  In a previous paper, we have put forward an interpretation of quantum
mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed
Universe $M$, existing on timeless configuration space $\mathcal{M}$. However,
not much was said there about the role of locality, which was not assumed. This
paper is an attempt to fill that gap. To deal with the challenges gauge
symmetries may pose to a good definition of locality, I start by demanding
symmetries to have an action on $\mathcal{M}$ so that the quotient wrt the
symmetries respects certain factorizations of $\mathcal{M}$. These
factorizations are algebraic splits of $\mathcal{M}$ into sub-spaces
$\mathcal{M}=\bigoplus_i \mathcal{M}_{O_i}$-- each factor corresponding to a
physical sub-region $O_i$. This deals with kinematic locality, but locality in
full can only emerge dynamically, and is not postulated. I describe conditions
under which it can be said to have emerged. The dynamics of $O$ is independent
of its complement, $M-O$, if the projection of extremal curves on $M$ onto the
space of extremal curves intrinsic to $O$ is a surjective map. This roughly
corresponds to $e^{i\hat{H}t}\circ \mathsf{pr}_{\mbox{O}}= \mathsf{pr}_{\mbox{
O}}\circ e^{i\hat{H}t}$, where $\mathsf{pr}_{\mbox{ O}}:\mathcal{M}\rightarrow
\mathcal{M}_O^{\partial O}$ is a linear projection. This criterion for locality
can be made approximate -- an impossible feat had it been already postulated --
and it can be applied for theories which do not have hyperbolic equations of
motion, and/or no fixed causal structure. When two regions are \emph{mutually
independent} according to the criterion proposed here, the semi-classical path
integral kernel factorizes, showing cluster decomposition which is what one
would like to obtain from any definition of locality.
