  Recent timing observations of PSR J0045-7319 reveal that the neutron star/B
star binary orbit is decaying on a time scale of $|\Porb/\dot\Porb|=0.5$ Myr,
shorter than the characteristic age ($\tau_c=3$ Myr) of the pulsar (Kaspi et
al.~1996a). We study mechanisms for the orbital decay. The standard weak
friction theory based on static tide requires far too short a viscous time to
explain the observed $\dot\Porb$. We show that dynamical tidal excitation of
g-modes in the B star can be responsible for the orbital decay. However, to
explain the observed short decay timescale, the B star must have some
significant retrograde rotation with respect to the orbit --- The retrograde
rotation brings lower-order g-modes, which couple much more strongly to the
tidal potential, into closer ``resonances'' with the orbital motion, thus
significantly enhancing the dynamical tide. A much less likely possibility is
that the g-mode damping time is much shorter than the ordinary radiative
damping time. The observed orbital decay timescale combined with a generic
orbital evolution model based on dynamical tide can be used as a ``timer'',
giving an upper limit of $1.4$ Myr for the age of the binary system since the
neutron star formation. Thus the characteristic age of the pulsar is not a good
age indicator. Assuming standard magnetic dipole braking for the pulsar and no
significant magnetic field decay on a timescale $\lo 1$ Myr, the upper limit
for the age implies that the initial spin of the neutron star at birth was
close to its current value.
