  We investigate some aspects of relativistic classical theories with "relative
locality", in which pairs of events established to be coincident by nearby
observers may be described as non-coincident by distant observers. While
previous studies focused mainly on the case of longitudinal relative locality,
where the effect occurs along the direction connecting the distant observer to
the events, we here focus on transverse relative locality, in which instead the
effect is found in a direction orthogonal to the one connecting the distant
observer to the events. Our findings suggest that, at least for theories of
free particles such as the one in arXiv:1006.2126, transverse relative locality
is as significant as longitudinal relative locality both conceptually and
quantitatively. And we observe that "dual gravity lensing", first discussed in
arXiv:1103.5626, can be viewed as one of two components of transverse relative
locality. We also speculate about a type of spacetime noncommutativity for
which transverse relative locality could be particularly significant.
