Stephen Handel
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195169645
- eISBN:
- 9780199786732
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195169645.003.0010
- Subject:
- Psychology, Cognitive Psychology
Auditory and visual perception is the construction of meaningful objects in the world. Auditory and visual information is substitutable and tradable, and both exist in a common space/time framework. ...
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Auditory and visual perception is the construction of meaningful objects in the world. Auditory and visual information is substitutable and tradable, and both exist in a common space/time framework. However, the construction of objects is not simply based on local regions or temporal segments, but involves contextual information from cells that encode adjacent temporal segments or distant retinal points.Less
Auditory and visual perception is the construction of meaningful objects in the world. Auditory and visual information is substitutable and tradable, and both exist in a common space/time framework. However, the construction of objects is not simply based on local regions or temporal segments, but involves contextual information from cells that encode adjacent temporal segments or distant retinal points.
C. B. Martin
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199234103
- eISBN:
- 9780191715570
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234103.003.0016
- Subject:
- Philosophy, Philosophy of Mind
This chapter attempts to establish ontologically some of what Einstein established in physics. Einstein was himself driven by ontological forms of argument. Seeing what might have been underneath and ...
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This chapter attempts to establish ontologically some of what Einstein established in physics. Einstein was himself driven by ontological forms of argument. Seeing what might have been underneath and behind some of Einstein's most basic thoughts should teach us something valuable. It presents a model that is not limited to particle-objects-in-space-time; it also fits well for explanations in terms of warps and woofs of space-time as infinitesimal energy-loops or superstrings. It is argued that space-time has properties, yet it is not itself had as a property or even a set of properties, and it could not exist without properties. A propertied space-time is a one-object universe and space-time satisfies the correct definitions of ‘substratum’.Less
This chapter attempts to establish ontologically some of what Einstein established in physics. Einstein was himself driven by ontological forms of argument. Seeing what might have been underneath and behind some of Einstein's most basic thoughts should teach us something valuable. It presents a model that is not limited to particle-objects-in-space-time; it also fits well for explanations in terms of warps and woofs of space-time as infinitesimal energy-loops or superstrings. It is argued that space-time has properties, yet it is not itself had as a property or even a set of properties, and it could not exist without properties. A propertied space-time is a one-object universe and space-time satisfies the correct definitions of ‘substratum’.
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:
- 10.1093/0199278245.003.0002
- Subject:
- Philosophy, Philosophy of Science
This chapter presents a summary of the history of classical statistical mechanics, emphasizing the underlying assumptions regarding particle individuality. It is argued that the relevant sense of ...
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This chapter presents a summary of the history of classical statistical mechanics, emphasizing the underlying assumptions regarding particle individuality. It is argued that the relevant sense of individuality is articulated within the theory in two different forms: transcendental individuality and space-time individuality. Huggett’s claim that classical statistics is metaphysically neutral is analyzed with regard to individuality, and it is shown that a form of space-time individuality is presupposed. This is articulated in the context of a ‘field theoretic’ re-writing of the theory free of any underlying presupposition of ‘transcendental individuality’. Hence, classical statistical mechanics supports (at least) two different accounts of particle individuality, and hence we have a weak form of underdetermination of the relevant metaphysics by the physics. Talk of ‘space-time’ individuality leads into a discussion of the individuality and identity of the space-time points themselves, covering the debate between Grünbaum and Stein, and the recent work of Hoefer and others.Less
This chapter presents a summary of the history of classical statistical mechanics, emphasizing the underlying assumptions regarding particle individuality. It is argued that the relevant sense of individuality is articulated within the theory in two different forms: transcendental individuality and space-time individuality. Huggett’s claim that classical statistics is metaphysically neutral is analyzed with regard to individuality, and it is shown that a form of space-time individuality is presupposed. This is articulated in the context of a ‘field theoretic’ re-writing of the theory free of any underlying presupposition of ‘transcendental individuality’. Hence, classical statistical mechanics supports (at least) two different accounts of particle individuality, and hence we have a weak form of underdetermination of the relevant metaphysics by the physics. Talk of ‘space-time’ individuality leads into a discussion of the individuality and identity of the space-time points themselves, covering the debate between Grünbaum and Stein, and the recent work of Hoefer and others.
