  Bell's inequality plays an important role with respect to the Einsteinian
question about the physical reality of quantum theory. While Bell's inequality
is usually viewed within the geometric framework of a Hilbert space quantum
model, the present note extends the theory of Heisenberg measurements to
quantum systems with representations in general orthogonal geometric spaces
and, in particular, the Minkowski spaces of relativity theory. A Feynmanian
numerical example exhibits two measurements that admit a joint probabilistic
interpretation in Minkowski space while they are not jointly observable in
Hilbert space.
  The analysis shows that probabilistic interpretations of quantum measurements
may depend not only on the measuring instruments and the system states but also
on the geometric space in which the measurements are conducted. In particular,
an explicit numerical example is given of a Heisenberg measurement with a
complete set of common observables that violates Bell's inequality in Minkowski
space but, mutatatis mutandis, satisfies it in Hilbert space.
