  We explore a possible link between the structure of space at short length
scales and the emergence of classical phenomena at macroscopic scales. To this
end we adopt the paradigm of non-commutative space at short length scales and
explicitly compute the outcomes of a double slit experiment and a von Neumann
measurement in the non-commutative plane. A very consistent picture of a
continuous quantum-to-classical transition emerges. The mechanism driving this
transition is standard decoherence, but here the ``environment'' arises quite
naturally from the tensor product structure of the non-commutative quantum
Hilbert space. The double slit calculation enables us to establish a lower
bound on the non-commutative parameter for this transition to become effective
at particle numbers of the order of Avogadro's number. Similarly, the result of
the von Neumann measurement establishes a criterium involving the
non-commutative parameter, apparatus size and coupling between system and
apparatus for classicality to emerge.
