Nick Huggett
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195379518
- eISBN:
- 9780199776559
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379518.001.0001
- Subject:
- Philosophy, Philosophy of Science
Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are ...
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Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are Zeno's paradoxes? Are there just three dimensions? Are there other universes? What is the shape of space and how do we know? Why does time seem to pass while space does not? What is the difference between the past and future? Is time travel possible? What is spacetime? What is time according to relativity? What is the difference between left and right? What is a quantum particle? Some of these questions are among the oldest humanity has asked about our place in the world, but some are among the most recent: the book both explores their history and the thinkers that have shaped them, and explains the fundamentals of their current understanding. Readers aren't just spectators to the journey, but are engaged in the debates. This book shows that philosophy, by analyzing fundamental concepts and their relationship to the human experience, has a great deal to say about these profound topics. They are not reserved for physics; as the book demonstrates, philosophy can not only address but help advance our view of our deepest questions about the universe, space, and time, and their implications for humanity. It is aimed at inspiring the reader to think philosophically about the universe revealed by physics.Less
Everywhere and Everywhen is an introduction to the ideas and arguments of the central questions that arise when physics meets philosophy: for instance, what are space and time? What are Zeno's paradoxes? Are there just three dimensions? Are there other universes? What is the shape of space and how do we know? Why does time seem to pass while space does not? What is the difference between the past and future? Is time travel possible? What is spacetime? What is time according to relativity? What is the difference between left and right? What is a quantum particle? Some of these questions are among the oldest humanity has asked about our place in the world, but some are among the most recent: the book both explores their history and the thinkers that have shaped them, and explains the fundamentals of their current understanding. Readers aren't just spectators to the journey, but are engaged in the debates. This book shows that philosophy, by analyzing fundamental concepts and their relationship to the human experience, has a great deal to say about these profound topics. They are not reserved for physics; as the book demonstrates, philosophy can not only address but help advance our view of our deepest questions about the universe, space, and time, and their implications for humanity. It is aimed at inspiring the reader to think philosophically about the universe revealed by physics.
Frank Arntzenius
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, ...
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Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!Less
Much of this book can be seen as an attempt to show that physics is geometry, an attempt to show that the fundamental structure of the physical world is purely geometrical structure. Along the way, some non-standard views about the structure of spacetime and its inhabitants are examined, such as the idea that space and time, literally, are pointless, the idea that quantum mechanics is a completely local and separable theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, metaphysics in particular, plays an important role in this book: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one’s peril!
Walter T. Grandy, Jr.
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199546176
- eISBN:
- 9780191720161
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546176.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The ...
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This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.Less
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic governs all of the thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs — dating from the 19th century and extended considerably over the following 100 years — is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-20th Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.
Gary Bowman
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228928
- eISBN:
- 9780191711206
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228928.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that ...
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Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that focuses on the fundamental structure, concepts, and methods of quantum mechanics, filling the gap between introductory and advanced studies, between popularizations and technical treatises. Although physical understanding is emphasized, the mathematical sophistication necessary to achieve that understanding is also developed. A modern perspective is adopted throughout, the goal being to gain entry into quantum mechanics as used by practicing scientists. This perspective includes a focus on quantum states generally, not just wavefunctions, and a strong emphasis on Dirac notation. Many standard topics are developed, such as the Schrödinger equation, quantum states, operators, and matrix mechanics. Some non-standard topics are also discussed, such as the complex nature of quantum states, and various interpretations of the uncertainty relations. Discussion of applications is limited, and focuses on elucidating the structure of quantum mechanics.Less
Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that focuses on the fundamental structure, concepts, and methods of quantum mechanics, filling the gap between introductory and advanced studies, between popularizations and technical treatises. Although physical understanding is emphasized, the mathematical sophistication necessary to achieve that understanding is also developed. A modern perspective is adopted throughout, the goal being to gain entry into quantum mechanics as used by practicing scientists. This perspective includes a focus on quantum states generally, not just wavefunctions, and a strong emphasis on Dirac notation. Many standard topics are developed, such as the Schrödinger equation, quantum states, operators, and matrix mechanics. Some non-standard topics are also discussed, such as the complex nature of quantum states, and various interpretations of the uncertainty relations. Discussion of applications is limited, and focuses on elucidating the structure of quantum mechanics.
