vast scale of the cosmos - perhaps, in the future, to reveal a new understanding of the big bang and the nature of space and time.ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.
The Quantum World: The disturbing theory at the heart of reality (New Scientist Instant Expert)
by New ScientistForget everything you thought you knew about reality.The world is a seriously bizarre place. Things can exist in two places at once and travel backwards and forwards in time. Waves and particles are one and the same, and objects change their behaviour according to whether they are being watched. This is not some alternative universe but the realm of the very small, where quantum mechanics rules. In this weird world of atoms and their constituents, our common sense understanding of reality breaks down - yet quantum mechanics has never failed an experimental test. What does it all mean? For all its weirdness, quantum mechanics has given us many practical technologies including lasers and the transistors that underlie computers and all digital technology. In the future, it promises computers more powerful than any built before, the ability to communicate with absolute privacy, and even quantum teleportation. The Quantum World explores the past, present and future of quantum science, its applications and mind-bending implications. Discover how ideas from quantum mechanics are percolating out into the vast scale of the cosmos - perhaps, in the future, to reveal a new understanding of the big bang and the nature of space and time.ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.
The Quantum World: The disturbing theory at the heart of reality (New Scientist Instant Expert)
by New ScientistForget everything you thought you knew about reality.The world is a seriously bizarre place. Things can exist in two places at once and travel backwards and forwards in time. Waves and particles are one and the same, and objects change their behaviour according to whether they are being watched. This is not some alternative universe but the realm of the very small, where quantum mechanics rules. In this weird world of atoms and their constituents, our common sense understanding of reality breaks down - yet quantum mechanics has never failed an experimental test. What does it all mean? For all its weirdness, quantum mechanics has given us many practical technologies including lasers and the transistors that underlie computers and all digital technology. In the future, it promises computers more powerful than any built before, the ability to communicate with absolute privacy, and even quantum teleportation. The Quantum World explores the past, present and future of quantum science, its applications and mind-bending implications. Discover how ideas from quantum mechanics are percolating out into the vast scale of the cosmos - perhaps, in the future, to reveal a new understanding of the big bang and the nature of space and time.ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.
The Quantum World
by J. C. PolkinghorneIn paperback for the first time, this compact volume presents quantum mechanics for the general reader. It offers a lucid description of the intellectual challenges and disagreements in the study of the behavior of atomic and sub-atomic particles--a field that has completely changed our view of the physical world, but that is still the subject of unresolved debate about its own fundamental interpretation. The work is accessible to those with no background in higher mathematics, but will also interest readers who have a more specialized knowledge of scientific topics. <p><p> The author has spent most of his working life as a theoretical elementary particle physicist and from 1968 to 1979 was Professor of Mathematical Physics at the University of Cambridge. In 1979 he resigned to train for the ministry of the Church of England, and he is now an ordained priest. Here he describes a theory that has been spectacularly successful in predicting the behavior of objects the size of atoms and smaller but that has aroused conflicting views about the nature of reality and the degree of independence between the world around us and ourselves as observers.
The Quantum World: The Disturbing Theory At The Heart Of Reality (New Scientist Instant Expert Ser.)
by New ScientistForget everything you thought you knew about reality.The world is a seriously bizarre place. Things can exist in two places at once and travel backwards and forwards in time. Waves and particles are one and the same, and objects change their behavior according to whether they are being watched. This is not some alternative universe but the realm of the very small, where quantum mechanics rules. In this weird world of atoms and their constituents, our common sense understanding of reality breaks down - yet quantum mechanics has never failed an experimental test. What does it all mean? For all its weirdness, quantum mechanics has given us many practical technologies including lasers and the transistors that underlie computers and all digital technology. In the future, it promises computers more powerful than any built before, the ability to communicate with absolute privacy, and even quantum teleportation. The Quantum World explores the past, present and future of quantum science, its applications and mind-bending implications. Discover how ideas from quantum mechanics are percolating out into the vast scale of the cosmos - perhaps, in the future, to reveal a new understanding of the big bang and the nature of space and time. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.