Craig Bourne
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199212804
- eISBN:
- 9780191707094
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199212804.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology
Discusses the Galilean transformations, and the Newtonian conception of space, time, and motion, essentials for understanding the Lorentz transformations and Einstein's special theory of relativity. ...
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Discusses the Galilean transformations, and the Newtonian conception of space, time, and motion, essentials for understanding the Lorentz transformations and Einstein's special theory of relativity. Discusses, with the aid of many diagrams, the properties of Minkowski space‐time, such as the relativity of simultaneity, and concludes with some reflections on their philosophical significance.Less
Discusses the Galilean transformations, and the Newtonian conception of space, time, and motion, essentials for understanding the Lorentz transformations and Einstein's special theory of relativity. Discusses, with the aid of many diagrams, the properties of Minkowski space‐time, such as the relativity of simultaneity, and concludes with some reflections on their philosophical significance.
David M. Armstrong
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199590612
- eISBN:
- 9780191723391
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590612.003.0001
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time ...
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The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time is subject to scientific investigation (Wilfrid Sellars' distinction between the manifest and the scientific image of the world). Is there room for metaphysics? Yes, because a number of topic neutral notions (of which causality is an important instance) are contested by philosophers and scientists. As argued by C.B. Martin, metaphysics seeks a more abstract model of the world than that provided by science.Less
The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time is subject to scientific investigation (Wilfrid Sellars' distinction between the manifest and the scientific image of the world). Is there room for metaphysics? Yes, because a number of topic neutral notions (of which causality is an important instance) are contested by philosophers and scientists. As argued by C.B. Martin, metaphysics seeks a more abstract model of the world than that provided by science.
Storrs McCall
- Published in print:
- 1996
- Published Online:
- October 2011
- ISBN:
- 9780198236221
- eISBN:
- 9780191679209
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198236221.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
This book presents a philosophical theory of the nature of the universe based on a new model of its space-time structure. The book shows how his model illuminates a broad range of subjects, including ...
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This book presents a philosophical theory of the nature of the universe based on a new model of its space-time structure. The book shows how his model illuminates a broad range of subjects, including causation, probability, quantum mechanics, identity, and free will, and argues that the fact that the model throws light on such a large number of problems constitutes strong evidence that the universe is as the model portrays it.Less
This book presents a philosophical theory of the nature of the universe based on a new model of its space-time structure. The book shows how his model illuminates a broad range of subjects, including causation, probability, quantum mechanics, identity, and free will, and argues that the fact that the model throws light on such a large number of problems constitutes strong evidence that the universe is as the model portrays it.
Harvey R. Brown
- Published in print:
- 2005
- Published Online:
- September 2006
- ISBN:
- 9780199275830
- eISBN:
- 9780191603914
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199275831.003.0001
- Subject:
- Philosophy, Philosophy of Science
Following Einstein's brilliant 1905 work on the electrodynamics of moving bodies, and its geometrization by Minkowski which proved to be so important for the development of Einstein's general theory ...
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Following Einstein's brilliant 1905 work on the electrodynamics of moving bodies, and its geometrization by Minkowski which proved to be so important for the development of Einstein's general theory of relativity, it became standard to view the FitzGerald-Lorentz hypothesis as the right idea based on the wrong reasoning. This chapter expresses doubts that this standard view is correct, and believes that posterity will look kindly on the merits of the pre-Einsteinian, ‘constructive’ reasoning of FitzGerald, if not Lorentz. The theories of FitzeGerald, Michelson, Heaviside, Einstein, and Bell are discussed. The chapter also considers what space-time is not.Less
Following Einstein's brilliant 1905 work on the electrodynamics of moving bodies, and its geometrization by Minkowski which proved to be so important for the development of Einstein's general theory of relativity, it became standard to view the FitzGerald-Lorentz hypothesis as the right idea based on the wrong reasoning. This chapter expresses doubts that this standard view is correct, and believes that posterity will look kindly on the merits of the pre-Einsteinian, ‘constructive’ reasoning of FitzGerald, if not Lorentz. The theories of FitzeGerald, Michelson, Heaviside, Einstein, and Bell are discussed. The chapter also considers what space-time is not.
