Steven French and Décio Krause
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.001.0001
- Subject:
- Philosophy, Philosophy of Science
Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum ...
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Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.Less
Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.
Jeremy Butterfield (ed.)
- Published in print:
- 2006
- Published Online:
- January 2012
- ISBN:
- 9780197263464
- eISBN:
- 9780191734748
- Item type:
- book
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197263464.001.0001
- Subject:
- Philosophy, General
These nine chapters, commissioned on the initiative of the Philosophy section of the British Academy, address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are ...
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These nine chapters, commissioned on the initiative of the Philosophy section of the British Academy, address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are there facts about the future? Could we affect the past? Physics, general relativity and quantum theory give contradictory treatments of time. So in the search for a theory of quantum gravity, which should give way: general relativity or quantum theory? In linguistics and psychology, how does our language represent time, and how do our minds keep track of it?Less
These nine chapters, commissioned on the initiative of the Philosophy section of the British Academy, address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are there facts about the future? Could we affect the past? Physics, general relativity and quantum theory give contradictory treatments of time. So in the search for a theory of quantum gravity, which should give way: general relativity or quantum theory? In linguistics and psychology, how does our language represent time, and how do our minds keep track of it?
Steven French and Décio Krause
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199278244
- eISBN:
- 9780191603952
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199278245.003.0009
- Subject:
- Philosophy, Philosophy of Science
This chapter begins with a philosophically-oriented outline of quantum field theory that looks at the different ways in which a quantum field can be constructed. The difficulties in articulating a ...
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This chapter begins with a philosophically-oriented outline of quantum field theory that looks at the different ways in which a quantum field can be constructed. The difficulties in articulating a particle ontology are discussed, and it is argued that any putative interpretation of the theory must accommodate the observed particle ‘grin’. A range of metaphysical options are explored, including trope theory and Davudson’s theory of events. The foundations of Fock space are presented in detail from the model-theoretic perspective, and it is suggested that quasi-set theory provides the appropriate formal foundation. Thus, the quanta of quantum field theory can also be accommodated in terms of the overall framework of this work.Less
This chapter begins with a philosophically-oriented outline of quantum field theory that looks at the different ways in which a quantum field can be constructed. The difficulties in articulating a particle ontology are discussed, and it is argued that any putative interpretation of the theory must accommodate the observed particle ‘grin’. A range of metaphysical options are explored, including trope theory and Davudson’s theory of events. The foundations of Fock space are presented in detail from the model-theoretic perspective, and it is suggested that quasi-set theory provides the appropriate formal foundation. Thus, the quanta of quantum field theory can also be accommodated in terms of the overall framework of this work.
Richard Swinburne (ed.)
- Published in print:
- 2011
- Published Online:
- January 2013
- ISBN:
- 9780197264898
- eISBN:
- 9780191754074
- Item type:
- book
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264898.001.0001
- Subject:
- Philosophy, Philosophy of Mind
Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the ...
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Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe — if neuroscience does not rule this out — there is a role for intentions after all. Finally, a theorem of mathematics, Gödel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. The extent to which human behaviour is determined by brain events may well depend on whether conscious events, such as intentions, are themselves merely brain events, or whether they are separate events which interact with brain events (perhaps in the radical form that intentions are events in our soul, and not in our body). This book considers what kind of free will we need in order to be morally responsible for our actions or be held guilty in a court of law. Is it sufficient merely that our actions are uncaused by brain events?Less
Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe — if neuroscience does not rule this out — there is a role for intentions after all. Finally, a theorem of mathematics, Gödel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. The extent to which human behaviour is determined by brain events may well depend on whether conscious events, such as intentions, are themselves merely brain events, or whether they are separate events which interact with brain events (perhaps in the radical form that intentions are events in our soul, and not in our body). This book considers what kind of free will we need in order to be morally responsible for our actions or be held guilty in a court of law. Is it sufficient merely that our actions are uncaused by brain events?
Jeremy Butterfield and Chris Isham
- Published in print:
- 2006
- Published Online:
- January 2012
- ISBN:
- 9780197263464
- eISBN:
- 9780191734748
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197263464.003.0006
- Subject:
- Philosophy, General
This chapter discusses the idea that the treatment of time in present-day physical theories, general relativity and quantum theory, might be an approximation to a very different treatment in the as ...
