Categories, Quanta, Concepts (CQC) http://pirsa.org/podcast/C09008 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:44:45 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:44:45 -0500 G 180 pirsa-admin@perimeterinstitute.ca Steve Bradwell's - Podcast Generator TBA Ross Duncan http://streamer.perimeterinstitute.ca/mp3/61a072a1-4218-4652-ad03-1346967d342c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/61a072a1-4218-4652-ad03-1346967d342c.mp3 Mon, 01 Jun 2009 10:15:00 -0400 TBA Bob Coecke http://streamer.perimeterinstitute.ca/mp3/3ac583ff-560d-4fc5-8e43-b0fe91ce4da0.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3ac583ff-560d-4fc5-8e43-b0fe91ce4da0.mp3 Mon, 01 Jun 2009 11:30:00 -0400 I will rephrase the question, "What is a quantal reality?" as "What is a quantal history?" (the word history having here the same meaning as in the phrase sum-over-histories). The answer I will propose modifies the rules of logical inference in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical logic, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular. Rafael Sorkin http://streamer.perimeterinstitute.ca/mp3/93210614-9697-4cd7-8c54-1d01871cc26f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/93210614-9697-4cd7-8c54-1d01871cc26f.mp3 Mon, 01 Jun 2009 12:15:00 -0400 Work on formulating general probabilistic theories in an operational context has tended to concentrate on the probabilistic aspects (convex cones and so on) while remaining relatively naive about how the operational structure is built up (combining operations to form composite systems, and so on). In particular, an unsophisticated notion of a background time is usually taken for granted. It pays to be more careful about these matters for two reasons. First, by getting the foundations of the operational structure correct it can be easier to prove theorems. And second, if we want to construct new theories (such as a theory of Quantum Gravity) we need to start out with a sufficiently general operational structure before we introduce probabilities. I will present an operational structure which is sufficient to provide a foundation for the probabilistic concepts necessary to formulate quantum theory. According to Bob Coecke, this operational structure corresponds to a symmetric monoidal category. I will then discuss a more general operational framework (which I call Object Oriented Operationalism) which provides a foundation for a more general probabilistic framework which may be sufficient to formulate a theory of Quantum Gravity. This more general operational structure does not admit an obvious category theoretic formulation. Lucien Hardy http://streamer.perimeterinstitute.ca/mp3/2d1d8f84-a903-4e8f-b559-84cc0d7a4eb2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2d1d8f84-a903-4e8f-b559-84cc0d7a4eb2.mp3 Tue, 02 Jun 2009 09:30:00 -0400 TBA Peter Selinger http://streamer.perimeterinstitute.ca/mp3/ce3c5d07-7b1f-4bd2-a723-bb1f6018bfd5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ce3c5d07-7b1f-4bd2-a723-bb1f6018bfd5.mp3 Tue, 02 Jun 2009 10:15:00 -0400 TBA Andreas Doering http://streamer.perimeterinstitute.ca/mp3/15a57864-95fc-4209-b187-eca6623a4066.mp3 Science http://streamer.perimeterinstitute.ca/mp3/15a57864-95fc-4209-b187-eca6623a4066.mp3 Tue, 02 Jun 2009 11:30:00 -0400 TBA Mehrnoosh Sadrzadeh http://streamer.perimeterinstitute.ca/mp3/dae8e8d7-05db-4e03-b32a-dc0ae4854f76.mp3 Science http://streamer.perimeterinstitute.ca/mp3/dae8e8d7-05db-4e03-b32a-dc0ae4854f76.mp3 Tue, 02 Jun 2009 12:15:00 -0400 TBA Nikolaas Landsman http://streamer.perimeterinstitute.ca/mp3/b267f2e7-611a-497b-9dd3-d00fa049954f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b267f2e7-611a-497b-9dd3-d00fa049954f.mp3 Wed, 03 Jun 2009 09:30:00 -0400 TBA Marni Sheppeard http://streamer.perimeterinstitute.ca/mp3/60ebc6a6-67d9-4a82-9212-72c64184b74a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/60ebc6a6-67d9-4a82-9212-72c64184b74a.mp3 Wed, 03 Jun 2009 10:15:00 -0400 The notion of a conditional probability is critical for Bayesian reasoning. Bayes’ theorem, the engine of inference, concerns the inversion of conditional probabilities. Also critical are the concepts of conditional independence and sufficient