Harvey R. Brown
- Published in print:
- 2005
- Published Online:
- September 2006
- ISBN:
- 9780199275830
- eISBN:
- 9780191603914
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199275831.003.0002
- Subject:
- Philosophy, Philosophy of Science
This chapter discusses the physics of coordinate transformations. Topics covered include coordinatization of space-time, inertial coordinate systems, the linearity of inertial coordinate ...
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This chapter discusses the physics of coordinate transformations. Topics covered include coordinatization of space-time, inertial coordinate systems, the linearity of inertial coordinate transformations, and the rod and clock protocols.Less
This chapter discusses the physics of coordinate transformations. Topics covered include coordinatization of space-time, inertial coordinate systems, the linearity of inertial coordinate transformations, and the rod and clock protocols.
James Ladyman, Don Ross, David Spurrett, and John Collier
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199276196
- eISBN:
- 9780191706127
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199276196.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
This chapter examines Ontic Structural Realism (OSR) and its relationship with the philosophy of physics. OSR is the view that the world has an objective modal structure that is ontologically ...
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This chapter examines Ontic Structural Realism (OSR) and its relationship with the philosophy of physics. OSR is the view that the world has an objective modal structure that is ontologically fundamental, in the sense of not supervening on the intrinsic properties of a set of individuals. According to OSR, even the identity and individuality of objects depends on the relational structure of the world. In keeping with the principle of naturalistic closure (PNC), this account must not imply revision of special sciences for the sake of metaphysical comfort. The purpose of this chapter is to motivate OSR from contemporary fundamental physics, as the PNC requires. This chapter argues for a position that consists in the conjunction of eliminativism about self-subsistent individuals, the view that relational structure is ontologically fundamental, and structural realism (interpreted as the claim that science describes the objective modal structure of the world).Less
This chapter examines Ontic Structural Realism (OSR) and its relationship with the philosophy of physics. OSR is the view that the world has an objective modal structure that is ontologically fundamental, in the sense of not supervening on the intrinsic properties of a set of individuals. According to OSR, even the identity and individuality of objects depends on the relational structure of the world. In keeping with the principle of naturalistic closure (PNC), this account must not imply revision of special sciences for the sake of metaphysical comfort. The purpose of this chapter is to motivate OSR from contemporary fundamental physics, as the PNC requires. This chapter argues for a position that consists in the conjunction of eliminativism about self-subsistent individuals, the view that relational structure is ontologically fundamental, and structural realism (interpreted as the claim that science describes the objective modal structure of the world).
Lynette A. Jones and Susan J. Lederman
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195173154
- eISBN:
- 9780199786749
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195173154.003.0011
- Subject:
- Psychology, Cognitive Neuroscience
This chapter draws some conclusions about human hand function from the research reviewed in the book and argues that the categorization of hand function along the sensorimotor continuum has provided ...
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This chapter draws some conclusions about human hand function from the research reviewed in the book and argues that the categorization of hand function along the sensorimotor continuum has provided a useful framework for analyzing manual performance. Future directions of research are proposed and these include the need for more detailed histological studies of human hands, analyses of space-time interactions and of the frames of reference used to perceive spatial patterns in the hand, further studies of highly skilled manual activities, such as microsurgery, that test the limits of manual dexterity, and additional research on understanding how multiple sources of sensory information are integrated to perceive an object and its properties.Less
This chapter draws some conclusions about human hand function from the research reviewed in the book and argues that the categorization of hand function along the sensorimotor continuum has provided a useful framework for analyzing manual performance. Future directions of research are proposed and these include the need for more detailed histological studies of human hands, analyses of space-time interactions and of the frames of reference used to perceive spatial patterns in the hand, further studies of highly skilled manual activities, such as microsurgery, that test the limits of manual dexterity, and additional research on understanding how multiple sources of sensory information are integrated to perceive an object and its properties.
