Quantum Foundations

We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches.

Natural critical phenomena are characterized by laminar periods separated by events where bursts of activity take place, and by the interrelated self-similarity of space-time scales and of the event sizes. One example are earthquakes: for this case a new approach to quantify correlations between events reveals new phenomenology. By linking correlated earthquakes one creates a scale-free network of events, which can have applications in hazard assessment.