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This chapter discusses the idea that the treatment of time in present-day physical theories, general relativity and quantum theory, might be an approximation to a very different treatment in the as yet unknown quantum theory of gravity. It considers the general idea that one theory could be emergent from another, emergence being a relation analogous to, but weaker than, intertheoretic reduction. It also gives a broad description of the search for a quantum theory of gravity and some of its interpretative problems. Thereafter, the discussion focuses on the emergence of time in two specific quantum gravity programmes: quantum geometrodynamics and the Euclidean programme. It also addresses the so-called ‘problem of time’. It is really a cluster of problems; technical and conceptual, arising from how time is treated very differently in general relativity and quantum theory.Less
This chapter discusses the idea that the treatment of time in present-day physical theories, general relativity and quantum theory, might be an approximation to a very different treatment in the as yet unknown quantum theory of gravity. It considers the general idea that one theory could be emergent from another, emergence being a relation analogous to, but weaker than, intertheoretic reduction. It also gives a broad description of the search for a quantum theory of gravity and some of its interpretative problems. Thereafter, the discussion focuses on the emergence of time in two specific quantum gravity programmes: quantum geometrodynamics and the Euclidean programme. It also addresses the so-called ‘problem of time’. It is really a cluster of problems; technical and conceptual, arising from how time is treated very differently in general relativity and quantum theory.
David Wallace
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199546961
- eISBN:
- 9780191741418
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546961.001.0001
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This book defends the view that the Everett interpretation of quantum theory, often called the ‘many worlds theory’, is not some new physical theory or some metaphysical addition to quantum theory, ...
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This book defends the view that the Everett interpretation of quantum theory, often called the ‘many worlds theory’, is not some new physical theory or some metaphysical addition to quantum theory, but simply quantum theory itself understood in a straightforwardly literal way. As such ‐ despite its radical implications for the nature of our universe ‐ the Everett interpretation is actually the conservative way to approach quantum theory, requiring revisions neither to our best theories of physics, nor to conventional philosophy of science. The book is in three parts. Part I explains how quantum theory implies the existence of an emergent branching structure in physical reality, and explores the conceptual and technical details of decoherence theory, the theory which allows us to quantify that branching. Part II is concerned with the problem of probability, and makes the case that probability, far from being the key difficulty for the Everett interpretation, actually makes more sense from a many‐worlds viewpoint. Part III explores the implications of an Everettian perspective on a variety of topics in physics and philosophy.Less
This book defends the view that the Everett interpretation of quantum theory, often called the ‘many worlds theory’, is not some new physical theory or some metaphysical addition to quantum theory, but simply quantum theory itself understood in a straightforwardly literal way. As such ‐ despite its radical implications for the nature of our universe ‐ the Everett interpretation is actually the conservative way to approach quantum theory, requiring revisions neither to our best theories of physics, nor to conventional philosophy of science. The book is in three parts. Part I explains how quantum theory implies the existence of an emergent branching structure in physical reality, and explores the conceptual and technical details of decoherence theory, the theory which allows us to quantify that branching. Part II is concerned with the problem of probability, and makes the case that probability, far from being the key difficulty for the Everett interpretation, actually makes more sense from a many‐worlds viewpoint. Part III explores the implications of an Everettian perspective on a variety of topics in physics and philosophy.
Kazuo Fujikawa and Hiroshi Suzuki
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry ...
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This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.Less
This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.
Lee Smolin
- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780199269693
- eISBN:
- 9780191699436
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269693.003.0007
- Subject:
- Philosophy, Philosophy of Science
This chapter explains the arguments behind the assertion that the correct quantum theory of gravity must be background independent. It begins by recounting how the debate over whether quantum gravity ...
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This chapter explains the arguments behind the assertion that the correct quantum theory of gravity must be background independent. It begins by recounting how the debate over whether quantum gravity must be background independent is a continuation of a long-standing argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background-independent theory. The leading background-independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity, and dynamical triangulations, and their main achievements are summarized along with the problems that remain open. The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The chapter reviews recent issues concerning the string theory landscape and argues that they can only be resolved within the context of a background-independent formulation. Finally, it reviews some recent proposals to make quantum theory more relational.Less
This chapter explains the arguments behind the assertion that the correct quantum theory of gravity must be background independent. It begins by recounting how the debate over whether quantum gravity must be background independent is a continuation of a long-standing argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background-independent theory. The leading background-independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity, and dynamical triangulations, and their main achievements are summarized along with the problems that remain open. The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The chapter reviews recent issues concerning the string theory landscape and argues that they can only be resolved within the context of a background-independent formulation. Finally, it reviews some recent proposals to make quantum theory more relational.