Oliver Johns
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A ...
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This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac’s formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics, such as the development of quantum information technology and the problem of quantising the gravitational field, require a rethinking of the quantum-classical connection.Less
This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac’s formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics, such as the development of quantum information technology and the problem of quantising the gravitational field, require a rethinking of the quantum-classical connection.
Roy F. Baumeister, Alfred R. Mele, and Kathleen D. Vohs (eds)
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195389760
- eISBN:
- 9780199863341
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195389760.001.0001
- Subject:
- Psychology, Social Psychology, Cognitive Psychology
This volume is aimed at readers who wish to move beyond debates about the existence of free will and the efficacy of consciousness and closer to appreciating how free will and consciousness might ...
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This volume is aimed at readers who wish to move beyond debates about the existence of free will and the efficacy of consciousness and closer to appreciating how free will and consciousness might operate. It draws from philosophy and psychology, the two fields that have grappled most fundamentally with these issues. In this wide-ranging volume, the contributors explore issues such as how free will is connected to rational choice, planning, and self-control; roles for consciousness in decision making; the nature and power of conscious deciding; connections among free will, consciousness, and quantum mechanics; why free will and consciousness might have evolved; how consciousness develops in individuals; the experience of free will; effects on behavior of the belief that free will is an illusion; and connections between free will and moral responsibility in lay thinking. Collectively, these state-of-the-art chapters by accomplished psychologists and philosophers provide a glimpse into the future of research on free will and consciousness.Less
This volume is aimed at readers who wish to move beyond debates about the existence of free will and the efficacy of consciousness and closer to appreciating how free will and consciousness might operate. It draws from philosophy and psychology, the two fields that have grappled most fundamentally with these issues. In this wide-ranging volume, the contributors explore issues such as how free will is connected to rational choice, planning, and self-control; roles for consciousness in decision making; the nature and power of conscious deciding; connections among free will, consciousness, and quantum mechanics; why free will and consciousness might have evolved; how consciousness develops in individuals; the experience of free will; effects on behavior of the belief that free will is an illusion; and connections between free will and moral responsibility in lay thinking. Collectively, these state-of-the-art chapters by accomplished psychologists and philosophers provide a glimpse into the future of research on free will and consciousness.
J. N. Reddy
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of ...
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This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (that is, time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book that is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises, in a tutorial, user-oriented style. In addition, the book is a useful reference for industrial engineers and scientists, and serves as a prelude to more advanced books on the subject.Less
This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (that is, time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book that is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises, in a tutorial, user-oriented style. In addition, the book is a useful reference for industrial engineers and scientists, and serves as a prelude to more advanced books on the subject.
Nancy Cartwright
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198235071
- eISBN:
- 9780191597169
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198235070.001.0001
- Subject:
- Philosophy, Philosophy of Science
This book on the philosophy of science argues for an empiricism, opposed to the tradition of David Hume, in which singular rather than general causal claims are primary; causal laws express facts ...
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This book on the philosophy of science argues for an empiricism, opposed to the tradition of David Hume, in which singular rather than general causal claims are primary; causal laws express facts about singular causes whereas the general causal claims of science are ascriptions of capacities or causal powers, capacities to make things happen. Taking science as measurement, Cartwright argues that capacities are necessary for science and that these can be measured, provided suitable conditions are met. There are case studies from both econometrics and quantum mechanics.Less
This book on the philosophy of science argues for an empiricism, opposed to the tradition of David Hume, in which singular rather than general causal claims are primary; causal laws express facts about singular causes whereas the general causal claims of science are ascriptions of capacities or causal powers, capacities to make things happen. Taking science as measurement, Cartwright argues that capacities are necessary for science and that these can be measured, provided suitable conditions are met. There are case studies from both econometrics and quantum mechanics.
