Comment on Complex Extension of Quantum Mechanics

In their Erratum [Phys. Rev. Lett. 92, 119902 (2004), quant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and Jones propose a revised definition for a physical observable in PT -symmetric quantum mechanics. We show that although this definition avoids the dynamical inconsistency revealed in quant-ph/0310164, it is still not a physically viable definition. In particular, we point out that a general proof that this definition is consistent with the requirements of the quantum measurement theory is lacking, give such a proof for a class of PT -symmetric systems by establishing the fact that this definition implies that the observables are pseudo-Hermitian operators, and show that for all the cases that this definition is consistent with the requirements of measurement theory it reduces to a special case of a more general definition given in [quant-ph/0310164]. The latter is the unique physically viable definition of observables in PT -symmetric quantum mechanics. Bender, Brody and Jones [Phys. Rev. Lett. 92, 119902 (2004), quant-ph/0208076] have recently proposed the following definition of a physical observable in PT -symmetric quantum mechanics. Def. 1: A linear operator A is called an observable if it satisfies [1]