  We investigate stochastic quantization as a method to go from a classical PDE
(with stochastic time $\lambda$) to a corresponding quantum theory in the limit
$\lambda\to\infty$. We test the method for a linear PDE satisfied by the free
scalar field. We begin by giving some background about the importance of
establishing the property of {\em reflection positivity} for the limit
$\lambda\to\infty$. We then prove that the measure determined through
stochastic quantization of the free scalar field violates reflection positivity
(with respect to reflection of the physical time) for every $\lambda<\infty$.
If a non-linear perturbation of the linear equation is continuous in the
perturbation parameter, the same result holds for small perturbations. For this
reason, one needs to find a modified procedure for stochastic quantization, in
order to use that method to obtain a quantum theory.
