This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
It is well known that the derivation of the Bell Inequality rests on two major assumptions, usually called outcome independence and parameter independence. Parameter independence seems to have a straightforward motivation: it expresses a non-signalling requirement between space-like separated sites and is thus motivated by locality. The status of outcome independence is much les clear. Many authors have argued that this assumption too expresses a locality requirement, in the form of a \'screening off\' condition.
The focus of this talk is a particular feature of the statistical behavior of elementary particles, simple composite systems of them and the quantum probability theory to which this behavior gives rise. The standard interpretation of a generalized probability theory of the sort found in quantum mechanics is that its probabilities are probabilities of propositions belonging to particles, where a proposition belongs to a particle if its constituent dynamical property is a possible property of the particle.
Some theoretical physicists, Chris Fuchs among them, take quantum mechanics to go hand in hand with an anti-representationalist account of truth and reality such as that offered by the American pragmatists - William James, Charles Peirce, Richard Rorty, etc. On this view, scientific theories are instruments, rather than mirrors of the real world. In this talk, I’ll suggest that if the quantum physicist is to team up with the pragmatist, he’d do best to join not with James and Rorty, who see the world as radically plastic or malleable.
Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony\'s and Jarrett\'s condition of parameter independence (or `locality\') and Jones and Clifton\'s condition of conditional parameter independence (or `constrained locality\') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result.
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown.
Chris Isham in pre-recorded video, with Andreas Doring fielding questions and clarifications. Like watching commentators Scott Hamilton and Katarina Witt analyze Kristi Yamaguchi\'s performance at the World Figure Skating Championships for CBS News, join us for something different in quantum foundations. Chris Isham parries the intricacies of topos theory; Andreas Doring shows us how to see the moves in slow motion. Bring your own popcorn and plenty of questions.
Quantum measure theory describes quantum theory as a generalization of a classical stochastic process, which may be fruitful for quantum gravity. I will describe the approach, and show that, in the context of an EPRB setup with two distant experimenters, two alternative experiments, and two outcomes per experiment, any set of no signaling probabilities can be realized, albeit by violating a `strong positivity\' condition.
It is usually expected that nonrelativistic many-body Schroedinger equations emerge from some QFT models in the limit of infinite masses. For instance, from Yukawa\'s QFT, if the initial state contains 2 fermions, we expect to recover a 2-fermion nonrelativistic Schroedinger equation with 2-body Yukawa potential (in the limit of infinite fermion mass). I will give an easy (but still heuristic) derivation of this, based on the analysis of the corresponding Feynman diagrams and on the behaviour of the complete propagators for large spacetime distances.