  The possibility of matter coupling to two metrics at once is considered. This
appears natural in the most general ghost-free, bimetric theory of gravity,
where it unlocks an additional symmetry with respect to the exchange of the
metrics. This double coupling, however, raises the problem of identifying the
observables of the theory. It is shown that if the two metrics couple minimally
to matter, then there is no physical metric to which all matter would
universally couple, and that moreover such an effective metric generically does
not exist even for an individual matter species. By studying point particle
dynamics, a resolution is suggested in the context of Finsler geometry.
