Tracy Lupher - Academia.edu (original) (raw)
Papers by Tracy Lupher
The British Journal for the Philosophy of Science, 2016
Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quan... more Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. 1 Introduction 2 Weak Equivalence and Physical Equivalence 3 Mathematical Overview of Algebraic Quantum Field Theory 4 Fell’s Theorem and Philosophical Responses to Weak Equivalence 5 Weak Equivalence in C*-Algebras and W*-Algebras 6 Classical Equivalence and Weak Equivalence 7 Interlude: Is Weak Equivalence Really Physical Equivalence? 8 The Unruh Effect 9 Time Evolution and Symmetries 10 Conclusions Appendix 1 Introduction 2 Weak Equivalence and Physical Equivalence 3 Mathematical Overview of Algebraic Quantum Field Theory 4 Fell’s Theorem and Philosophical Responses to Weak Equivalence 5 Weak Equivalence in C*-Algebras and W*-Algebras 6 Classical Equivalence and Weak Equivalence 7 Interlude: Is Weak Equivalence Really Physical Equivalence? 8 The Unruh Effect 9 Time Evolution and Symmetries 10 Conclusions Appendix
repositories.lib.utexas.edu
... Mark Sainsbury Hans Halvorson Lawrence Sklar Page 3. ... dissertation and greatly appreciated... more ... Mark Sainsbury Hans Halvorson Lawrence Sklar Page 3. ... dissertation and greatly appreciated comradeship. I would like to extend my gratitude and sympathy to members of my dissertation committee: Fred Kronz, Hans Halvorson, Cory Juhl, Josh Dever, and Larry Sklar. ...
Synthese, 2007
The conserved quantities theory of causation (CQTC) attempts to use physics as the basis for an a... more The conserved quantities theory of causation (CQTC) attempts to use physics as the basis for an account of causation. However, a closer examination of the physics involved in CQTC reveals several critical failures. Some of the conserved quantities in physics cannot be used to distinguish causal interactions. Other conserved quantities cannot always be the properties of fields or particles. Finally, CQCT does not account for causal interactions that are static.
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2003
International Journal of Theoretical Physics, 2005
International Journal of Theoretical Physics, 2005
Southwest Philosophy Review, 2012
There are significant problems involved in determining the ontology of quantum field theory (QFT)... more There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.
and my family and friends … Acknowledgements The journey of this dissertation has been possible d... more and my family and friends … Acknowledgements The journey of this dissertation has been possible due to the support, generosity, and love of many people. When I began thinking about writing a dissertation in the philosophy of physics, I did not want to write yet another tome on an interpretation of quantum mechanics or Bell’s inequalities. I wanted a fresh new topic. In an advanced topics course in the philosophy of quantum theory, Fred Kronz introduced me to the algebraic approach to quantum field theory. Harald Atmanspacher gave some guest lectures on the algebraic approach, the puzzle of unitarily inequivalent representations, and Haag’s theorem. I was intrigued. After class I was talking with Harald and Fred on the steps of Waggener hall about these topics, I asked Harald if he could recommend a good book to start learning the algebraic approach to quantum field theory. He thought for a moment and then told me that there were no good introductory books! The results were scattered...
In the physics literature, there are several different characterizations of Haag’s theorem and it... more In the physics literature, there are several different characterizations of Haag’s theorem and its consequences for quantum field theory. These different versions of Haag’s theorem are due in part to various generalizations and more “rigorous” proofs of Haag’s theorem as well as to the fact that many of these proofs were done using different formulations of quantum field theory. As a result, there is confusion about what Haag’s theorem is and when it was proved. This paper clears up some of this confusion by examining the history and development of Haag’s theorem up to 1959. It is argued that the question of who proved Haag’s theorem is tied up with what the theorem is taken to show. 1.
counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . How... more counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . However, they will have an abstract counterpart in . There is also a natural embedding of A into ∗∗ ∗∗ ∗∗ ⊆ A A A such that . The most common way to construct a von Neumann algebra is to start with a C*-algebra and an abstract state A ω , construct a representation ( , ω ) π ω π H ( via the GNS theorem, and then close ) ω π A ( ) ω π A ′′ ( ) ω π A ′′ ∗∗ A in the weak topology .10F63 However, there is an equivalent alternative way to build using the bidual . Since C*-algebras and W*-algebras are both *-algebras, the GNS theorem can be used to construct Hilbert spaces from both algebras. In order for ∗∗ A ω to be a state for it must be extended to be a normal state ω ∗∗ A on .11F64 If the GNS construction is done using ∗ ω and ∗ A , then a von ( ) ω π _ 63 Though the notation for a von Neumann algebra closed in the weak topology is A , a von Neumann algebra is usually symbolized as ( ) ω π (...
There are significant problems involved in determining the ontology of quantum field theory (QFT)... more There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.
Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quan... more Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. 1 Introduction 2 Weak Equivalence and Physical Equivalence ...
The British Journal for the Philosophy of Science, 2016
Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quan... more Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. 1 Introduction 2 Weak Equivalence and Physical Equivalence 3 Mathematical Overview of Algebraic Quantum Field Theory 4 Fell’s Theorem and Philosophical Responses to Weak Equivalence 5 Weak Equivalence in C*-Algebras and W*-Algebras 6 Classical Equivalence and Weak Equivalence 7 Interlude: Is Weak Equivalence Really Physical Equivalence? 8 The Unruh Effect 9 Time Evolution and Symmetries 10 Conclusions Appendix 1 Introduction 2 Weak Equivalence and Physical Equivalence 3 Mathematical Overview of Algebraic Quantum Field Theory 4 Fell’s Theorem and Philosophical Responses to Weak Equivalence 5 Weak Equivalence in C*-Algebras and W*-Algebras 6 Classical Equivalence and Weak Equivalence 7 Interlude: Is Weak Equivalence Really Physical Equivalence? 8 The Unruh Effect 9 Time Evolution and Symmetries 10 Conclusions Appendix
repositories.lib.utexas.edu
... Mark Sainsbury Hans Halvorson Lawrence Sklar Page 3. ... dissertation and greatly appreciated... more ... Mark Sainsbury Hans Halvorson Lawrence Sklar Page 3. ... dissertation and greatly appreciated comradeship. I would like to extend my gratitude and sympathy to members of my dissertation committee: Fred Kronz, Hans Halvorson, Cory Juhl, Josh Dever, and Larry Sklar. ...
Synthese, 2007
The conserved quantities theory of causation (CQTC) attempts to use physics as the basis for an a... more The conserved quantities theory of causation (CQTC) attempts to use physics as the basis for an account of causation. However, a closer examination of the physics involved in CQTC reveals several critical failures. Some of the conserved quantities in physics cannot be used to distinguish causal interactions. Other conserved quantities cannot always be the properties of fields or particles. Finally, CQCT does not account for causal interactions that are static.
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2003
International Journal of Theoretical Physics, 2005
International Journal of Theoretical Physics, 2005
Southwest Philosophy Review, 2012
There are significant problems involved in determining the ontology of quantum field theory (QFT)... more There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.
and my family and friends … Acknowledgements The journey of this dissertation has been possible d... more and my family and friends … Acknowledgements The journey of this dissertation has been possible due to the support, generosity, and love of many people. When I began thinking about writing a dissertation in the philosophy of physics, I did not want to write yet another tome on an interpretation of quantum mechanics or Bell’s inequalities. I wanted a fresh new topic. In an advanced topics course in the philosophy of quantum theory, Fred Kronz introduced me to the algebraic approach to quantum field theory. Harald Atmanspacher gave some guest lectures on the algebraic approach, the puzzle of unitarily inequivalent representations, and Haag’s theorem. I was intrigued. After class I was talking with Harald and Fred on the steps of Waggener hall about these topics, I asked Harald if he could recommend a good book to start learning the algebraic approach to quantum field theory. He thought for a moment and then told me that there were no good introductory books! The results were scattered...
In the physics literature, there are several different characterizations of Haag’s theorem and it... more In the physics literature, there are several different characterizations of Haag’s theorem and its consequences for quantum field theory. These different versions of Haag’s theorem are due in part to various generalizations and more “rigorous” proofs of Haag’s theorem as well as to the fact that many of these proofs were done using different formulations of quantum field theory. As a result, there is confusion about what Haag’s theorem is and when it was proved. This paper clears up some of this confusion by examining the history and development of Haag’s theorem up to 1959. It is argued that the question of who proved Haag’s theorem is tied up with what the theorem is taken to show. 1.
counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . How... more counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . However, they will have an abstract counterpart in . There is also a natural embedding of A into ∗∗ ∗∗ ∗∗ ⊆ A A A such that . The most common way to construct a von Neumann algebra is to start with a C*-algebra and an abstract state A ω , construct a representation ( , ω ) π ω π H ( via the GNS theorem, and then close ) ω π A ( ) ω π A ′′ ( ) ω π A ′′ ∗∗ A in the weak topology .10F63 However, there is an equivalent alternative way to build using the bidual . Since C*-algebras and W*-algebras are both *-algebras, the GNS theorem can be used to construct Hilbert spaces from both algebras. In order for ∗∗ A ω to be a state for it must be extended to be a normal state ω ∗∗ A on .11F64 If the GNS construction is done using ∗ ω and ∗ A , then a von ( ) ω π _ 63 Though the notation for a von Neumann algebra closed in the weak topology is A , a von Neumann algebra is usually symbolized as ( ) ω π (...
There are significant problems involved in determining the ontology of quantum field theory (QFT)... more There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.
Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quan... more Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. 1 Introduction 2 Weak Equivalence and Physical Equivalence ...