Theodore Sider
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199244430
- eISBN:
- 9780191598425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019924443X.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology
The ‘B‐theory’ of time says that all temporal facts ‘reduce’ to tenseless facts about a manifold of equally real past, present, and future objects; the ‘A‐theory’ denies this reduction. Presentism is ...
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The ‘B‐theory’ of time says that all temporal facts ‘reduce’ to tenseless facts about a manifold of equally real past, present, and future objects; the ‘A‐theory’ denies this reduction. Presentism is a version of the A‐theory that denies the existence of part of the B‐theorist's manifold: the part containing merely past and future objects. Some say that the B‐theory cannot account for the irreducibly temporal nature of our psychological attitudes, but this is incorrect. B‐theorists can defend temporal versions of well‐known theories of ‘indexical’, or ‘de se’, attitudes. Presentism, on the other hand, is vulnerable to powerful objections: (1) The irreducible tense‐operators to which presentists must appeal are objectionably ungrounded in reality. (2) Presentists cannot account for the fundamental ‘cross‐time spatial relations’ that ground the structure of space‐time, and thus cannot account for spatiotemporal continuity, acceleration, and other states of motion. (3) Presentism conflicts with the special theory of relativity.Less
The ‘B‐theory’ of time says that all temporal facts ‘reduce’ to tenseless facts about a manifold of equally real past, present, and future objects; the ‘A‐theory’ denies this reduction. Presentism is a version of the A‐theory that denies the existence of part of the B‐theorist's manifold: the part containing merely past and future objects. Some say that the B‐theory cannot account for the irreducibly temporal nature of our psychological attitudes, but this is incorrect. B‐theorists can defend temporal versions of well‐known theories of ‘indexical’, or ‘de se’, attitudes. Presentism, on the other hand, is vulnerable to powerful objections: (1) The irreducible tense‐operators to which presentists must appeal are objectionably ungrounded in reality. (2) Presentists cannot account for the fundamental ‘cross‐time spatial relations’ that ground the structure of space‐time, and thus cannot account for spatiotemporal continuity, acceleration, and other states of motion. (3) Presentism conflicts with the special theory of relativity.
Michele Maggiore
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570745
- eISBN:
- 9780191717666
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570745.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses how to go beyond the limit of sources moving in flat space-time. For a self-gravitating system such as a binary star, assuming that space-time is flat means that its dynamics ...
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This chapter discusses how to go beyond the limit of sources moving in flat space-time. For a self-gravitating system such as a binary star, assuming that space-time is flat means that its dynamics is described using Newtonian gravity, rather than general relativity. When dealing with a (moderately) relativistic system, held together by gravitational forces, the source is better described by a post-Newtonian formalism. After recalling the post-Newtonian expansion in general relativity and how to obtain the lowest-order correction to the Newtonian equations of motion, GW generation by post-Newtonian sources is described, and the application to sources with strong gravitational fields, such as neutron stars and black holes, is then presented. The results of this chapter have an intrinsic conceptual interest, since the full non-linear structure of general relativity at work can be seen here. Furthermore, this formalism is of paramount importance in the computation of the waveform from an inspiraling binary system, and its extraction from the data of interferometric GW detectors.Less
This chapter discusses how to go beyond the limit of sources moving in flat space-time. For a self-gravitating system such as a binary star, assuming that space-time is flat means that its dynamics is described using Newtonian gravity, rather than general relativity. When dealing with a (moderately) relativistic system, held together by gravitational forces, the source is better described by a post-Newtonian formalism. After recalling the post-Newtonian expansion in general relativity and how to obtain the lowest-order correction to the Newtonian equations of motion, GW generation by post-Newtonian sources is described, and the application to sources with strong gravitational fields, such as neutron stars and black holes, is then presented. The results of this chapter have an intrinsic conceptual interest, since the full non-linear structure of general relativity at work can be seen here. Furthermore, this formalism is of paramount importance in the computation of the waveform from an inspiraling binary system, and its extraction from the data of interferometric GW detectors.
