  We formulate physically-motivated axioms for a physical theory which for
systems with a finite number of degrees of freedom uniquely lead to Quantum
Mechanics as the only nontrivial consistent theory. Complex numbers and the
existence of the Planck constant common to all systems arise naturally in this
approach. The axioms are divided into two groups covering kinematics and basic
measurement theory respectively. We show that even if the second group of
axioms is dropped, there are no deformations of Quantum Mechanics which
preserve the kinematic axioms. Thus any theory going beyond Quantum Mechanics
must represent a radical departure from the usual a priori assumptions about
the laws of Nature.
