  We study the physical content of the PT-symmetric complex extension of
quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998)
and 89, 270401 (2002), and show that as a fundamental probabilistic physical
theory it is neither an alternative to nor an extension of ordinary quantum
mechanics. We demonstrate that the definition of a physical observable given in
the above papers is inconsistent with the dynamical aspect of the theory and
offer a consistent notion of an observable.
