"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)."