The Quantum World
by Hervé Zwirn Bernard D'EspagnatIn this largely nontechnical book, eminent physicists and philosophers address the philosophical impact of recent advances in quantum physics. These are shown to shed new light on profound questions about realism, determinism, causality or locality. The participants contribute in the spirit of an open and honest discussion, reminiscent of the time when science and philosophy were inseparable. After the editors’ introduction, the next chapter reveals the strangeness of quantum mechanics and the subsequent discussions examine our notion of reality. The spotlight is then turned to the topic of decoherence. Bohm’s theory is critically examined in two chapters, and the relational interpretation of quantum mechanics is likewise described and discussed. The penultimate chapter presents a proposal for resolving the measurement problem, and finally the topic of loop quantum gravity is presented by one of its founding fathers, Carlo Rovelli. The original presentations and discussions on which this volume is based took place under the auspices of the French “Académie des Sciences Morales et Politiques”. The book will appeal to everybody interested in knowing how our description of the world is impacted by the results of the most powerful and successful theory that physicists have ever built.
Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics
by Olimpia Lombardi Sebastian Fortin Cristian López Federico HolikQuantum theory underpins much of modern physics and its implications draw the attention of industry, academia and public funding agencies. However there are many unsettled conceptual and philosophical problems in the interpretation of quantum mechanics which are a matter of extensive debate. These hotly debated topics include the meaning of the wave function, the nature of the quantum objects, the role of the observer, the non-locality of the quantum world, and the emergence of classicality from the quantum domain. Containing chapters written by eminent researchers from the fields of physics and philosophy, this book provides interdisciplinary, comprehensive and up-to-date perspectives of the problems related to the interpretation of quantum theory. It is ideal for academic researchers in physics and philosophy working on the ontology of quantum mechanics.
Quantum‐Enhanced Sensing Based on Time Reversal of Entangling Interactions (Springer Theses)
by Daniel LinnemannQuantum mechanics entails effects like superpositions and entanglement, which have no classical counterparts. From a technological standpoint these counterintuitive quantum aspects can be viewed as an unexploited resource that can be harnessed to support various tasks, e.g. in the domains of computation, communication, and metrology. In many applications, however, the potential of nonclassical states cannot practically be exploited due to detection inefficiencies. The authors address this limitation by experimentally realizing a novel detection scheme in which entangling interactions are time reversed. In this way, nonclassical many-particle states are disentangled, allowing them to be detected in a robust and technically feasible manner. In the context of quantum metrology, these nonlinear readout techniques extend the class of entangled probe states that can be leveraged for sensing applications without being limited by finite detector resolution. The authors present an active atom interferometer, where both the entangled state preparation and disentangling readout involve parametric amplification. This “SU(1,1)” interferometer is implemented with the help of spinor Bose–Einstein condensates, where amplification is implemented by atomic collisions leading to spin exchange.
The Quarantine and Certification of Martian Samples
by Committee on Planetary Lunar ExplorationSamples of Martian soil, rocks, and atmosphere are expected to be returned to Earth as early as 2015, so in 1999 the Committee of Planetary and Lunar Exploration of the National Research Council set out to identify what criteria must be satisfied before such samples can be released from a quarantine facility. This final report supersedes their several interim reports. It is not indexed. Annotation (c)2003 Book News, Inc. , Portland, OR (booknews. com)
Quarantine Treatments For Pests Of Food Plants
by Jennifer L Sharp Guy J HallmanThis volume provides an overview of quarantine treatment for pests of food plants that involve heat, cold, irradiation, fumigants, modified atmospheres, and other techniques alone or in combination. The contributors discuss strategies for eliminating or reducing the need for post-harvest treatment by ensuring that commodities are free of all pests
The Quark Structure of Hadrons: An Introduction To The Phenomenology And Spectroscopy (Lecture Notes in Physics #949)
by Claude AmslerNovel forms of matter, such as states made of gluons (glueballs), multiquark mesons or baryons and hybrid mesons are predicted by low energy QCD, for which several candidates have recently been identified. Searching for such exotic states of matter and studying their production and decay properties in detail has become a flourishing field at the experimental facilities now available or being built - e.g. BESIII in Beijing, BELLE II at SuperKEKB, GlueX at Jefferson Lab, PANDA at FAIR, J-PARC and in the upgraded LHC experiments, in particular LHCb. A modern primer in the field is required so as to both revive and update the teaching of a new generation of researchers in the field of QCD. These lectures on hadron spectroscopy are intended for Master and PhD students and have been originally developed for a course delivered at the Stefan Meyer Institute of the Austrian Academy of Sciences. They are phenomenologically oriented and intended as complementary material for basic courses in particle and nuclear physics. The book describes the spectra of light and heavy mesons and baryons, and introduces the fundamental properties based on symmetries. Further, it derives multiplet structures, mixing angle, decay coupling constants, magnetic moments of baryons, and predictions for multiquark states and compares these with suitable experimental data. Basic methods of calculating decay angular distributions and determining masses and widths of resonances are also presented. The appendices provide students and newcomers to the field with the necessary background information, and include a set of problems and solutions.
