Speaker
Description
When canonically quantising general relativity, one is faced with the problem of frozen dynamics, also known as the problem of time, which arises due to the presence of constraints in the theory. In this talk, I will provide an overview of the problem of frozen dynamics in general relativity and explain why it is a significant challenge in the field. To study this problem, we have limited ourselves to highly symmetric spacetimes, such as cosmological toy models, which allow us to explore the these issues in a more tractable setting. The problem of time is usually solved by gauge fixing the constraint classically (reduced quantisation) or solving the constraint after quantising the theory, for example, by projecting from the too big kinematical Hilbert space to the physical Hilbert space using the constraint operator (Dirac programme). In these toy models, it has already been proven that ambiguites in the reduced quantisation procedure will lead to different quantum theories. In our work we have focused in solving the constraint in the quantum level and we have seen how ambiguities in the definition of the kinematical Hilbert space and the constraint operator may also lead to different physical Hilbert spaces. These ambiguities arise from the different boundary conditions resulting from considering unitary evolution of our universes. In this talk, I will recap the principal results of our work, explain their significance for the broader field of quantum gravity. Additionally, I will briefly introduce other approaches to the problem of time. In particular, I will focus in the main alternative to canonical quantisation, namely, path integral quantisation. I will introduce how the problem of time and unitarity conditions may be manifested in this approach to quantum gravity and discuss the advantages and limitations of this approach compared to other quantisation methods. Overall, my talk will provide a comprehensive overview of the problem of frozen dynamics in general relativity and the various approaches that have been developed to address it.
