Title: Epistemic Logic in a Quantum World
Abstract: A natural assumption in multi-agent scenarios is that “agent A knows that agent B knows that w is true” implies “agent A knows that w is true”. It is therefore natural to ask whether this assumption is compatible with quantum theory. In my talk, I will present an argument which shows that this cannot be the case in general. The argument is based on the assumption that quantum theory is universal, and thus can also be employed to describe the agents’ own reasoning.
Title: The Philosophy of Open Quantum Systems
Abstract: Open systems features such as dissipation and pumping play a crucial role in many standard quantum optical applications (for instance in lasers and resonance fluorescence) and a proper quantum theoretical account of these (and other) applications requires that one models the environment, and not just the system of interest, quantum mechanically. To do so, one typically employs a Markovian quantum master equation which is of the “Lindblad form”. Note that, importantly, the Schrödinger equation governing the unitary evolution of closed systems is a special case of the Lindblad equation. To derive the master equation, there are two possible routes. The first is a microscopic and specific derivation that must be carried out for the particular system under consideration in a given application. The second is a general and abstract derivation which does not relate to a particular system, but rather begins from general constraints on the dynamical evolution of quantum systems. These include, in particular, the requirement that the dynamical map governing the state transitions of a quantum system be “completely positive”, i.e. such that it will never evolve (i.e. no matter what the system’s initial state) a valid state description for a particular quantum system to an invalid state description. In this talk, we consider both the general and the more specific derivation in some detail and argue that in both cases one can discern clear and strong physical motivations for considering the open-systems view of quantum systems (rather than the traditional closed-systems view) as the fundamental one from which to consider the metaphysics of quantum systems, and discuss the consequences of so doing. The talk is based on joint work with Mike Cuffaro (Western).
Title: The atemporal big bang
Abstract: Cosmological models based on quantum theories of gravity promise to offer a quantum treatment of the big bang. While they tend to erase what is classically a singularity, the quantum evolution that replaces it may not correspond to classical spacetime; instead, it seems to posit a non-spatiotemporal region, which somehow ‘transitions’ to a macroscopically spatiotemporal state. I will discuss the relation between the two different kinds of transitions and how they interact to yield a potential answer to the emergence of time and its direction. This will raise the bigger question of the emergence of classicality in a cosmological setting.
Title: Bayes + Hilbert = Quantum Mechanics
Abstract: Quantum mechanics (QM) is based on four main axioms, which were derived after a long process of trial and error. The motivations for the axioms are not always clear and even to experts the basic axioms of QM often appear counter-intuitive. In a recent paper, we have shown that: (i) It is possible to derive quantum mechanics from a single principle of self-consistency or, in other words, that QM laws of Nature are logically consistent; (ii) QM is just the Bayesian theory generalised to the complex Hilbert space. In particular, we have considered the problem of gambling on a quantum experiment and enforced rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalised to the space of Hermitian matrices. This very theory is QM: in fact, we have derived all its four postulates from the generalised Bayesian theory. This implies that QM is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes’ rule (measurement), marginalisation (partial tracing), independence (tensor product). To say it with a slogan, we have obtained that quantum mechanics is the Bayesian theory in the complex numbers. The talk is based on joint work with Alessandro Facchini and Marco Zaffalon.
Gemma De Las Cuevas
Title: On the concept of universality: ubiquity and limitations
Abstract: I will talk about the concept of universality in computer science, in physics, and more broadly. I will explain how in computer science and in physics there is universality everywhere. This ubiquity entails its own limitations: in the form of lack of predictive power from a universal machine, which is related to the notion of emergence, and in the fact that most statements are undecidable, i.e. that there is also undecidability everywhere.
Title: QBism, or taking Wigner’s friend seriously
Title: Grothendieck toposes as unifying ‘bridges’ in Mathematics
Abstract: After recalling the necessary topos-theoretic preliminaries, I will explain the sense in which Grothendieck toposes can act as unifying ‘bridges’ for relating different mathematical theories to each other and studying them from a multiplicity of different points of view. I will also survey a number of selected applications of this methodology in different mathematical fields, and argue about its possible uses in the context of Quantum Physics.