On the Problem of Eigenschaften in Quantum and Classical Mechanics

Abstract

We argue that in contrast to the classical physics, measurements in quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant relative phases. Simultaneity is needed since measurement changes the state of the system (in both quantum and in classical physics). We call that measurement procedure holographic detection. Mathematically, it is described by a set of mutually commuting selfadjoint operators that are similar and closely related to projections. We present explicit examples and discuss general features of the corresponding experimental setup which we identify as the quantum reference frame.