Bohr's concept of complementarity enters any statistical description of physical phenomena. In quantum theory the complementary quantities are dynamical variables. In classical theory complementarity exists between dynamical and statistical variables. Slowing down of a large particle of mass $m$ by multiple collisions with a gas of small molecules leads to certainty for times. For times, the multiple collisions introduce statistics leading to uncertainty. An uncertainty relation has been derived for the coordinate $q$ as the dynamical and the drift momentum ${p}_{d}$ as the statistical complementary variable: $\ensuremath{\Delta}{p}_{d}\ensuremath{\Delta}q\ensuremath{\ge}mD(1\ensuremath{-}{e}^{\ensuremath{-}\frac{t}{\ensuremath{\tau}}})$, where $D$ is a diffusion coefficient and $\ensuremath{\tau}$ a relaxation time. This relation gives uncertainty for long and certainty for short times.The existence of such a classical uncertainty relation poses the question of whether a generalization of (relativistic) quantum theory is possible, such that for high $\ensuremath{\Delta}p\ensuremath{\Delta}q\ensuremath{\rightarrow}0$, while for low energies $\ensuremath{\Delta}p\ensuremath{\Delta}q\ensuremath{\geqq}\frac{\ensuremath{\hbar}}{2}$. This question is not answered in this note; however, it is pointed out that the telegrapher's equation (which classically implies the aforementioned generalized uncertainty principle) with $\ensuremath{\tau}=\frac{i\ensuremath{\hbar}}{2m{c}^{2}}$ is satisfied by the Klein-Gordon (also Dirac) wave function for a free particle if the time dependence of the rest mass is split off from it.