M. S. Sozzi
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199296668
- eISBN:
- 9780191712074
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296668.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter discusses charge conjugation symmetry, which emerges naturally out of the mating of quantum theory to special relativity, with the antiparticle concept. Despite not being related to ...
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This chapter discusses charge conjugation symmetry, which emerges naturally out of the mating of quantum theory to special relativity, with the antiparticle concept. Despite not being related to space-time, this symmetry turns out to be closely linked to space-time inversions; its consequences are somewhat less widespread than those of parity symmetry, mainly because only neutral systems can be eigenstates of charge conjugation. Charge conjugation symmetry is maximally violated by weak interactions in a way that is closely linked to parity violation. The large violation of parity and charge conjugation symmetries in weak interactions, the intrinsic difficulties in experimenting with composite antimatter systems, and the fact that CPT symmetry constrains several properties of matter and antimatter to be equal, all contribute to the fact that investigations shifted towards the study of the combined symmetry CP instead. A list of further reading and a selection of exercise problems are presented at the end of the chapter.Less
This chapter discusses charge conjugation symmetry, which emerges naturally out of the mating of quantum theory to special relativity, with the antiparticle concept. Despite not being related to space-time, this symmetry turns out to be closely linked to space-time inversions; its consequences are somewhat less widespread than those of parity symmetry, mainly because only neutral systems can be eigenstates of charge conjugation. Charge conjugation symmetry is maximally violated by weak interactions in a way that is closely linked to parity violation. The large violation of parity and charge conjugation symmetries in weak interactions, the intrinsic difficulties in experimenting with composite antimatter systems, and the fact that CPT symmetry constrains several properties of matter and antimatter to be equal, all contribute to the fact that investigations shifted towards the study of the combined symmetry CP instead. A list of further reading and a selection of exercise problems are presented at the end of the chapter.
Kazuo Fujikawa and Hiroshi Suzuki
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter discusses chiral anomalies associated with the gravitational field, namely, gravitational anomalies. It discusses gravitational generalization of chiral U(1) anomalies for ordinary gauge ...
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This chapter discusses chiral anomalies associated with the gravitational field, namely, gravitational anomalies. It discusses gravitational generalization of chiral U(1) anomalies for ordinary gauge fields. A method for evaluating the Dirac genus and Chern characters in general 2n-dimensional Euclidean space-time is given. It is explained that there appear to be quantum anomalies in general coordinate and local Lorentz transformations for chiral Dirac fields in (4n+2)-dimensional curved space-time. If these anomalies are not cancelled, the basic principles of general relativity and quantum theory become incompatible with each other.Less
This chapter discusses chiral anomalies associated with the gravitational field, namely, gravitational anomalies. It discusses gravitational generalization of chiral U(1) anomalies for ordinary gauge fields. A method for evaluating the Dirac genus and Chern characters in general 2n-dimensional Euclidean space-time is given. It is explained that there appear to be quantum anomalies in general coordinate and local Lorentz transformations for chiral Dirac fields in (4n+2)-dimensional curved space-time. If these anomalies are not cancelled, the basic principles of general relativity and quantum theory become incompatible with each other.
R. E. Raab and O. L. de Lange
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Polar and axial vectors and tensors are defined in terms of their behaviour under coordinate transformations. The effect of the time-reversal operator on kets and matrix elements is considered, ...
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Polar and axial vectors and tensors are defined in terms of their behaviour under coordinate transformations. The effect of the time-reversal operator on kets and matrix elements is considered, followed by a tabulation of the space and time properties of various tensors — mechanical, electromagnetic, isotropic, and multipole. An account is given of the point-group symmetries of molecules and non-magnetic and magnetic crystals, with worked examples of the effect of symmetry on the components of a property tensor. The origin dependence of multipole moment operators is derived and used to obtain that of polarizability tensors up to electric octopole-magnetic quadrupole order. A pictorial approach is described for determining the symmetry conditions for the existence of an equilibrium effect and this is illustrated for the Faraday effect in a fluid and crystal.Less
Polar and axial vectors and tensors are defined in terms of their behaviour under coordinate transformations. The effect of the time-reversal operator on kets and matrix elements is considered, followed by a tabulation of the space and time properties of various tensors — mechanical, electromagnetic, isotropic, and multipole. An account is given of the point-group symmetries of molecules and non-magnetic and magnetic crystals, with worked examples of the effect of symmetry on the components of a property tensor. The origin dependence of multipole moment operators is derived and used to obtain that of polarizability tensors up to electric octopole-magnetic quadrupole order. A pictorial approach is described for determining the symmetry conditions for the existence of an equilibrium effect and this is illustrated for the Faraday effect in a fluid and crystal.
