ProfessorJonathan Halliwell

My broad interests over my whole career are the foundations of quantum mechanics and quantum gravity with my present focus being on theoretical questions concerning tests for the presence of quantum coherence in macroscopic systems.

I started out in 1983 in the relativity group in Cambridge and worked on quantum cosmology -- the attempt to describe models of the early universe in completely quantum-mechanical terms -- for ten years or more and this area still remains one of interest to me and a source of interesting problems in quantum theory. I subsequently became very interested in the decoherent histories approach to quantum theory, a novel formulation of standard quantum theory which gives histories a central role. This is of particular interest in quantum cosmology, where the notorious problem of time makes it difficult to define a time-evolving state. It also provides an extremely powerful framework in which to address the emergence of classical behaviour from quantum theory, another area on which I have worked for many years, mainly in the context of non-relativistic quantum mechanics. I have also worked on the closely related and perennially interesting problem of constructing hybrid models in which classical and quantum variables are consistently coupled.

I have worked extensively on aspects of time in quantum mechanics and associated phenomena, including the arrival time problem, quantum Zeno effect and also the intriuging phenomenon of backflow -- the (so far unobserved) fact that for a state of purely positive momenta the probability can flow in the opposite direction. I have written papers on Fine's theorem, which is essentially the logical converse of Bell's inequalities and used some of these ideas to offer a sensible interpretation of negative probabilities.

Since 2016 my primary focus has been on developing a theoretical understanding of Leggett-Garg tests for macroscopic realims. The Leggett-Garg inequalities are a (partial)  temporal analogue of Bell inequalities and enjoy many common mathematical properties. Many aspects of this area are explored in a number of papers (some of which have been implemented experimentally in Raymond Laflamme's lab in Waterloo, Ontario) and this area will remain a major focus for the next few years. 

Most recently I have also been interested in the development of laboratory tests for quantum gravitational effects.