[PhilPhys] Sigma Club at LSE - Summer Term 2008

[R.P.Frigg at lse.ac.uk]

Sigma Club Talks - Summer Term 2008

Room T206, LSE, all welcome.


Monday 19 May, 5:00-7:00 pm

Tim Palmer

University of Cambridge and ECWMF

Bell Inequalities, Free Variables and the Undecidability of Fractal Invariant Sets.

As emphasised by recent "Free-Will" theorems, the notion that quantum theory is not locally causal and cannot be embedded in a locally-causal theory, depends on treating experimental parameters as free variables. Whilst "superdeterminism" - there are no free variables - may provide a way out of this conceptual difficulty, it is hard to see how such a strong constraint could ever emerge from the sort of primitive notions of invariance and symmetry that underlie theoretical physics. By contrast, based on the notion of dynamical invariance, a new class of locally-causal physical theory is proposed which imposes weaker (but nevertheless important) constraints on the notion of free variables. Specifically, we consider a class of physical theory whose states are constrained to lie on dynamically-invariant subsets of state space: the Invariant Set Conjecture. It is shown that any nontrivial property of fractal invariant sets is algorithmically undecidable. We discuss how quantum theory might be embedded within such a class of theory - leading to the notion of the Schrödinger equation as a singular limit. As such, it is claimed that it is unprovable that quantum theory cannot be embedded into one of the members of this class of locally-causal theory.

These ideas are used to put forward a new type of locally-causal quantum ontology, relevant to some of the problems of quantum theory, such as preferred bases, delayed-choice experiments and of course nonlocality. Since the Invariant Set Conjecture is geometric and hence general relativistically covariant, these results may in turn provide a new conceptual basis for the role of gravity in quantum theory.

 

Monday 9 June, 5:00-7:00 pm

Andreas Doering

Imperial College, London

Topos Theory in the Foundations of Physics

I will report on current work with Chris Isham on the application of topos theory, a branch of category theory, to physics. The starting point is the famous Kochen-Specker theorem, which shows that in quantum theory it is impossible to consistently assign "true" and "false" to all propositions about the values of physical quantities. This failure of Boolean logic in quantum theory can be overcome by the use of topos theory. I will explain what a topos is and then show that using the internal, intuitionistic logic of a certain topos, truth-values can be assigned to all propositions. This gives a 'neo-realist' formulation of quantum theory.

 

Monday 23 June, 5:00-7:00 pm

Frank Arntzenius

University of Oxford

More Space, Less Clutter?

Physicists sometimes represent the state of the world by giving the locations of all elementary particles in ordinary 3-dimensional space, and sometimes they represent the state of the world by giving the location of one particle, the 'world' particle, in a multi-dimensional space, configuration space. Some philosophers have argued that there is a real choice to be made here; that there is a real question as to whether there exists only one fundamental object which lives in a multi-dimensional space, or whether there are many fundamental objects living in good old 3-dimensional space. Moreover, especially in the context of quantum mechanics, some have argued that configuration space is the true arena of events. I will discuss whether all of this is right.


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