statistics. The conditional density operator introduced by Leifer is a natural generalization of conditional probability to quantum theory. This talk will pursue this generalization to define quantum analogues of Bayes' theorem, conditional independence and sufficient statistics. These can be used to provide simple proofs of certain well-known results in quantum information theory, such as the isomorphism between POVMs and convex decompositions of a mixed state and the remote collapse postulate, and to prove some novel results on how to pool quantum states. This is joint work with Matt Leifer. I will also briefly discuss the possibility of a diagrammatic calculus for classical and quantum Bayesian inference (joint work with Bob Coecke). Robert Spekkens http://streamer.perimeterinstitute.ca/mp3/8935e560-6620-4c31-afde-dc205610db1f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8935e560-6620-4c31-afde-dc205610db1f.mp3 Wed, 03 Jun 2009 11:30:00 -0400 TBA Mike Stay http://streamer.perimeterinstitute.ca/mp3/1f992901-c2c9-40f9-bef9-01f5992b0285.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1f992901-c2c9-40f9-bef9-01f5992b0285.mp3 Wed, 03 Jun 2009 12:15:00 -0400 TBA Richard Blute http://streamer.perimeterinstitute.ca/mp3/bb17b8c8-6719-44f2-9688-65f5e6fae209.mp3 Science http://streamer.perimeterinstitute.ca/mp3/bb17b8c8-6719-44f2-9688-65f5e6fae209.mp3 Thu, 04 Jun 2009 09:30:00 -0400 TBA William Edwards http://streamer.perimeterinstitute.ca/mp3/31d97c87-1ef6-4dc6-89f5-9c54c25b3503.mp3 Science http://streamer.perimeterinstitute.ca/mp3/31d97c87-1ef6-4dc6-89f5-9c54c25b3503.mp3 Thu, 04 Jun 2009 10:15:00 -0400 Tensor product is described in a family of categories that includes Set and Hilbert spaces. Such categories admit a "scalar" object which enables a definition of bi-arrows with two domains, generalizing functions of two variables. The tensor product is characterized by the expected universal property relating bi-arrows to arrows. Daniel Lehman http://streamer.perimeterinstitute.ca/mp3/76fb0007-5c9b-45ff-87ed-081cb0b5a8b0.mp3 Science http://streamer.perimeterinstitute.ca/mp3/76fb0007-5c9b-45ff-87ed-081cb0b5a8b0.mp3 Thu, 04 Jun 2009 11:30:00 -0400 We sketch some ideas about how higher-dimensional categories could be used to extend conventional quantum mechanics. The physical motivation comes from quantum field theory, for which higher-dimensional category theory is very relevant. We discuss how this new approach would affect familiar aspects of quantum theory, such as observables and the Copenhagen interpretation. Few solid answers will be given, but hopefully some discussion will be generated! Jamie Vicary http://streamer.perimeterinstitute.ca/mp3/5a849db4-0e2c-415e-becc-c7c750f78299.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5a849db4-0e2c-415e-becc-c7c750f78299.mp3 Thu, 04 Jun 2009 12:15:00 -0400 TBA Howard Barnum http://streamer.perimeterinstitute.ca/mp3/7369ba5c-f071-4dc5-8488-68a82dd0341b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/7369ba5c-f071-4dc5-8488-68a82dd0341b.mp3 Fri, 05 Jun 2009 10:15:00 -0400 We give a mathematical framework to describe the evolution of quantum systems subject to finitely many interactions with classical apparatuus and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. The evolution is coded in a mathematical structure in such a way that the properties of causality, covariance and entanglement are faithfully represented. The key to this scheme is to use a special family of spacelike slices -- we call them locative -- that are not so large as to permit acausal influences but large enough to capture nonlocal correlations. I will briefly describe how the dynamics can be described as a functor to a suitable category of Hilbert spaces and will also give some connections with logic. Prakash Panangaden http://streamer.perimeterinstitute.ca/mp3/8ffa3fa3-eeed-495e-9a7c-d2e57641e823.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8ffa3fa3-eeed-495e-9a7c-d2e57641e823.mp3 Fri, 05 Jun 2009 11:30:00 -0400 TBA Ivan Ivanov http://streamer.perimeterinstitute.ca/mp3/72a89674-98d8-4f7d-b3ed-16dc47849f17.mp3 Science http://streamer.perimeterinstitute.ca/mp3/72a89674-98d8-4f7d-b3ed-16dc47849f17.mp3 Fri, 05 Jun 2009 12:15:00 -0400