Indefinite Causal Structure
Relative locality is a quantum gravity phenomenon in which whether an event is local or not-and the degree of non-locality-is dependent on the position and motion of the observer, as well as on the energy of the observer’s probes. It was first discovered and studied, beginning in 2010, in a limit in which h and G both go to zero, with their ratio, which is the Planck energy-squared, and c held fixed (arXiv:1101.0931, arXiv:1103.5626).
Quadratic gravity is a renormalizeable theory of quantum gravity which is unitary, but which violates causality by amounts proportional to the inverse Planck scale. To understand this, I will first discuss the arrow of causality in quantum field theory (with a detour concerning the arrow of time), and then discuss theories with dueling arrows of causality. But the causality violation might be better described by causality uncertainty. This is discussed both in quadratic gravity and in the effective field theory of general relativity.
There are a number of cases in the history of particle physics in which analogies to non-relativistic condensed matter physics models guided the development of new relativistic particle physics models. This heuristic strategy for model construction depended for its success on the causal structure of the non-relativistic models and the fact that this causal structure is not preserved in the relativistic models. Focusing on the case of spontaneous symmetry breaking, the heuristic role of representations of causal structure and time in the non-relativistic models will be examined.
I will discuss how the standard frameworks for operational theories involve a scrambling of causal and inferential concepts. I will then present a new framework for operational theories which separates out the inferential and the causal aspects of a given physical theory. Generalized probabilistic theories and operational probabilistic theories are recovered within our framework when one ignores some of these distinctions.
We are building an experiment in which a levitated 1 µm diamond containing a nitrogen vacancy (NV) centre would be put into a spatial quantum superposition [1-3]. This would be able to test theories of spontaneous wavefunction collapse [4]. We have helped theory collaborators to propose how to do this experiment [5-9], as well as a much more experimentally ambitious extension which would test if gravity permits a quantum superposition [10]. There are related proposals from other groups [11-13].
The lesson of general relativity is background independence: a physical theory should not be formulated in terms of external structures. This motivates a relational approach to quantum dynamics, which is necessary for a quantum theory of gravity. Using a covariant POVM to define a time observable, I will introduce the so-called trinity of relational quantum dynamics comprised of three distinct formulations of the same relational quantum theory: evolving constants of motion, the Page-Wootters formalism, and a symmetry reduction procedure.
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”.