Michael Munowitz
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195167375
- eISBN:
- 9780199787104
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195167375.003.0005
- Subject:
- Physics, History of Physics
Newtonian mechanics is revisited in the light of Einsteinian relativity, and the repercussions shake physics to its core. Special relativity, by placing all inertial observers on the same footing, ...
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Newtonian mechanics is revisited in the light of Einsteinian relativity, and the repercussions shake physics to its core. Special relativity, by placing all inertial observers on the same footing, leads to the equivalence of mass and energy: E = mc2 . General relativity, by granting the same rights to observers even in accelerated reference frames, leads to a revolutionary new theory of gravity: a force-free warping of space-time in the presence of mass.Less
Newtonian mechanics is revisited in the light of Einsteinian relativity, and the repercussions shake physics to its core. Special relativity, by placing all inertial observers on the same footing, leads to the equivalence of mass and energy: E = mc2 . General relativity, by granting the same rights to observers even in accelerated reference frames, leads to a revolutionary new theory of gravity: a force-free warping of space-time in the presence of mass.
Kazuo Fujikawa and Hiroshi Suzuki
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this ...
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This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this anomaly is related to the renormalization group and the calculation of the $β$ function in the renormalization group equation is related to the calculation of the Weyl anomaly. In other words, the renormalization group equation is regarded as an expression of the Weyl anomaly in terms of Green’s functions. The calculation of the one-loop functions in QED and QCD by means of the Jacobians for the Weyl symmetry is illustrated. The Weyl anomalies in curved space-time are briefly explained. An improved finite energy-momentum tensor in renormalizable theory is also mentioned based on an analysis of the Weyl anomaly.Less
This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this anomaly is related to the renormalization group and the calculation of the $β$ function in the renormalization group equation is related to the calculation of the Weyl anomaly. In other words, the renormalization group equation is regarded as an expression of the Weyl anomaly in terms of Green’s functions. The calculation of the one-loop functions in QED and QCD by means of the Jacobians for the Weyl symmetry is illustrated. The Weyl anomalies in curved space-time are briefly explained. An improved finite energy-momentum tensor in renormalizable theory is also mentioned based on an analysis of the Weyl anomaly.
Simon Palfrey and Tiffany Stern
- Published in print:
- 2007
- Published Online:
- October 2011
- ISBN:
- 9780199272051
- eISBN:
- 9780191699580
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199272051.003.0016
- Subject:
- Literature, Shakespeare Studies
This chapter shows that in The Tempest, Shakespeare takes the basic stakes in the cue — what happens if a cue is taken, what happens if it is not, what happens if it is taken twice — and creates an ...
