2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167754Why do we not experience a violation of macroscopic realism in every-day life? Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coarse-grained measurements. Then we demonstrate that there exist "non-classical" Hamiltonians whose time evolution cannot be understood classically, although at every instant of time the quantum spin state appears as a classical mixture. We suggest that such Hamiltonians are unlikely to be realized in nature because of their high computational complexity.4 pages, 2 figures, revised version, journal reference addedQuantum Physicstext