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.
The Critique of the Quantum Power of Judgement analyzes the a priori principles which underlie the empirical knowledge provided by quantum theory. In contrast to other transcendental approaches to quantum physics, none of the transcendental principles established by Kant is modified in order to cope with the new epistemological situation that arises with the asumption of the quantum postulate. Rather, by considering Bohr’s views, it is argued that classical concepts provide the mathematical formalism of quantum theory with physical reference through symbolic analogies in the strict Kantian sense. The main result of the investigation is the determination of the highest principle under which quantum objects are subsumed. This principle states that the conditions of the possibility of the systematic unity of contextual experience are at the same time the conditions of the possibility of quantum objects. Upon this principle rests the possibility of any a priori synthetic knowledge of quantum objects. Therefore, the Critique of the Quantum Power of Judgement yields the prolegomena to any future quantum metaphysics.