Stephen Gaukroger
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199296446
- eISBN:
- 9780191711985
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296446.003.0012
- Subject:
- Philosophy, History of Philosophy
This chapter looks at attempts to quantify natural phenomena and, in particular, forces. Early efforts along these lines — notably by Galileo and Descartes — tried to extrapolate from statics to ...
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This chapter looks at attempts to quantify natural phenomena and, in particular, forces. Early efforts along these lines — notably by Galileo and Descartes — tried to extrapolate from statics to dynamics, whereas later in the century kinematics, as pioneered by Galileo, was taken as the model by Huygens and Newton. Newton, building on Hooke's suggestion that planetary orbits were not a given and unquestionable feature of the cosmos, was able to show how such orbits were generated and clarify the dynamics needed to account for the processes involved. In this way, mechanics, traditionally excluded from natural philosophy in the Aristotelian sense, is transformed not only into a natural-philosophical discipline, but into what was in many respects the natural-philosophical discipline par excellence.Less
This chapter looks at attempts to quantify natural phenomena and, in particular, forces. Early efforts along these lines — notably by Galileo and Descartes — tried to extrapolate from statics to dynamics, whereas later in the century kinematics, as pioneered by Galileo, was taken as the model by Huygens and Newton. Newton, building on Hooke's suggestion that planetary orbits were not a given and unquestionable feature of the cosmos, was able to show how such orbits were generated and clarify the dynamics needed to account for the processes involved. In this way, mechanics, traditionally excluded from natural philosophy in the Aristotelian sense, is transformed not only into a natural-philosophical discipline, but into what was in many respects the natural-philosophical discipline par excellence.
Victor F. Petrenko and Robert W. Whitworth
- Published in print:
- 2002
- Published Online:
- February 2010
- ISBN:
- 9780198518945
- eISBN:
- 9780191707247
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198518945.001.0001
- Subject:
- Physics, Crystallography: Physics
Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject ...
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Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject the physics of ice: the properties of the material itself and the ways in which these properties are interpreted in terms of water molecules and crystalline structure. Although ice has a simple crystal structure its hydrogen bonding results in unique properties, which continue to be the subject of active research. An understanding of these properties is essential in fields such as glaciology, ice mechanics, ice adhesion, the dating of ice cores in Antarctica and Greenland, meteorology, thunderstorm electricity, and the study of comets or the icy moons of the outer planets in the solar system. In this book the physical principles underlying the properties of ice are carefully developed. Much work on important topics such as the current understanding of the electrical, mechanical, and surface properties of ice, or the occurrence of many different crystalline phases, are developed.Less
Ice is one of the most abundant and environmentally important materials on Earth, and its unique and intriguing physical properties present fascinating areas of study. This book takes as its subject the physics of ice: the properties of the material itself and the ways in which these properties are interpreted in terms of water molecules and crystalline structure. Although ice has a simple crystal structure its hydrogen bonding results in unique properties, which continue to be the subject of active research. An understanding of these properties is essential in fields such as glaciology, ice mechanics, ice adhesion, the dating of ice cores in Antarctica and Greenland, meteorology, thunderstorm electricity, and the study of comets or the icy moons of the outer planets in the solar system. In this book the physical principles underlying the properties of ice are carefully developed. Much work on important topics such as the current understanding of the electrical, mechanical, and surface properties of ice, or the occurrence of many different crystalline phases, are developed.
Sönke Johnsen
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691139906
- eISBN:
- 9781400840663
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691139906.001.0001
- Subject:
- Biology, Evolutionary Biology / Genetics
Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book ...
