  We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically
natural way to define a "system" in general relativity. An RQF is defined as a
two-parameter family of timelike worldlines comprising the worldtube boundary
of the history of a finite spatial volume, with the rigidity conditions that
the congruence of worldlines is expansion-free (constant size) and shear-free
(constant shape). This definition of a system is anticipated to yield simple,
exact geometrical insights into the problem of motion in general relativity. It
begins by answering the questions what is in motion (a rigid two-dimensional
system boundary), and what motions of this rigid boundary are possible. Nearly
a century ago Herglotz and Noether showed that a three-parameter family of
timelike worldlines in Minkowski space satisfying Born's 1909 rigidity
conditions has only three degrees of freedom instead of the six we are familiar
with from Newtonian mechanics. We argue that in fact we can implement Born's
notion of rigid motion in both flat spacetime (this paper) and arbitrary curved
spacetimes containing sources (subsequent papers) - with precisely the expected
three translational and three rotational degrees of freedom - provided the
system is defined quasilocally as the two-dimensional set of points comprising
the boundary of a finite spatial volume, rather than the three-dimensional set
of points within the volume.
