This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories. This opens up a flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have.
Since the 1909 work of Carathéodory, an axiomatic approach to thermodynamics has gained ground which highlights the role of the the binary relation of adiabatic accessibility between equilibrium states. A feature of Carathédory's system is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law.
There has recently been much interest in finding simple principles that explain the particular sets of experimental probabilities that are possible with quantum mechanics in Bell-type experiments. In the quantum gravity community, similar questions had been raised, about whether a certain generalisation of quantum mechanics allowed more than quantum mechanics in this regard. We now bring these two strands of work together to see what can be learned on both sides.
Central to quantum theory, the wavefunction is a complex distribution associated with a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate measurement outcome probabilities through the Born Rule. Tomographic methods can reconstruct the wavefunction from measured probabilities.
The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if every pair of pure states corresponds to a pair of measures that do not overlap, and is otherwise epistemic.
If a wave function does not describe microscopic reality then what does? Reformulating quantum mechanics in path-integral terms leads to a notion of ``precluded event" and thence to the proposal that quantal reality differs from classical reality in the same way as a set of worldlines differs from a single worldline. One can then ask, for example, which sets of electron trajectories correspond to a Hydrogen atom in its ground state and how they differ from those of an excited state.
The purpose of this talk is twofold: First, following Spekkens, to motivate noncontextuality as a natural principle one might expect to hold in nature and introduce operational noncontextuality inequalities motivated by a contextuality scenario first considered by Ernst Specker. These inequalities do not rely on the assumption of outcome-determinism which is implicit in the usual Kochen-Specker (KS) inequalities.
It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics.
On the face of it, quantum physics is nothing like classical physics. Despite its oddity, work in the foundations of quantum theory has provided some palatable ways of understanding this strange quantum realm. Most of our best theories take that story to include the existence of a very non-classical entity: the wave function. Here I offer an alternative which combines elements of Bohmian mechanics and the many-worlds interpretation to form a theory in which there is no wave function.
We present a method for determining the maximum possible violation of any linear Bell inequality per quantum mechanics. Essentially this amounts to a constrained optimization problem for an observable’s eigenvalues, but the problem can be reformulated so as to be analytically tractable. This opens the door for an arbitrarily precise characterization of quantum correlations, including allowing for non-random marginal expectation values. Such a characterization is critical when contrasting QM to superficially similar general probabilistic theories.