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Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book introduces the fundamentals of optics to biologists and nonphysicists, giving them the tools they need to successfully incorporate optical measurements and principles into their research. The book starts with the basics, describing the properties of light and the units and geometry of measurement. It then explores how light is created and propagates and how it interacts with matter, covering topics such as absorption, scattering, fluorescence, and polarization. The book also provides a tutorial on how to measure light as well as an informative discussion of quantum mechanics. The book features a host of examples drawn from nature and everyday life, and several appendixes that offer further practical guidance for researchers. This concise book uses a minimum of equations and jargon, explaining the basic physics of light in a succinct and lively manner. It is the essential primer for working biologists and for anyone seeking an accessible introduction to optics.Less
Optics—a field of physics focusing on the study of light—is also central to many areas of biology, including vision, ecology, botany, animal behavior, neurobiology, and molecular biology. This book introduces the fundamentals of optics to biologists and nonphysicists, giving them the tools they need to successfully incorporate optical measurements and principles into their research. The book starts with the basics, describing the properties of light and the units and geometry of measurement. It then explores how light is created and propagates and how it interacts with matter, covering topics such as absorption, scattering, fluorescence, and polarization. The book also provides a tutorial on how to measure light as well as an informative discussion of quantum mechanics. The book features a host of examples drawn from nature and everyday life, and several appendixes that offer further practical guidance for researchers. This concise book uses a minimum of equations and jargon, explaining the basic physics of light in a succinct and lively manner. It is the essential primer for working biologists and for anyone seeking an accessible introduction to optics.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's ...
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In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.Less
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.
Hidetoshi Nishimori
- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198509417
- eISBN:
- 9780191709081
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509417.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical ...
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Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have offered new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. A vast, interdisciplinary field has consequently been developing between physics and information, or more specifically, between the statistical physics of spin glasses and several important aspects of information processing tasks. This book provides a broad overview of this new field. It also contains detailed descriptions of the theory of spin glasses.Less
Spin glasses are magnetic materials with strong disorder. Statistical mechanics has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have offered new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. A vast, interdisciplinary field has consequently been developing between physics and information, or more specifically, between the statistical physics of spin glasses and several important aspects of information processing tasks. This book provides a broad overview of this new field. It also contains detailed descriptions of the theory of spin glasses.
Jean Zinn-Justin
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of ...
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Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. They are powerful tools for the study of quantum mechanics, since they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding of physical quantities in the semi-classical limit, as well as simple calculations of such quantities. This observation can be illustrated with scattering processes, spectral properties, or barrier penetration effects. Even though the formulation of quantum mechanics based on path integrals seems mathematically more complicated than the usual formulation based on partial differential equations, the path integral formulation is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows simple construction of a many-body theory both for bosons and fermions.Less
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. They are powerful tools for the study of quantum mechanics, since they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding of physical quantities in the semi-classical limit, as well as simple calculations of such quantities. This observation can be illustrated with scattering processes, spectral properties, or barrier penetration effects. Even though the formulation of quantum mechanics based on path integrals seems mathematically more complicated than the usual formulation based on partial differential equations, the path integral formulation is well adapted to systems with many degrees of freedom, where a formalism of Schrödinger type is much less useful. It allows simple construction of a many-body theory both for bosons and fermions.
Martin Schöneld
- Published in print:
- 2000
- Published Online:
- May 2006
- ISBN:
- 9780195132182
- eISBN:
- 9780199786336
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195132181.003.0003
- Subject:
- Philosophy, History of Philosophy
This chapter explores the text and contentions of Kant’s first book, Thoughts on the True Estimation of Living Forces (1747). Section 1 describes how Kant’s debut turned into a debacle. Section 2 ...
