The role of dimensionality, symmetry, and correlation in quantum time scales

Time, though ubiquitous in our daily experience, is a physical quantity not very well understood. It lies at the crux of efforts to unify the physical paradigms, being regarded as a constant background in some paradigms such as Newtonian mechanics or quantum mechanics, while completely internal to the objects in other paradigms such as general relativity. In quantum mechanics, specifically, the inability to find an operator for time as for spatial positions indicates the impossibility to find an observable which represents the external time \textit{coordinate}. Nevertheless, an operator can often be found to represent the internal time \textit{duration} of some certain process. The Eisenbud-Wigner-Smith (EWS) time scale is a famous example of such a time duration operator, which describes the single-particle scattering or ionization time scale.

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Thesis: https://infoscience.epfl.ch/handle/20.500.14299/256290 
Newton article: https://doi.org/10.1016/j.newton.2025.100374