  We define a conformal reference frame, i.e., a special projection of the
six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional
twistor space) to a three-dimensional manifold. We construct an example, a
conformal compactification, for Minkowski space. Based on the complex structure
on the skies, we define the celestial transform of Lorentzian vectors, a kind
of spinor correspondence. We express a 1-form generating the contact structure
explicitly as a (line bundle)-valued form. We prove a theorem on the projection
of this 1-form to the fiberwise normal bundle of a reference frame; its
corollary is an equation for the flow of time.
  The Appendix is less mathematical than the main body and discusses the causal
relation in context of the FLRW cosmology and its natural conformal reference
frame.
