Quantum Measuring Systems: Considerations from the Holographic Principle

Document Type : Regular article


Graduate School of Human and Environmental Studies, Kyoto University


In quantum mechanics without application of any superselection rule to

the set of the observables, a closed quantum system temporally evolves unitarily, and

this Lorentzian regime is characterized by von Neumann entropy of exactly zero.

In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to

an imaginary-time classical stochastic process with real-valued conditional probability

density in the Euclidean regime, where the von Neumann entropy of the classicalized

hologram and the information of a particle trajectory acquired by the classicalized hologram are positive valued.

This argument could shed light on the Euclidean regime of the holographic Universe.


Main Subjects