Dean Rickles, Steven French, and Juha T. Saatsi (eds)
- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780199269693
- eISBN:
- 9780191699436
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269693.001.0001
- Subject:
- Philosophy, Philosophy of Science
Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing ...
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Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing non-gravitational forces. This book brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This book closes that gap, with chapters written by some of the leading researchers in the field. Individual chapters defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems.Less
Quantum gravity is the name given to a theory that unites general relativity — Einstein's theory of gravitation and spacetime — with quantum field theory, our framework for describing non-gravitational forces. This book brings together philosophers and physicists to discuss a range of conceptual issues that surface in the effort to unite these theories, focusing in particular on the ontological nature of the spacetime that results. Although there has been a great deal written about quantum gravity from the perspective of physicists and mathematicians, very little attention has been paid to the philosophical aspects. This book closes that gap, with chapters written by some of the leading researchers in the field. Individual chapters defend or attack a structuralist perspective on the fundamental ontologies of our physical theories, which offers the possibility of shedding new light on a number of foundational problems.
Richard Healey
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199287963
- eISBN:
- 9780191713453
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199287963.003.0008
- Subject:
- Philosophy, Philosophy of Science
This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The ...
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This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The difficulty stems from the problems of interpreting any quantum field theory. Even the non-relativistic quantum mechanics of particles is a theory whose interpretation remains at best controversial, and at worst simply lacking. Interpretations of quantum field theory face the additional hurdle that it is not clear what the theory is about: neither a field nor a particle ontology is readily squared with the mathematics of the theory. The chapter explores the status of loop representations in several approaches toward the interpretation of quantum field theory.Less
This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The difficulty stems from the problems of interpreting any quantum field theory. Even the non-relativistic quantum mechanics of particles is a theory whose interpretation remains at best controversial, and at worst simply lacking. Interpretations of quantum field theory face the additional hurdle that it is not clear what the theory is about: neither a field nor a particle ontology is readily squared with the mathematics of the theory. The chapter explores the status of loop representations in several approaches toward the interpretation of quantum field theory.
David Wallace
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199546961
- eISBN:
- 9780191741418
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546961.003.0011
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
How is the microscopic ontology of quantum mechanics to be understood according to the Everett interpretation? And how, in particular, are we to understand concepts like spatial locality in ...
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How is the microscopic ontology of quantum mechanics to be understood according to the Everett interpretation? And how, in particular, are we to understand concepts like spatial locality in Everettian quantum mechanics? Building on joint work with Chris Timpson, the chapter develops a general approach to these questions (‘spacetime state realism’) and apply it to questions of locality and entanglement. After a digression on the general metaphysical problem of how we should think about ontology, the chapter compares this approach with others in the literature.Less
How is the microscopic ontology of quantum mechanics to be understood according to the Everett interpretation? And how, in particular, are we to understand concepts like spatial locality in Everettian quantum mechanics? Building on joint work with Chris Timpson, the chapter develops a general approach to these questions (‘spacetime state realism’) and apply it to questions of locality and entanglement. After a digression on the general metaphysical problem of how we should think about ontology, the chapter compares this approach with others in the literature.
David Wallace
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199546961
- eISBN:
- 9780191741418
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546961.003.0008
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that ...
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This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that Everettian quantum mechanics is correct. The chapter proves — initially with informal arguments, but in due course with full mathematical rigor — that rational scientists should treat the branch weights assigned by quantum theory to quantum-mechanical branches exactly as if they were probabilities; as such, the chapter argues, probability is actually on firmer conceptual footing in quantum theory than in classical physics. After a brief digression to consider probability in approaches to quantum theory other than the Everett interpretation, the chapter concludes by placing the work in the broader context of recent work on Everett probability.Less
This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that Everettian quantum mechanics is correct. The chapter proves — initially with informal arguments, but in due course with full mathematical rigor — that rational scientists should treat the branch weights assigned by quantum theory to quantum-mechanical branches exactly as if they were probabilities; as such, the chapter argues, probability is actually on firmer conceptual footing in quantum theory than in classical physics. After a brief digression to consider probability in approaches to quantum theory other than the Everett interpretation, the chapter concludes by placing the work in the broader context of recent work on Everett probability.