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This chapter explores the text and contentions of Kant’s first book, Thoughts on the True Estimation of Living Forces (1747). Section 1 describes how Kant’s debut turned into a debacle. Section 2 discusses Kant’s dynamic ontology, such as his ideas on substantial interaction and energetic space. Section 3 analyzes Kant’s experimental and kinematic appraisals, which form the bulk of his first book. Section 4 describes Kant’s proposed synthesis of Cartesian momentum and Leibnizian energy as “true estimation” of force.Less
This chapter explores the text and contentions of Kant’s first book, Thoughts on the True Estimation of Living Forces (1747). Section 1 describes how Kant’s debut turned into a debacle. Section 2 discusses Kant’s dynamic ontology, such as his ideas on substantial interaction and energetic space. Section 3 analyzes Kant’s experimental and kinematic appraisals, which form the bulk of his first book. Section 4 describes Kant’s proposed synthesis of Cartesian momentum and Leibnizian energy as “true estimation” of force.
Paul Nunez
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195340716
- eISBN:
- 9780199776269
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195340716.001.0001
- Subject:
- Neuroscience, Development
Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? ...
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Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? Tentative answers in this book follow from a synthesis of profound ideas, borrowed from philosophy, religion, politics, economics, neuroscience, physics, mathematics, and cosmology, the knowledge structures supporting our meager grasp of reality. This search for new links in the web of human knowledge extends in many directions: the shadows of our thought processes revealed by brain imagining, brains treated as complex adaptive systems that reveal fractal-like behavior in the brain's nested hierarchy, resonant interactions facilitating functional connections in brain tissue, probability and entropy as measures of human ignorance, fundamental limits on human knowledge, and the central role played by information in both brains and physical systems. The author discusses the possibility of deep connections between relativity, quantum mechanics, thermodynamics, and consciousness; all entities involved with fundamental information barriers. This study elaborates on possible new links in this nested web of human knowledge that may tell us something new about the nature and origins of consciousness. In the end, does the brain create the mind? Or is the mind already out there?Less
Does the brain create the mind, or is some external entity involved? In addressing this hard problem of consciousness, we face a central human challenge: what do we really know and how do we know it? Tentative answers in this book follow from a synthesis of profound ideas, borrowed from philosophy, religion, politics, economics, neuroscience, physics, mathematics, and cosmology, the knowledge structures supporting our meager grasp of reality. This search for new links in the web of human knowledge extends in many directions: the shadows of our thought processes revealed by brain imagining, brains treated as complex adaptive systems that reveal fractal-like behavior in the brain's nested hierarchy, resonant interactions facilitating functional connections in brain tissue, probability and entropy as measures of human ignorance, fundamental limits on human knowledge, and the central role played by information in both brains and physical systems. The author discusses the possibility of deep connections between relativity, quantum mechanics, thermodynamics, and consciousness; all entities involved with fundamental information barriers. This study elaborates on possible new links in this nested web of human knowledge that may tell us something new about the nature and origins of consciousness. In the end, does the brain create the mind? Or is the mind already out there?
Alfonso Sorrentino
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.001.0001
- Subject:
- Mathematics, Applied Mathematics
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ...
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John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach—known as Aubry–Mather theory—singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic. Starting with the mathematical background from which Mather's theory was born, the book first focuses on the core questions the theory aims to answer—notably the destiny of broken invariant KAM tori and the onset of chaos—and describes how it can be viewed as a natural counterpart of KAM theory. The book achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. It then describes the whole theory and its subsequent developments and applications in their full generality.Less
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach—known as Aubry–Mather theory—singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic. Starting with the mathematical background from which Mather's theory was born, the book first focuses on the core questions the theory aims to answer—notably the destiny of broken invariant KAM tori and the onset of chaos—and describes how it can be viewed as a natural counterpart of KAM theory. The book achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. It then describes the whole theory and its subsequent developments and applications in their full generality.
JESPER LÜTZEN
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0016
- Subject:
- Physics, History of Physics
In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every ...
