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Non-commutative geometry deals with spaces where the uncertainty principle of quantum mechanics thwarts even one's ability to simultaneously measure two position co-ordinates. It finds applications in models where geometry is emergent including the matrix model approach to string theory.

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Why can't noncontextual ontological theories have stronger correlations than commutative the...

Non-commutativity of operators ensures that in general we can't construct a joint probability distribution over the observables that we model using those operators. In some states and for some choices …
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