  This paper concerns the absolute versus relative motion debate. The Barbour
and Bertotti 1982 work may be viewed as an indirectly set up relational
formulation of a portion of Newtonian mechanics. I consider further direct
formulations of this and argue that the portion in question -- universes with
zero total angular momentum, that are conservative and with kinetic terms that
are (homogeneous) quadratic in their velocities -- is capable of accommodating
a wide range of classical physics phenomena. Furthermore, as I develop in Paper
II, this relational particle model is a useful toy model for canonical general
relativity.
  I consider what happens if one quantizes relational rather than absolute
mechanics, indeed whether the latter is misleading. By exploiting Jacobi
coordinates, I show how to access many examples of quantized relational
particle models and then interpret these from a relational perspective. By
these means, previous suggestions of bad semiclassicality for such models can
be eluded. I show how small (particle number) universe relational particle
model examples display eigenspectrum truncation, gaps, energy interlocking and
counterbalanced total angular momentum. These features mean that these small
universe models make interesting toy models for some aspects of closed universe
quantum cosmology. While, these features do not compromise the recovery of
reality as regards the practicalities of experimentation in a large universe
such as our own.
