  Ever since the work of von Ignatowsky circa 1910 it has been known (if not
always widely appreciated) that the relativity principle, combined with the
basic and fundamental physical assumptions of locality, linearity, and
isotropy, leads almost uniquely to either the Lorentz transformations of
special relativity or to Galileo's transformations of classical Newtonian
mechanics. Thus, if one wishes to entertain the possibility of Lorentz symmetry
breaking within the context of the class of local physical theories, then it
seems likely that one will have to abandon (or at the very least grossly
modify) the relativity principle. Working within the framework of local
physics, we reassess the notion of spacetime transformations between inertial
frames in the absence of the relativity principle, arguing that significant and
nontrivial physics can still be extracted as long as the transformations are at
least linear. An interesting technical aspect of the analysis is that the
transformations now form a groupoid/pseudo-group --- it is this technical point
that permits one to evade the von Ignatowsky argument. Even in the absence of a
relativity principle we can nevertheless deduce clear and compelling rules for
the transformation of space and time, rules for the composition of
3-velocities, and rules for the transformation of energy and momentum. As part
of the analysis we identify two particularly elegant and physically compelling
models implementing "minimalist" violations of Lorentz invariance --- in the
first of these minimalist models all Lorentz violations are confined to
carefully delineated particle physics sub-sectors, while the second minimalist
Lorentz-violating model depends on one free function of absolute velocity, but
otherwise preserves as much as possible of standard Lorentz invariant physics.
