  Several quantum gravity and string theory thought experiments indicate that
the Heisenberg uncertainty relations get modified at the Planck scale so that a
minimal length do arises. This modification may imply a modification of the
canonical commutation relations and hence quantum mechanics at the Planck
scale. The corresponding modification of classical mechanics is usually
considered by replacing modified quantum commutators by Poisson brackets
suitably modified in such a way that they retain their main properties
(antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that
there exists an alternative interesting possibility. Koopman-Von Neumann's
Hilbert space formulation of classical mechanics allows, as Sudarshan remarked,
to consider the classical mechanics as a hidden variable quantum system. Then
the Planck scale modification of this quantum system naturally induces the
corresponding modification of dynamics in the classical substrate.
Interestingly, it seems this induced modification in fact destroys the
classicality: classical position and momentum operators cease to be commuting
and hidden variables do appear in their evolution equations.
