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Human perceptions of quantum mechanical phenomena

Suppose we strip away all classical and relativity physics and set up a topological space containing only the minimal entitities relevant to quantum phenomena together with their relations such as connectedness (of a kind), superposition/entanglement, etc. There might have to be some ongoing adjustments to the number of entities as well as to the functions defined on this space.

Might mathematicians recognise in the structure of this space deep patterns?

If so, it might then be possible of 'annex' bit by bit the objects of classical space, introducing the particles, forces, laws, etc., finding that this basic topology underlies and gives rise to a unification.

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