Quark's Academy
by Catherine PelosiSCIENCE IN PROGRESS - ENTER AT YOUR OWN RISK!Junior science geniuses Augustine, Celeste and Oscar can't believe their luck when they're accepted into an elite and mysterious science academy summer camp run by the elusive Inventor Quark.From the moment they step inside the gates of Quark's Academy at the end of Molecule Drive, they know they're in for a week they'll never forget. But things at the academy are not quite what they seem, and the three quickly realise that they'll need to put their squabbles aside and their heads together if they're ever to get out of there alive...A page-turning adventure for readers aged eight to twelve, QUARK'S ACADEMY is bound to cause a hair-raising reaction!'an engaging and entertaining debut for readers aged eight and up with an interest in STEM - or those who just love a well-paced adventure story with fantastical elements.' 4.5 stars - BOOKS + PUBLISHING
Quarks and Leptons From Orbifolded Superstring (Lecture Notes in Physics #954)
by Kang-Sin Choi Jihn E. KimThis book offers a detailed guide on the journey towards the minimal supersymmetric standard model down the orbifold road. It takes the viewpoint that the chirality of matter fermions is an essential aspect that orbifold compactification allows to derive from higher-dimensional string theories in a straightforward manner. Halfway between textbook and tutorial review, the book is intended for the graduate student and particle phenomenologist wishing to get acquainted with this field.
Quarks, chaos & Christianity: questions to science and religion
by John Polkinghorne"As someone who's both a scientist and an Anglican priest, I've been concerned with trying to understand how the scientific and religious views of the world relate to each other. Do we have to choose between them or are they, instead, complementary understandings that, seen together, give us a fuller picture than either on their own would provide? I find the best way to sort out what I really think is to try to write it down. The late Bishop John Robinson once said to me that he couldn't think without a pen in his hand, and I knew exactly what he meant. In consequence, I've written six books on different aspects of this question. Now I've decided it would be useful to try to provide an overview that surveyed the whole scene, rather than concentrating on this or that particular feature of it, as my earlier books have done. At the same time, it gives me the chance to try to set out the main lines of the argument without having to reproduce all the detailed discussion that I've gone into previously. I do a fair amount of speaking on these issues, and I always greatly enjoy the discussion period that normally follows a lecture. This experience has given me some idea of what the main questions are in people's minds, and what are the most helpful insights to offer them. I actually think that we need both science and religion, and that they have many important things to say to each other. I hope this short book may help others to share in such a conversation."
Quarks, Leptons and the Big Bang
by Jonathan AlldayCHOICE: Highly Recommended Quarks, Leptons and The Big Bang, Third Edition, is a clear, readable and self-contained introduction to particle physics and related areas of cosmology. It bridges the gap between non-technical popular accounts and textbooks for advanced students. The book concentrates on presenting the subject from the modern perspective of quarks, leptons and the forces between them. This book will appeal to students, teachers and general science readers interested in fundamental ideas of modern physics. This edition brings the book completely up to date by including advances in particle physics and cosmology, such as the discovery of the Higgs boson, the LIGO gravitational wave discovery and the WMAP and PLANCK results.
Quarks to Culture: How We Came to Be
by Tyler VolkOur world is nested, both physically and socially, and at each level we find innovations that are necessary for the next. Consider: atoms combine to form molecules, molecules combine to form single-celled organisms; when people come together, they build societies. Physics has gone far in mapping the basic mechanics of the simplest things and the dynamics of the overall nesting, as have biology and the social sciences for their fields. But what can we say about this beautifully complex whole? How does one stage shape another, and what can we learn about human existence through understanding an enlarged field of creation and being?In Quarks to Culture, Tyler Volk answers these questions, revealing how a universal natural rhythm—building from smaller things into larger, more complex things—resulted in a grand sequence of twelve fundamental levels across the realms of physics, biology, and culture. He introduces the key concept of “combogenesis,” the building-up from combination and integration to produce new things with innovative relations. He explores common themes in how physics and chemistry led to biological evolution, and biological evolution to cultural evolution. Volk also provides insights into linkages across the sciences and fields of scholarship, and presents an exciting synthesis of ideas along a sequence of things and relations, from physical to living to cultural. The resulting inclusive natural philosophy brings clarity to our place in the world, offering a roadmap for those who seek to understand big history and wrestle with questions of how we came to be.