David Wallace
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199546961
- eISBN:
- 9780191741418
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546961.003.0013
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This chapter reviews a collection of other philosophical and conceptual consequences of the Everett interpretation: the popular-science idea that chaos theory makes the future sensitively dependent ...
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This chapter reviews a collection of other philosophical and conceptual consequences of the Everett interpretation: the popular-science idea that chaos theory makes the future sensitively dependent upon our present actions; some exotic situations involving quantum probability, such as the infamous ‘quantum suicide’ thought experiment; the proposal by Deutsch that other worlds are directly observed in quantum-mechanical interference processes; the ontologica status of mixed states; and the nature of time travel in an Everettian universe.Less
This chapter reviews a collection of other philosophical and conceptual consequences of the Everett interpretation: the popular-science idea that chaos theory makes the future sensitively dependent upon our present actions; some exotic situations involving quantum probability, such as the infamous ‘quantum suicide’ thought experiment; the proposal by Deutsch that other worlds are directly observed in quantum-mechanical interference processes; the ontologica status of mixed states; and the nature of time travel in an Everettian universe.
Roger E. Raab and Owen L. de Lange
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the ...
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The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.Less
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.
John Stachel
- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780199269693
- eISBN:
- 9780191699436
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269693.003.0003
- Subject:
- Philosophy, Philosophy of Science
This chapter reviews various interpretations of structural realism and then adopts a definition that allows both relations between things that are already individuated (‘relations between things’) ...
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This chapter reviews various interpretations of structural realism and then adopts a definition that allows both relations between things that are already individuated (‘relations between things’) and relations that individuate previously un-individuated entities (‘things between relations’). Since both spacetime points in general relativity and elementary particles in quantum theory fall into the latter category, the chapter proposes a principle of maximal permutability as a criterion for the fundamental entities of any future theory of ‘quantum gravity’; i.e., a theory yielding both general relativity and quantum field theory in appropriate limits. It reviews a number of current candidates for such a theory. The chapter ends by suggesting a new approach to the question of which spacetime structures should be quantized.Less
This chapter reviews various interpretations of structural realism and then adopts a definition that allows both relations between things that are already individuated (‘relations between things’) and relations that individuate previously un-individuated entities (‘things between relations’). Since both spacetime points in general relativity and elementary particles in quantum theory fall into the latter category, the chapter proposes a principle of maximal permutability as a criterion for the fundamental entities of any future theory of ‘quantum gravity’; i.e., a theory yielding both general relativity and quantum field theory in appropriate limits. It reviews a number of current candidates for such a theory. The chapter ends by suggesting a new approach to the question of which spacetime structures should be quantized.
Claus Kiefer
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199585205
- eISBN:
- 9780191739378
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199585205.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches ...
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This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant approaches - perturbation theory and Feynman diagrammes, path integrals, and supergravity. The third chapter discusses the important concept of reparametrization invariance in the framework of simple systems: particle models, bosonic string, and parametrized field theory. This concept plays a crucial role in the Hamiltonian formulation of general relativity, which is the topic of Chapter 4. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while the sixth chapter presents loop quantum gravity. The next two chapters 7 and 8 then discuss the major applications - quantization of black holes and quantum cosmology. Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: the relevance of quantum gravity for the foundations of quantum theory and the arrow of time. It also contains a brief review of quantum-gravity phenomenology. The emphasis throughout is on conceptual and formal clarity. Wherever possible, connections between the various approaches are examined.Less
This book is concerned with the attempts to unify Einstein's theory of general relativity and quantum theory into a theory of quantum gravity. It presents, for the first time, most of the approaches in a single textbook. Among them are canonical quantum gravity (including loop quantum gravity), covariant quantum gravity, and string theory. The book also discusses the relevance of these theories for cosmology and the physics of black holes. The first chapter gives a general introduction to the problem of quantizing the gravitational field. The second chapter then presents the main covariant approaches - perturbation theory and Feynman diagrammes, path integrals, and supergravity. The third chapter discusses the important concept of reparametrization invariance in the framework of simple systems: particle models, bosonic string, and parametrized field theory. This concept plays a crucial role in the Hamiltonian formulation of general relativity, which is the topic of Chapter 4. Chapter 5 presents the canonical quantization in the metric variables, leading to the central Wheeler-DeWitt equation, while the sixth chapter presents loop quantum gravity. The next two chapters 7 and 8 then discuss the major applications - quantization of black holes and quantum cosmology. Chapter 9 gives an introduction to string theory by focusing on its quantum gravitational aspects. Chapter 10 contains a discussion of interpretational issues: the relevance of quantum gravity for the foundations of quantum theory and the arrow of time. It also contains a brief review of quantum-gravity phenomenology. The emphasis throughout is on conceptual and formal clarity. Wherever possible, connections between the various approaches are examined.
