Consistency of PT-symmetric quantum mechanics

TL;DR

This paper demonstrates that PT-symmetric quantum mechanics is consistent with standard quantum mechanics and cannot be distinguished through measurement, challenging previous claims of incompatibility with causality.

Contribution

It shows that the metric operator in PT-symmetric quantum mechanics is not physically observable, establishing the indistinguishability from standard quantum mechanics in finite-dimensional closed systems.

Findings

PT-symmetric and Hermitian quantum mechanics are indistinguishable in finite dimensions

The metric operator is not physically observable

Physical effects of PT symmetry are expected in open systems with gain and loss

Abstract

In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric---the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.