Hans Coessens | Birkbeck College, University of London (original) (raw)
Uploads
Papers by Hans Coessens
Christian Wut¨ hrich: Office hours are Th 3:30-5, and by appointmentRoom 8047 HSS T 858-534-6548 B ... more Christian Wut¨ hrich: Office hours are Th 3:30-5, and by appointmentRoom 8047 HSS T 858-534-6548 B wuthrich@ucsd.eduAfter having equipped ourselves with the necessary mathematical tools, we will plunge intoa careful study of the venerable mystery of quantum nonlocality. In exactly what sense isnonlocality enshrined in the theorems by Bell and by Kochen and Specker? Any solutionof the measurement problem in quantum mechanics (another venerable mystery)—indeedany future physical theory—must acknowledge this nonlocality. Nonlocality is disconcertingnot only because it contravenes our deeply engrained intuitions, but also because it standsin a stark tension to relativity. But both quantum mechanics (and with it, nonlocality)and special relativity have given us the most accurate empirical predictions we have everhad from physical theories. This seminar will focus its attention on this tension and trackdown how it plays out in all the most important interpretations of quantum mechanicsavailable today: hidden variables/Bohmian mechanics, collapse theories/GRW, and many-worlds interpretations and recent developments of Everett’s original proposal.Prerequisites: As announced earlier, I plan to do this at an intermediate level, i.e. I amassuming that students will have something like my Phil 146 under their belt. Alternatively,if you have worked through most of David Albert’s book, or have done something equivalent,or are prepared to work extra hard to make up for that. In particular, I assume that studentsare familiar with the basics of the theory and its formalism (as presented e.g. in the secondchapter of Albert), what the measurement problem is, and what the basic interpretationaloptions are.
In this dissertation we propose to investigate, after a thorough presentation of what the basic s... more In this dissertation we propose to investigate, after a thorough presentation of what the basic structures of quantum mechanics are, the main philosophical problem which arises as the theory is formulated in its non-relativistic manner. This problem has yielded physicists since the conception of the theory to develop "interpretations" which experimentally are all equivalent or underdetermined. These questions over how to interpret quantum mechanics are philosophical by their very nature. The American physicist Richard Feynman once famously stated: "I think I can safely say that nobody understands quantum mechanics." Whether or not this statement is an extrapolation of reality can be decided based upon the interpretation one has of the theory altogether. We here shall argue that of all of the interpretations concerning the philosophical problem of non-relativistic quantum mechanics, the most satisfying is the reformulation of the theory in terms of a pilot-wave dynamics. This reformulation was first given by Louis de Broglie and later on perfected by David Bohm and J.S. Bell. It will become clear throughout the dissertation that it is the most satisfying solution to what has become known as the measurement problem.
Drafts by Hans Coessens
With the quest for a solid foundation for mathematics raging for over a century, the debate withi... more With the quest for a solid foundation for mathematics raging for over a century, the debate within the philosophical community has shifted from the initial concerns shared by Gottlob Frege and Bertrand Russell over whether or not mathematics, more specifically arithmetic, is reducible to logic. Set theory, with all of its ontological commitments has given rise to a new debate in the philosophy of mathematics over whether or not it requires an interpretation before establishing itself as a foundation for mathematics. The aim of this dissertation is to investigate particularly whether the naïve conception of sets is adequate for grounding the system of numbers. Within this discussion we shall briefly examine rival theories or conceptions of sets. One of the main defenders of the naïve conception is Alan Weir. We shall examine his work to defend it and assess its strength. By reviewing the traditional paradoxes associated with naïve set theory, I will provide Weir's answer to them within the framework of naïve set theory. His strategy will be shown to be erroneous. We shall also compare the naïve conception of sets to other conceptions to see how it squares within the debate over the foundations of mathematics. One such conception is known as the iterative conception, which claims that sets are formed by sequences of previous members; this view is exemplified in the work of Ernest Zermelo and George Boolos. A similar strategy provided by Linnebo will also be presented in this paper for discussion. We shall conclude by demonstrating that thus far no conception of sets provided by logicians and philosophers has adequately answered all questions of consistency without compromising strength in its axioms. It shall be evident that the naïve conception of sets is yet another theory that faces problems in accounting for the foundations of mathematics.
