  Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012);
arXiv:1105.4014], we demonstrate that any finite-dimensional representation of
quantum and classical dynamics violates the Ehrenfest theorems. Other
peculiarities are also revealed, including the nonexistence of the free
particle and ambiguity in defining potential forces. Non-Hermitian mechanics is
shown to have the same problems. This work compromises a popular belief that
finite-dimensional mechanics is a straightforward discretization of the
corresponding infinite-dimensional formulation.