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This chapter shows that in The Tempest, Shakespeare takes the basic stakes in the cue — what happens if a cue is taken, what happens if it is not, what happens if it is taken twice — and creates an island in its image. The cue is always a hinge-point between one subject and another, and one subject's space-time and another. It is a point where minds almost meet, or where they overlap, commingle, and yet remain discrete and unknowable. It can be likened to a synapse — the junction between two neurons or nerve-cells. For the cue is likewise at once a terminal point, a beginning, and a supercharged gap between the two. But if the sensory or motor impulses of a part are relayed in its cues, there is never a simple forward movement, from one cell to another in an onrushing succession. This is the case with all cues, whatever their apparently orderly succession: but it is all the more emphatically the case with repeated cues. For with repeated cues we find that at crucial points the system is not relaying information as it supposedly should: the nerve impulses at issue start looping or ricocheting back upon their origin.Less
This chapter shows that in The Tempest, Shakespeare takes the basic stakes in the cue — what happens if a cue is taken, what happens if it is not, what happens if it is taken twice — and creates an island in its image. The cue is always a hinge-point between one subject and another, and one subject's space-time and another. It is a point where minds almost meet, or where they overlap, commingle, and yet remain discrete and unknowable. It can be likened to a synapse — the junction between two neurons or nerve-cells. For the cue is likewise at once a terminal point, a beginning, and a supercharged gap between the two. But if the sensory or motor impulses of a part are relayed in its cues, there is never a simple forward movement, from one cell to another in an onrushing succession. This is the case with all cues, whatever their apparently orderly succession: but it is all the more emphatically the case with repeated cues. For with repeated cues we find that at crucial points the system is not relaying information as it supposedly should: the nerve impulses at issue start looping or ricocheting back upon their origin.
John Hawthorne
- Published in print:
- 2006
- Published Online:
- September 2010
- ISBN:
- 9780199291236
- eISBN:
- 9780191710612
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199291236.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter examines modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of ...
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This chapter examines modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of qualitative locations excludes certain possibilities for qualitative reality. In each case the excluded possibilities are pre-analytically possible. Some of the possibilities can be reinstated by modifying the locationless theories, but at the cost of an unattractive holism.Less
This chapter examines modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of qualitative locations excludes certain possibilities for qualitative reality. In each case the excluded possibilities are pre-analytically possible. Some of the possibilities can be reinstated by modifying the locationless theories, but at the cost of an unattractive holism.
H. Asada, T. Futamase, and P. A. Hogan
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199584109
- eISBN:
- 9780191723421
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199584109.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
To model a small black hole moving in an external field we follow the approach of Futamase, Hogan, and Itoh. The space‐time model of the external field provides us with a background space‐time. If ...
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To model a small black hole moving in an external field we follow the approach of Futamase, Hogan, and Itoh. The space‐time model of the external field provides us with a background space‐time. If the external field is a vacuum gravitational field, due to a large black hole for example, then the background space‐time is a non‐flat solution of Einstein's vacuum field equations. If we wish to model a small charged black hole moving in external gravitational and electromagnetic fields then the background space‐time is a solution of the vacuum Einstein‐Maxwell field equations. This chapter includes the charged case because it provides a relatively easily manageable example to illustrate the method of derivation of the equations of motion including radiation reaction. The world‐line or history of the black hole will be a non‐singular time‐like world‐line in the background space‐time. The field of the small black hole is introduced as a small perturbation of the background space‐time which, inter alia, is singular on this world‐line. The equations of motion of the black hole will be differential equations for this world‐line, obtained using the field equations which determine the small perturbation. The perturbed space‐time will be an approximate solution of the vacuum Einstein or Einstein‐Maxwell field equations as appropriate. To lay the foundations for this approach to equations of motion the geometry of background space-time must be studied.Less
To model a small black hole moving in an external field we follow the approach of Futamase, Hogan, and Itoh. The space‐time model of the external field provides us with a background space‐time. If the external field is a vacuum gravitational field, due to a large black hole for example, then the background space‐time is a non‐flat solution of Einstein's vacuum field equations. If we wish to model a small charged black hole moving in external gravitational and electromagnetic fields then the background space‐time is a solution of the vacuum Einstein‐Maxwell field equations. This chapter includes the charged case because it provides a relatively easily manageable example to illustrate the method of derivation of the equations of motion including radiation reaction. The world‐line or history of the black hole will be a non‐singular time‐like world‐line in the background space‐time. The field of the small black hole is introduced as a small perturbation of the background space‐time which, inter alia, is singular on this world‐line. The equations of motion of the black hole will be differential equations for this world‐line, obtained using the field equations which determine the small perturbation. The perturbed space‐time will be an approximate solution of the vacuum Einstein or Einstein‐Maxwell field equations as appropriate. To lay the foundations for this approach to equations of motion the geometry of background space-time must be studied.
