Complementarity and Classical Limit of Quantum Mechanics: Energy Measurement aspects

TL;DR

This paper explores how experimental limitations and environmental effects influence the classical limit of quantum mechanics, especially regarding energy measurements and the discreteness of energy spectra in integrable systems.

Contribution

It introduces a precise limit for classical measurements of energy levels and links the classical limit to environmental diffusion effects, providing new insights into quantum-classical transition.

Findings

Quantum mechanics does not reproduce classical predictions without considering experimental limitations.

Discrete energy levels in integrable systems can be accessed through classical measurements within a defined limit.

Environmental diffusion causes the discreteness of spectra to have a finite lifetime approximately equal to the inverse of the diffusion constant.

Abstract

In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we consider the experimental limitations ruled by uncertainty principle. We have shown that the discrete nature of energy levels of integrable systems can be accessed by classical measurements. We have defined a precise limit for this procedure. It may be used as a tool to define the classical limit as far as the discrete spectra of integrable systems are concerned. If a diffusive environment is considered, we conclude that the "lifetime" of discreteness is approximately $1/\kappa$ ($\kappa$ is the diffusion constant), thus it was possible to relate the classical limit of a spectra with the action of an environment and experimental resolution.