  We reinterpret special relativity, or more precisely its de Sitter
deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime
geometry. An inertial observer, usually described by a geodesic in spacetime,
becomes instead a choice of ways to reverse the conformal compactification of a
Euclidean vector space up to scale. The observer's "current time," usually
given by a point along the geodesic, corresponds to the choice of scale in the
decompactification. We also show how arbitrary conformal 3-geometries give rise
to "observer space geometries," as defined in recent work, from which spacetime
can be reconstructed under certain integrability conditions. We conjecture a
relationship between this kind of "holographic relativity" and the "shape
dynamics" proposal of Barbour and collaborators, in which conformal space takes
the place of spacetime in general relativity. We also briefly survey related
pictures of observer space, including the AdS analog and a representation
related to twistor theory.
