General Relativity & Quantum Cosmology

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). Relative locality was also found in a different, non-relativistic limit, involving quantum reference frames, in which c is taken to infinity while h and G are held fixed. I describe some of what we learned in the first studies, in the hope it might be useful to people developing the quantum reference frame approach.

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 reflect on whether the use of non-relativistic causal models to construct relativistic quantum field theory models offers methodological lessons for the shift from definite causal structures in pre-general relativistic quantum theories to indefinite causal structures in quantum gravity.

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 then make similar refinements to the traditional notion of ontological theories, and discuss how our framework revises the standard notions of ontological representations and of generalized noncontextuality.

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]. [1] A. T. M. A. Rahman, A. C. Frangeskou, M. S. Kim, S. Bose, G. W. Morley & P. F. Barker, Sci. Rep. 6, 21633 (2016). [2] A. T. M. A. Rahman, A. C. Frangeskou, P. F. Barker & G. W. Morley, Rev. Sci. Instrum. 89, 023109 (2018). [3] A. C. Frangeskou, A. T. M. A. Rahman, L. Gines, S. Mandal, O. A. Williams, P. F. Barker & G. W. Morley, NJP 20, 043016 (2018). [4] A. Bassi, K. Lochan, S. Satin, T. P. Singh & H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013). [5] S. Bose & G. W. Morley, arXiv:1810.07045 (2018). [6] M. Scala, M. S. Kim, G. W. Morley, P. F. Barker & S. Bose, PRL 111, 180403 (2013). [7] C. Wan, M. Scala, G. W. Morley, A. T. M. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose & M. S. Kim, PRL 117, 143003 (2016). [8] R. J. Marshman, A. Mazumdar, G. W. Morley, P. F. Barker, H. Steven & S. Bose, arXiv:1807.10830 (2018). [9] J. S. Pedernales, G. W. Morley & M. B. Plenio, arXiv:1906.00835 (2019). [10] S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim & G. Milburn, PRL 119, 240401 (2017). [11] Z.-q. Yin, T. Li, X. Zhang & L. M. Duan, PRA 88, 033614 (2013). [12] A. Albrecht, A. Retzker & M. B. Plenio, PRA 90, 033834 (2014). [13] C. Marletto & V. Vedral, PRL 119, 240402 (2017).

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. The equivalence between these formulations yields a temporal frame change map that transforms between the dynamics seen by different clocks. This map will be used to illustrate a temporal nonlocality effect that results in a superposition of time evolutions from the perspective of a clock indicating a superposition of different times. Then, a time-nonlocal modification to the Schrödinger equation will be shown to manifest when a system is coupled to the clock that is tracking its evolution. Such clock-system interactions should be expected at some scale when the gravitational interaction between them is taken into account. Finally, I will examine relativistic particles with internal degrees of freedom that constitute a clock that tracks their proper time. By evaluating the conditional probability associated with two such clocks reading different proper times, I will show that these clocks exhibit a novel quantum time dilation effect when moving in a superposition of different momenta.

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”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.