  Wallstrom has argued that quantum interpretations which construct the wave
function starting from Madelung variables
$\psi(q)=\rho(q)\exp(\frac{i}{\hbar}S(q))$, in particular, many variants of
Nelsonian stochastics, are not equivalent to quantum theory. Accepting this, we
explicitly add the physical restriction $(\forall q\in Q)|\psi(q)|^2>0$ in the
configuration space representation to quantum theory. The resulting theories
depend on the choice of the configuration space $Q$.
  The restriction adds possibilities to falsify such theories, making them
preferable following Popper's criterion of empirical content until they have
been really falsified.
  Considering the case of a relativistic scalar field, we argue that it is
reasonable to expect that the variant based on particle ontology can be (or
even has been already) falsified, while to falsify the variant based on field
ontology seems much harder, if not impossible.
  If correct, switching to a field ontology seems a reasonable choice for
interpretations based on Madelung variables to circumvent the Wallstrom
objection.
