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The canonical commutation relation, $[Q,P] = i\hbar$, stands at thefoundation of quantum theory and the original Hilbert space. The interpretationof $P$ & $Q$ as observables has always relied on the analogies that existbetween the unitary transformations of Hilbert space and the canonical (a.k.a.contact) transformations of classical phase space. Now that the theory ofquantum measurement is essentially complete (this took a while), it is possibleto revisit the canonical commutation relation in a way that sets the foundationof quantum theory not on unitary transformations, but on positivetransformations. This paper shows how the concept of simultaneous measurementleads to a fundamental differential geometric problem whose solution shows usthe following: The simultaneous $P$ & $Q$ measurement (SPQM) defines auniversal measuring instrument, which takes the shape of a 7-dimensionalmanifold, a universal covering group we call the Instrumental Weyl-HeisenbergGroup, IWH. The group IWH connects the identity to classical phase space inunexpected ways that are significant enough that the positive-operator-valuedmeasure (POVM) offers a complete alternative to energy quantization. Five ofthe dimensions define processes that can be easily recognized and understood.The other two dimensions, the normalization and phase in the center of IWH, areless familiar. The normalization, in particular, requires special handling inorder to describe and understand the SPQM instrument.

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group