  We investigate the behaviour of quantum fields coupled to a spacetime
geometry exhibiting finite regions of Euclidean (Riemannian) signature.
Although from a gravity perspective this situation might seem somewhat far
fetched, we will demonstrate its direct physical relevance for an explicitly
realizable condensed matter system whose linearized perturbations experience an
effective emergent spacetime geometry with externally controllable signature.
This effective geometry is intrinsically quantum in origin, and its signature
is determined by the details of the microscopic structure. At the level of the
effective field theory arising from our condensed matter system we encounter
explicit anisotropic scaling in time and space. Here Lorentz symmetry is an
emergent symmetry in the infrared. This anisotropic scaling of time and space
cures some of the technical problems that arise when working within a canonical
quantisation scheme obeying strict Lorentz invariance at all scales, and so is
helpful in permitting signature change events to take place.
