``PT symmetry as a nickname for fresh developments in an old
 conflict between relativistic kinematics and quantum dynamics"


Abstract

Although it is a widely accepted fact that quantum mechanics is
one of the most ``robust" theories in physics, some of its
abstract postulates (concerning, e.g., the preparation of wave
functions) seem to be in a manifest conflict with special
relativity (cf., e.g., the famous EPR paradox or, on a more
technical level, difficulties connected with a consistent
probabilistic interpretation of the Klein-Gordon wave functions).

In my talk I intend to outline some very recent theoretical
developments which seem to throw new light on some of these old
problems.

More explicitly, I shall show that and how these developments were
initiated, innocently enough, by the mathematically surprising
observation (made, in 1999, within the so called PT-symmetric
quantum mechanics) that the postulates of quantum mechanics
(requiring, for stable systems, the reality of the energies) may
admit in fact a certain subtle violation of the unitarity of the
time evolution.

On this background, a new, slightly modified and extended
interpretation of the textbook quantum mechanics seems to be
emerging at present. Some of its main features and consequences
(involving not only an innovated interpretation of the
Klein-Gordon problem) will be discussed in some detail.