On the problem of Eigenschaften in the Quantum and Classical Mechanics

TL;DR

The paper proposes a new measurement approach called holographic detection in quantum mechanics that simultaneously captures all relevant amplitudes and phases, contrasting with classical measurement limitations.

Contribution

It introduces the concept of holographic detection, a measurement procedure that provides complete information about quantum states, and discusses its mathematical framework and experimental implications.

Findings

Holographic detection captures all relevant quantum information simultaneously.

The measurement involves mutually commuting self-adjoint operators.

Experimental setup is identified as a quantum reference frame.

Abstract

We argue that in contrast to the classical physics, the measurements in the 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 in general the measurement changes the state of the system (in quantum physics and in classical physics as well). We call that measurement procedure the holographic detection. Mathematically it is described by the set of mutually commuting self adjoint operators 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.