Physical theories ought to be built up from colloquial notions such as ’long bodies’, ’energetic sources’ etc. in terms of which one can define pre-theoretic ordering relations such as ’longer than’, ’more energetic than’. One of the questions addressed in previous work is how to make the transition from these pre-theoretic notions to quantification, such as making the transition from the ordering relation of ’longer than’ (if one body covers the other) to the notion of how much longer.
Weak values were introduced by Aharonov, Albert, and Vaidman 25 years ago, but it is only in the last 10 years that they have begun to enter into mainstream physics. I will introduce weak values as done by AAV, but then give them a modern definition in terms of generalized measurements. I will discuss their properties and their uses in experiment. Finally I will talk about what they have to contribute to quantum foundations.
Characterising quantum non-locality using simple physical principles has become a hot topic in quantum foundations of late. In the simpler case of local hidden variable models, the space of allowed correlations can be characterised by requiring that there exists a joint probability distribution over all possible experimental outcomes, from which the experimental probabilities arise as marginals. This follows from Bell’s causality condition. But the existing characterisations of quantum correlations are far from being so straightforward.
I argue that quantum mechanics cannot usefully be extended to a theory of the whole universe, so the task of quantum foundations is to discover that cosmological theory which reduces to quantum mechanics when restricted to small subsystems of the universe. I argue that that cosmological theory will be based on a global notion of physical time which implies the distinction between past, present and future is real and objective. These motivate two examples of novel formulations of quantum theory: the real ensemble formulation and the principle of precedence. Each may imply departur
The process of canonical quantization:is reexamined with the goal of
ensuring there is only one reality, where $\hbar>0$, in which classical
and quantum theories coexist. Two results are a clarification of the effect of
canonical coordinate transformations and the role of Cartesian coordinates.
Other results provide validation
The Pauli exclusion principle is a constraint on the
natural occupation numbers of fermionic states. It has been suspected for
decades, and only proved very recently, that there is a multitude of further
constraints on these numbers, generalizing the Pauli principle. Surprisingly,
these constraints are linear: they cut out a geometric object known as a
polytope. This is a beautiful mathematical result, but are there systems whose
physics is governed by these constraints?
The Wigner-Araki-Yanase (WAY) theorem delineates
circumstances under which a class of quantum measurements is ruled out.
Specifically, it states that any observable (given as a self adjoint operator)
not commuting with an additive conserved quantity of a quantum system and
measuring apparatus combined admits no repeatable measurements. I'll review the
content of this theorem and present some new work which generalises and
strengthens the existing results.
A recent development in
information theory is the generalisation of quantum Shannon information theory
to the operationally motivated smooth entropy information theory, which
originates in quantum cryptography research. In a series of papers the first
steps have been taken towards creating a statistical mechanics based on smooth
entropy information theory. This approach turns out to allow us to answer
questions one might not have thought were possible in statistical mechanics,