Consistency of PT-symmetric quantum mechanics

What is it about?

Over the past two decades a lot of work has been done by many authors on understanding the theory and experiments of physical systems described by Hamiltonians that are not Hermitian but are nevertheless invariant under the simultaneous space-time reflection, otherwise known as PT symmetry. Such Hamiltonians can describe either (a) closed systems, or (b) open systems with a balanced gain and loss. In this paper it is proved that in the case of closed systems, the degrees of freedom associated with the symmetry of the Hamiltonian, sometimes referred to as the metric operator in the literature, is not experimentally accessible. It follow that PT-symmetric quantum theories are entirely consistent with the standard quantum mechanics. In particular, there is no way in which an experimentalist can ascertain whether a given quantum system is described by a Hermitian Hamiltonian, or a non-Hermitian PT-symmetric Hamiltonian.

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Why is it important?

Various authors have attempted to show that the so-called PT-symmetric quantum theories are not consistent with physical reality, by assuming that experimentalists have the ability to choose or modify the metric operator. This paper shows that such an assumption is in itself not physically viable, thus making PT-symmetric quantum theories entirely consistent.

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