Categories, Logic and Foundations of Physics

Welcome!

This is the homepage of the workshop series Categories, Logic and Foundations of Physics. These workshops bring together researchers from the fields mentioned in the title and promote research on structural and conceptual aspects of fundamental physical theories, operational methodologies for general physical theories, as well as the general study of mathematical structures describing dynamics and space-time.

Please feel free to contact the workshop organizers if you have any questions, or if you want to attend one of our meetings.

There have been five workshops so far (9th January 2008, 14th May 2008, and 23rd/24th August 2008, 7th January 2009 and 6th August 2009). We intend to keep an informal atmosphere for the workshops, with no formal registration, and strongly encourage interaction and discussions between the participants.

Previous event: 5th CLP Workshop, 6th August 2009, Imperial College, London

The fifth workshop on "Categories, Logic and Foundations of Physics" took place at

Imperial College on Thursday, 6th August 2009, 11:00 - 19:00, Lecture Theatre 2, Blackett Laboratory.

SPEAKERS AND SCHEDULE:

  • 11:00 — 12:00: Paul Taylor, "A computable axiomatisation of the topology of \mathbb{R} and \mathbb{C}"
  • 12:00 — 13:00: Pedro Resende, "Stably Gelfand quantales, groupoids and Cartan sub-C^*-algebras" — In this talk I will describe the notion of stably Gelfand quantale, by which is meant an involutive quantale Q satisfying the condition aa^*a\leq a \Leftrightarrow aa^*a=a for all aa in Q, and as an application I will show that to each sub-C^*-algebra B of a C^*-algebra A one can associate in a canonical way an etale groupoid whose unit locale is that of two-sided ideals of B. This construction is related with earlier work of Kumjian, Renault and Exel on “diagonals” of C^*-algebras, and there are further applications of stably Gelfand quantales (also known by Garraway as pseudo-rightsided) in theories of sheaves on quantales.
  • 13:00 — 14:00: Lunch break
  • 14:00 — 15:00: Terry Rudolph, "Does knowing my lambda mean knowing my psi?" — All known hidden variable theories that completely reproduce all quantum predictions share the feature that they add some information to the quantum state \psi. That is, if one knew the "state of reality" given by the hidden variable(s) \lambda, then one could infer the quantum state - the hidden variables are additional to the quantum state. However, for the case of a single 2-dimensional quantum system Kochen and Specker gave a model which does not have this feature. A natural question arises whether a similar model is possible for higher dimensional systems. At the time of writing this abstract I have no clue. I will talk about various constraints on such theories (in particular on how they manifest contextuality) and I'll present some examples of failed attempts to construct such models for a 3-dimensional system. The annoying thing about my failed attempts is that they can be expected to reproduce physical things like atomic spectra, and they only deviate from the quantum predictions for the Born rule by about a percent or so. However I have wasted enough time trying to get them to agree properly with quantum mechanics, and so my goal in this talk is to motivate someone smarter than me to prove that such a class of non-hidden, hidden variable theories cannot exist.
  • 15:00 — 16:00: Andreas Doering, "States and Measures" — The most general kind of a state of a classical system is a probability measure on the state space of the system. This also defines an integral on the abelian algebra of physical quantities. A general state of a quantum system is a positive linear functional of norm 1 on the nonabelian algebra of physical quantities of the quantum system., i.e., an integral. We will show that quantum states also have a description as probability measures. These measures are not defined on a state space (which does not exist anyway, due to the Kochen-Specker theorem), but on the spectral presheaf, a generalised state object in a topos associated to the quantum system.
  • 16:00 — 16.45: Coffee/tea break
  • 16:45 — 17:45: Aleks Kissinger, "Entanglement Classification with Classical Structures and Graph Rewriting" — Graphical languages have proven a powerful tool for reasoning about arrows in various kinds of monoidal categories, and in particular about quantum states and processes. We review a graphical language that exploits the relationships between simple maps on mutually unbiased bases. This is the language of complementary classical structures, or the "red-green" calculus. We show how this language can encode many multipartite entangled states, and how the behaviour of these states is emergent as the result of graph rewriting. However, manual manipulation of medium to large graphs quickly becomes difficult and error-prone. Worse still, the expansion of the red-green theory in light of relationships discovered in the underlying (e.g. qubit) semantics requires arduous translations between graphical and matrix representations of quantum states. To combat these issues, we introduce Quantomatic, a program that allows automated and semi-automated explorations of graph rewrite systems. It also interfaces with a computer algebra system to do concrete calculations on the underlying semantics of a graph. In this talk, we shall demonstrate how Quantomatic uses rewriting and computer algebra to probe and help classify multipartite entangled states.
  • 17:45 — 18:45: Leron Borsten, "Black Holes, Qubits and Octonions" — We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits, known as the 3-tangle, and the entropy of the 8-charge STU black hole of N=2 supergravity, both of which are given by the [SL(2)]^3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. The black hole/qubit correspondence extends, via the Fano plane, to the 56 charge N=8 black holes and the "tripartite entanglement of seven qubits". The Fano plane provides the multiplication table of the seven imaginary octonions, reflecting the fact that E_7 has a natural structure of an O-graded algebra. Turning to the microscopic picture of these black holes we may associate the qubits with the wrapping cycles of D3-branes in type IIB string theory. At present this correspondence remains at a purely mathematical level. However, further investigation, whether or not it eventually reveals a physical duality, will certainly provide insights into both sides of the QI/String equation. Recent examples include (1) A Freudenthal triple classification of three qubits and (2) Black holes admitting a Freudenthal dual (3) a new role for the octonions in M-theory.
  • 19:00 — …: Pub session ;-)

Andreas & Bob

About this site - the video archive

This site went live on 11th December 2007. Feedback is very welcome. One of the most important features of this site is an extensive archive of over 50 recorded talks relevant to categories, logic and the foundations of physics, given by over 40 different speakers at different events around the world. You can browse these talks by speaker or by event, you can download or stream the videos, and download the slides where available.

We are constantly adding new talks, so make sure to check back often!

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