  The Schr\"odinger-Robertson inequality for relativistic position and momentum
operators X^\mu, P_\nu, \mu, \nu = 0,1,2,3, is interpreted in terms of Born
reciprocity and `non-commutative' relativistic phase space geometry. For states
which saturate the Schr\"odinger-Robertson inequality, a typology of
semiclassical limits is pointed out, characterised by the orbit structure
within its unitary irreducible representations, of the full invariance group of
Born reciprocity, the so-called `quaplectic' group U(3,1)xH(3,1) (the
semi-direct product of the unitary relativistic dyamical symmetry U(3,1) with
the Weyl-Heisenberg group H(3,1)). The example of the `scalar' case, namely the
relativistic oscillator, and associated multimode squeezed states, is treated
in detail. In this case,it is suggested that the semiclassical limit
corresponds to the separate emergence of space-time and matter, in the form of
the stress-energy tensor, and the quadrupole tensor, which are in general
reciprocally equivalent.
