  We study a novel asymptotic limit of massive scalar fields in
nongravitational quantum field theories in four-dimensional flat space. We
foliate the spacetime into a set of dS$_3$ slices that are spacelike to, and at
a constant proper distance from, an arbitrarily chosen origin, and study the
boundary dS$_3$ obtained in the infinite-distance limit. Massive bulk fields
have an exponentially small tail in this limit, and by stripping off this tail
we obtain observables that are intrinsic to the boundary dS$_3$. A single
massive field in the bulk can be decomposed into an infinite set of dS$_3$
fields, and the Minkowski vacuum corresponds to the Euclidean vacuum for these
fields. Our procedure for extrapolating bulk observables induces potential
singularities in boundary correlators but we show how they can be cured in the
free theory by smearing the boundary operators. We show that by integrating
boundary operators with suitable smearing functions it is possible to
reconstruct all local bulk operators in the free theory. We argue, using
perturbation theory, that our extrapolation procedure continues to be well
defined in the presence of interactions. We demonstrate a relationship between
the width of the boundary smearing function and the localization of the bulk
field. We study other interesting properties of the boundary algebra including
the action of global translations and the manner in which local bulk
interactions are encoded on the boundary.
