Quantizing Time

In general relativity time requires an operational description, for example, associated with the reading of an idealised clock following some world line. I will show that in quantum physics idealised clocks can be modelled as composite quantum particles and discuss what foundational insights into the notion of time is enabled by this approach. Moreover, since quantum particles do do not follow classical trajectories a question arises to which extent idealised quantum clocks can be associated with semi-classical paths — in analogy with quantum particles in Gaussian states being associated with semi-classical trajectories? I will show that for quantum clocks semi-classical propagation is not described by Gaussian but by a new class of quantum states derived from a new uncertainty inequality for configuration space rather than for phase space variables of the quantum clock.

The kappa-Minkowski noncommutative spacetime has been studied for a long time as an example of quantum spacetime with nontrivial commutation relations between spatial and temporal coordinates which, at first sight, seem to break Poincaré invariance. However kappa-Minkowski is invariant under a Hopf-algebra deformation of the Poincaré group, which involves some noncommutative structures that prevent the sharp localization of reference frames. I will describe recent progress towards the consistent construction of quantum field theories on this spacetime, and the identification of physical predictions that genuinely distinguish kappa-Minkowski from ordinary, commutative Minkowski spacetime.

"Spatio-temporal relations are often taken to be more primitive than causal relations. Such a relationship is assumed whenever it is suggested that it is part of the definition of a causal relation that the cause must precede the effect in time. There are good reasons, however, to take causation to be the more primitive notion, with spatio-temporal relations merely describing aspects of causal relations. In such an approach, to understand what possibilities there are for an intrinsically quantum notion of time, it is helpful to understand what possibilities there are for an intrinsically quantum notion of causation. In short, how time is quantized is informed by how causation is quantized. The latter question will be the focus of this talk. I will describe a research program wherein the transition from classical to quantum is understood as an innovation to the notions of causation and inference. This is done by introducing the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. The possibility of defining causal-inferential theories by the axioms they satisfy provides a means of providing abstract and structural characterizations of the notions of causation and inference. In other words, within this approach, the new notions of causation and inference will stand to the traditional notions in much the same way that the notions of points and lines in nonEuclidean geometry stand to their traditional counterparts in Euclidean geometry. Based on: D. Schmid, J. Selby, and R. Spekkens, Unscrambling the omelette of causation and inference: The framework of causal-inferential theories, arXiv:2009.03297 (quant-ph)."

"The process matrix framework was invented to capture a phenomenon known as indefinite or quantum causal structure. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. We combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several observers, each with their own discrete quantum clock. This allows for implementing processes with indefinite casual order. The description via a history state with multiple clocks imposes constraints on the implementability of process matrices intros framework and on the perspectives of the observers. We describe how to to implement processes were the different definite causal orders are coherently controlled and explain why certain non-causal processes might not be implementable within this setting."

In physics, a reference frame is an abstract coordinate system that specifies observations within that frame. While quantum states depend on the choice of reference frame, the form of physical laws is assumed to be covariant. Recently, it has been proposed to consider reference frames as physical systems and as such assume that they obey quantum mechanics. In my talk, I will present recent results in the field of "quantum reference frames" (QRF). In particular, I will formulate the covariance of dynamical physical laws with respect to non-relativistic QRF transformations and show how relativistic QRFs can be used to solve a long-standing problem in relativistic quantum information or to address typical quantum gravity scenarios.

Time Reversal T is usually discussed in the traditional framework of quantum mechanics in which T is represented by an anti-unitary operator. But quantum gravity may well need generalization of standard quantum mechanics which may not preserve even its linear structure, let alone the unitarity of dynamics and anti-unitarity of T. Then the currently used arguments to conclude that T violation is a fundamental aspect of Nature will break down. Fortunately, it turns out that one can analyze the T-violation experiments in a much more general setting, of which classical and quantum mechanics are special cases. The setting does not require a Hilbert space, or linearity of either dynamics or symmetry operations such as T. Nonetheless, somewhat surprisingly, one would still be to use the current experiments to conclude that there is T violation at a fundamental level under rather minimal assumptions on the structure of the final quantum gravity theory.

I will present a quantum gravity approach based on a Lorentzian path integral for quantum geometries. The properties of quantum space time can be measured using geometric operators. This allows also to discuss fluctuations of causal structure as well as violations of (micro-) causality. I will explain how the Lorentzian path integral comes with various options regarding which quantum space times to sum over: e.g. whether to include causality violations or not, or whether to allow also for space times with Euclidean signatures in Lorentzian path integrals. I will sketch some consequences for the resulting theories.

Time cannot be both absolute (as in quantum mechanics) and dynamical (as in general relativity). I present general arguments for the absence of time at the most fundamental level of quantum gravity. I discuss possible concepts that could replace it and present the recovery of standard time as an approximate concept. My discussion is restricted to quantum geometrodynamics, but I argue for the validity of my conclusions beyond that scheme.

"We propose a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory assumes that time, events, causal structure, momentum and energy are fundamental. But space and the wave function are emergent. The beables of the theory are the views of the events, which are a subset of their causal pasts. Thus, this theory asserts that the universe is a causal network of events, which consists of partial views of itself as seen by looking backwards from each event. The theory is based on a simple action principle, which extremizes the variety of the universe, which is a measure of the diversity of its partial views. The Schroedinger equation is derived, while to higher order, there are computable corrections, non-linear in the wave function, from which new physical effects may be predicted. Finally, a relativistic version is sketched, in wqhich the views are built on the celestial sphere. "