  The problem of finding null geodesics in a stationary Lorentzian spacetime is
known to to be equivalent to finding the geodsics of a Randers-Finlser
structure. This latter problem is equivalent to finding the motion of charged
particles moving on a Riemannian manifold in a background magnetic field or
equivalently, by a generalization of Fermat's principle, to Zermelo's problem
of extremizing travel time of an aeroplane in the presence of a wind. In this
paper this triad of equivalences is extended to include recent model of the
spread of a forest fire which uses form of Huyghen's principle. The
construction may also be used to solve a problem in quantum control theory in
which one seeks a control Hamiltonia taking an initial state of a quantum
mechanical system with its own Hamiltonian to a desired final state in least
time.
  The associated stationary spacetime may be thought of as defined on an
extended quantum phase space (Souriau's evolution space), the space of quantum
stares being complex projective space equipped with its Fubini-Study K\"ahler
metric. It is possible that this spacetime view point may provide insights
relevant for our understanding of quantum gravity.
