In recent times, the study of parity-time symmetry has been quite active in diverse areas of physics (i.e. quantum field theory, open quantum systems) and in optics it has been experimentally realized in numerous kinds of settings, thus paving the way for more widespread investigation on it.
But recently, in a PRL paper in a thought experiment (PRL 112, 130404 (2014)), the authors claimed that although PT-symmetry may be a useful tool in studying systems, it still seems to be far doubtful to be a fundamental theory as it locally violates non-signaling principle.
That's why the very question as above arises.
Your views and comments are most welcome!
@Samit parity time symmetry is useful in the study of some particle interactions but is not universal as such.However CPT invariance is universal.
Thanks.
But, can you elaborate more this, why PT-symmetry might be lacking the fundamental aspect whereas not CPT?
Dear All,
This is in aid a confusion of mine that arose after looking at the prl paper mentioned in the question. While doing local evolution they maintain the norm which is consistent with PT symmetry in which the evolution operator becomes unitary corresponding to the non Hermitian PT symmetric Hamiltonian. But when they calculate probability they use usual norm. But as they say that it is not their assumption but it was an implicit assumption in the PT symmetric quantum theory. This kind of jump up between different norms is not well justified. I hope that this jump up between norms may lead to other unexpected things. For example it can be shown that local unitaries can change the entanglement content of a bipartite system. It is not possible and plausible in usual quantum mechanics. In fact, while defining a measure of quantum correlation for mixed states, one uses this assumption. So the assumption used in the paper abot evolution and calculation of probabilities should be lifted in order to probe the question of importance the PT symmetry.
See http://arxiv.org/abs/1312.7738 and a brief criticism by myself and others http://arxiv.org/abs/0804.2051. There are some fundamental difficulties with this theory that can be summed up by its process of starting with a non-Hermitian Hamiltonian and then introducing a new (PT-symmetric) inner product that actually renders the Hamiltonian hermitian (Hermiticity is defined w.r.t. an inner product). So now we have an Hermitian Hamiltonian but an inner product and Hilbert spaced whose structure is dependent on the Hamiltonian (so this theory is not about some sort of fundamental symmetry as one finds elsewhere in quantum mechanics or particle physics). An example of how this might lead to difficulties arises if one considers this non-hermitian part to be a function of time - does the inner product then also need to be time dependent? If it does - how many theorems from functional analysis still hold. The mathematical foundations of the subject then - to my mind - become quite shaky. In my view - there may be occasions where PT symmetric QM might be a useful modelling tool (although I not convinced on this point either) but I do doubt it has any value as a fundamental theory.
I agree with Samit, Carringtone, Uttam and Mark, very interesting cuestion and answers.
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