Effective field theories (EFTs) have been widely used as a framework in order
to place constraints on the Planck suppressed Lorentz violations predicted by
various models of quantum gravity. There are however technical problems in the
EFT framework when it comes to ensuring that small Lorentz violations remain
small -- this is the essence of the "naturalness" problem. Herein we present an
"emergent" space-time model, based on the "analogue gravity'' programme, by
investigating a specific condensed-matter system that is in principle capable
of simulating the salient features of an EFT framework with Lorentz violations.
Specifically, we consider the class of two-component BECs subject to
laser-induced transitions between the components, and we show that this model
is an example for Lorentz invariance violation due to ultraviolet physics.
Furthermore our model explicitly avoids the "naturalness problem", and makes
specific suggestions regarding how to construct a physically reasonable quantum
gravity phenomenology.Comment: V1:4 pages, revtex4; V2: slight changes in title, presentation, and
conclusions. This version to appear in Physical Review Letter