Christian Wut¨ hrich: Office hours are Th 3:30-5, and by appointmentRoom 8047 HSS T 858-534-6548 B ... more Christian Wut¨ hrich: Office hours are Th 3:30-5, and by appointmentRoom 8047 HSS T 858-534-6548 B wuthrich@ucsd.eduAfter having equipped ourselves with the necessary mathematical tools, we will plunge intoa careful study of the venerable mystery of quantum nonlocality. In exactly what sense isnonlocality enshrined in the theorems by Bell and by Kochen and Specker? Any solutionof the measurement problem in quantum mechanics (another venerable mystery)—indeedany future physical theory—must acknowledge this nonlocality. Nonlocality is disconcertingnot only because it contravenes our deeply engrained intuitions, but also because it standsin a stark tension to relativity. But both quantum mechanics (and with it, nonlocality)and special relativity have given us the most accurate empirical predictions we have everhad from physical theories. This seminar will focus its attention on this tension and trackdown how it plays out in all the most important interpretations of quantum mechanicsavailable today: hidden variables/Bohmian mechanics, collapse theories/GRW, and many-worlds interpretations and recent developments of Everett’s original proposal.Prerequisites: As announced earlier, I plan to do this at an intermediate level, i.e. I amassuming that students will have something like my Phil 146 under their belt. Alternatively,if you have worked through most of David Albert’s book, or have done something equivalent,or are prepared to work extra hard to make up for that. In particular, I assume that studentsare familiar with the basics of the theory and its formalism (as presented e.g. in the secondchapter of Albert), what the measurement problem is, and what the basic interpretationaloptions are.
In this dissertation we propose to investigate, after a thorough presentation of what the basic s... more In this dissertation we propose to investigate, after a thorough presentation of what the basic structures of quantum mechanics are, the main philosophical problem which arises as the theory is formulated in its non-relativistic manner. This problem has yielded physicists since the conception of the theory to develop "interpretations" which experimentally are all equivalent or underdetermined. These questions over how to interpret quantum mechanics are philosophical by their very nature. The American physicist Richard Feynman once famously stated: "I think I can safely say that nobody understands quantum mechanics." Whether or not this statement is an extrapolation of reality can be decided based upon the interpretation one has of the theory altogether. We here shall argue that of all of the interpretations concerning the philosophical problem of non-relativistic quantum mechanics, the most satisfying is the reformulation of the theory in terms of a pilot-wave dynamics. This reformulation was first given by Louis de Broglie and later on perfected by David Bohm and J.S. Bell. It will become clear throughout the dissertation that it is the most satisfying solution to what has become known as the measurement problem.
With the quest for a solid foundation for mathematics raging for over a century, the debate withi... more With the quest for a solid foundation for mathematics raging for over a century, the debate within the philosophical community has shifted from the initial concerns shared by Gottlob Frege and Bertrand Russell over whether or not mathematics, more specifically arithmetic, is reducible to logic. Set theory, with all of its ontological commitments has given rise to a new debate in the philosophy of mathematics over whether or not it requires an interpretation before establishing itself as a foundation for mathematics. The aim of this dissertation is to investigate particularly whether the naïve conception of sets is adequate for grounding the system of numbers. Within this discussion we shall briefly examine rival theories or conceptions of sets. One of the main defenders of the naïve conception is Alan Weir. We shall examine his work to defend it and assess its strength. By reviewing the traditional paradoxes associated with naïve set theory, I will provide Weir's answer to them within the framework of naïve set theory. His strategy will be shown to be erroneous. We shall also compare the naïve conception of sets to other conceptions to see how it squares within the debate over the foundations of mathematics. One such conception is known as the iterative conception, which claims that sets are formed by sequences of previous members; this view is exemplified in the work of Ernest Zermelo and George Boolos. A similar strategy provided by Linnebo will also be presented in this paper for discussion. We shall conclude by demonstrating that thus far no conception of sets provided by logicians and philosophers has adequately answered all questions of consistency without compromising strength in its axioms. It shall be evident that the naïve conception of sets is yet another theory that faces problems in accounting for the foundations of mathematics.