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In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every free system persists in its state of rest or of uniform motion in a straightest path. Hertz's fundamental law can be formulated as follows: a free system moves with constant speed along a path that is as straight as it can be without breaking the connections of the system. Hertz's formulation of the fundamental law was surprisingly stable throughout his work on mechanics. It was the geometry of systems of points that allowed Hertz to limit the laws of motion to his one simple, elegant and intuitively appealing fundamental law. Hertz mentioned one other law that could have replaced his fundamental law on free systems, namely, the law of least acceleration.Less
In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every free system persists in its state of rest or of uniform motion in a straightest path. Hertz's fundamental law can be formulated as follows: a free system moves with constant speed along a path that is as straight as it can be without breaking the connections of the system. Hertz's formulation of the fundamental law was surprisingly stable throughout his work on mechanics. It was the geometry of systems of points that allowed Hertz to limit the laws of motion to his one simple, elegant and intuitively appealing fundamental law. Hertz mentioned one other law that could have replaced his fundamental law on free systems, namely, the law of least acceleration.
JESPER LÜTZEN
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0017
- Subject:
- Physics, History of Physics
Heinrich Hertz's strategy for studying the motion of mechanical systems was to deal first with free systems, to which the fundamental law applies, and then with unfree systems considered as ...
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Heinrich Hertz's strategy for studying the motion of mechanical systems was to deal first with free systems, to which the fundamental law applies, and then with unfree systems considered as subsystems of free systems. This chapter discusses Hertz's treatment of free systems, which he dealt with in two steps. First, he discussed the purely geometric properties of straightest paths, then went on to investigate the dynamic theory — that is, how systems move in time. At each step he deduced the general differential equations, derived differential and integral principles, and dealt with the special phenomena of holonomic systems. Hertz's introduction of the concept of force, which in a sense is the highlight of the physical content of his mechanics, is explored by focusing on the differential equations of motion and those general differential principles of mechanics that follow from them.Less
Heinrich Hertz's strategy for studying the motion of mechanical systems was to deal first with free systems, to which the fundamental law applies, and then with unfree systems considered as subsystems of free systems. This chapter discusses Hertz's treatment of free systems, which he dealt with in two steps. First, he discussed the purely geometric properties of straightest paths, then went on to investigate the dynamic theory — that is, how systems move in time. At each step he deduced the general differential equations, derived differential and integral principles, and dealt with the special phenomena of holonomic systems. Hertz's introduction of the concept of force, which in a sense is the highlight of the physical content of his mechanics, is explored by focusing on the differential equations of motion and those general differential principles of mechanics that follow from them.
JESPER LÜTZEN
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0019
- Subject:
- Physics, History of Physics
In his book Principles of Mechanics, Heinrich Hertz discussed the motion of unfree systems. He made the crucial assumption that every unfree system is ‘a portion of a more extended free system’ (a ...
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In his book Principles of Mechanics, Heinrich Hertz discussed the motion of unfree systems. He made the crucial assumption that every unfree system is ‘a portion of a more extended free system’ (a so-called partial system). When Hertz considered an unfree system as a part of a free system ‘it is assumed that the rest of the system is more or less unknown, so that an immediate application of the fundamental law is impossible’. The question is then how to take the influence of the rest of the system into account without knowing its motion in detail. Hertz mentioned two cases where this can be done in different ways. In the first case the rest of the system ‘perform a determinate and prescribed motion’. Hertz introduced the term ‘guided system’ for this situation. The second, more important case, concerned ‘systems acted on by forces’.Less
In his book Principles of Mechanics, Heinrich Hertz discussed the motion of unfree systems. He made the crucial assumption that every unfree system is ‘a portion of a more extended free system’ (a so-called partial system). When Hertz considered an unfree system as a part of a free system ‘it is assumed that the rest of the system is more or less unknown, so that an immediate application of the fundamental law is impossible’. The question is then how to take the influence of the rest of the system into account without knowing its motion in detail. Hertz mentioned two cases where this can be done in different ways. In the first case the rest of the system ‘perform a determinate and prescribed motion’. Hertz introduced the term ‘guided system’ for this situation. The second, more important case, concerned ‘systems acted on by forces’.
