Causality in quantum theory and beyond: towards a theory of quantum gravity

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The way we combine operators in quantum theory depends on the causal relationship involved. For spacelike separated spacetime regions we use the tensor product. For immediately sequential regions of spacetime we use the direct product. In the latter case we lose information – that is we cannot go from the direct product of two operators to the two original operators. This is a kind of compression. We will see that such compression is associated with causal adjacency. We will situate this in the context of a much broader framework potentially suitable for developing a theory of quantum gravity.