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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.

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 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.

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.

"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."

"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 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.

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.

It is commonplace that quantum theory can be viewed as a ``non-classical" probability calculus. This observation has inspired the study of more general non-classical probabilistic theories modeled on QM, the so-called generalized probabilistic theories or GPTs. However, the boundary between these putatively non-classical probabilistic theories and classical probability theory is somewhat blurry, and perhaps even conventional. This is because, as is well known, any probabilistic model can be understood in classical terms if we are willing to embrace some form of contextuality. In this talk, I want to stress that this can often be done functorially: given a category $\Cat$ of probabilistic models, there are functors $F : \Cat \rightarrow \Set_{\Delta}$ where $\Set_{\Delta}$ is the category of sets and stochastic maps. In addition to the familiar Beltrametti-Bugajski representation, I'll exhibit two others that are less well known, one involving the ``semi-classical cover" and another, slightly more special, that allows one to represent a probabilistic model with sufficiently strong symmetry properties by a model having a completely classical probabilistic structure, in which any ``non-classicality" is moved into the dynamics, in roughly the spirit of Bohmian mechanics. 

(Based on http://philsci-archive.pitt.edu/16721/)

Zoom Link: https://pitp.zoom.us/j/91838172434?pwd=SUltOGlURWI5MDN6Qk45dnVRelBOQT09

In the last quarter century, Capra has grown from a mere handful of people to a fully international meeting, which now represents a large diversity of interests. In that time, much progress has been made: many aspects of the first order problem are now in hand, and a multitude of techniques has been formulated for eventually use in full EMRI waveform generation. Yet, much needs to be done, most notably at second order. In Capra meetings of the past, we have often recognized the need to reach out to the younger generation. I think efforts in that direction have clearly been effective. At some Capra meetings, specific problems have often taken focus, both in discussions at the meeting, and in the work that evolves over the coming year. From experience, we know this approach has also clearly paid off. From the discussions that have taken place here, we need to go forward with specific goals for the year ahead, drawing wherever possible on the diversity we now have before us. Great things can be achieved if great problems are tackled. What have we formulated to work on as a community together before we can meet again in 2022?