E. Brian Davies
- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199219186
- eISBN:
- 9780191711695
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219186.003.0007
- Subject:
- Physics, History of Physics
This chapter discusses a series of examples which illustrate various peculiarities of probability theory. It shows that there are many situations in which two people may legitimately ascribe ...
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This chapter discusses a series of examples which illustrate various peculiarities of probability theory. It shows that there are many situations in which two people may legitimately ascribe different probabilities to the same event. These observer-dependent aspects are important when the two people have differing information about the events being observed. A complete separation between observer and observation may be possible in Newtonian mechanics, but it does not always work in probability theory or in quantum theory. Topics covered include Kolmogorov's axioms, disaster planning, the paradox of the children, the letter paradox, the three door paradox, the history of atomic theory, quantum probability, and quantum modeling.Less
This chapter discusses a series of examples which illustrate various peculiarities of probability theory. It shows that there are many situations in which two people may legitimately ascribe different probabilities to the same event. These observer-dependent aspects are important when the two people have differing information about the events being observed. A complete separation between observer and observation may be possible in Newtonian mechanics, but it does not always work in probability theory or in quantum theory. Topics covered include Kolmogorov's axioms, disaster planning, the paradox of the children, the letter paradox, the three door paradox, the history of atomic theory, quantum probability, and quantum modeling.
Xiao-Gang Wen
- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new ...
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For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, and spin liquid and string-net condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, projective construction, and exactly soluble models beyond one-dimension.Less
For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, and spin liquid and string-net condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, projective construction, and exactly soluble models beyond one-dimension.
R. E. Peierls
- Published in print:
- 2001
- Published Online:
- September 2007
- ISBN:
- 9780198507819
- eISBN:
- 9780191709913
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507819.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book develops the quantum theory of solids from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to ...
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This book develops the quantum theory of solids from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to be used in the study of this subject. Care is taken to separate sound arguments from conjecture. The treatment covers the electron theory of metals as well as the dynamics of crystals, including the author's work on the thermal conductivity of crystals.Less
This book develops the quantum theory of solids from the basic principles of quantum mechanics. The emphasis is on a single statement of the ideas underlying the various approximations that have to be used in the study of this subject. Care is taken to separate sound arguments from conjecture. The treatment covers the electron theory of metals as well as the dynamics of crystals, including the author's work on the thermal conductivity of crystals.
Ted Honderich
- Published in print:
- 1990
- Published Online:
- October 2011
- ISBN:
- 9780198242826
- eISBN:
- 9780191680588
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198242826.003.0006
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
Among the living cells of the human body, and of the central and the peripheral nervous systems, it is neurons or nerve cells which are most immediately bound up with consciousness — with the ...
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Among the living cells of the human body, and of the central and the peripheral nervous systems, it is neurons or nerve cells which are most immediately bound up with consciousness — with the antecedents of mental events, mental events themselves, and their consequents, the latter being other mental events and also actions. Neurons vary from very short indeed to a considerable length, and are constituted of structures and substructures which are open to study by light and electron microscopy and by many other converging means. Inspite of how scientific this bodily system is, and this is not the most often point of controversy, there remains to be various questions on consequences and still comes three categories of theories: determinist, near-determinist, and indeterminist.Less
Among the living cells of the human body, and of the central and the peripheral nervous systems, it is neurons or nerve cells which are most immediately bound up with consciousness — with the antecedents of mental events, mental events themselves, and their consequents, the latter being other mental events and also actions. Neurons vary from very short indeed to a considerable length, and are constituted of structures and substructures which are open to study by light and electron microscopy and by many other converging means. Inspite of how scientific this bodily system is, and this is not the most often point of controversy, there remains to be various questions on consequences and still comes three categories of theories: determinist, near-determinist, and indeterminist.
