Reformulating and reconstructing quantum theory

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Quantum theory is a deeply fascinating theory challenging our common intuitions about the world round us. However, it is usually formulated in terms of rather mathematically obtuse axioms. Where do these axioms come from? Can we under stand quantum theory in terms of some simpler set of natural postulates? Further, the usual way of formulating quantum theory is in terms of a state across space evolving in time. This goes against the spirit of Einstein's theories of special and general relativity in which space and time are unified. I have shown how quantum theory can be formulated in a way that is more sympathetic to a point of view in which space and time are unified. In this case, rather than having a state across space at a given time, we have something like a state associated with a general region of space time. In fact, we consider the circuit analogue of this - namely general fragments of circuits. This different point of view may be helpful when we come to try to build a theory of quantum gravity (which would unify Einstein's theory of gravity with quantum theory). However, there are many things to understand in the meantime. In particular, we do not have a very good understanding of what types of states can be associated with general regions. Understanding this would allow us to have a much deeper idea of what this deeper formulation of quantum theory is about. Further, it would be good to have some natural postulates for quantum theory that respect this space time point of view. Then we would have a good launching point to go from a space time friendly understanding of quantum theory to a theory of quantum gravity.