  Gravitational wave memory is said to arise when a gravitational wave burst
produces changes in a physical system that persist even after that wave has
passed. This paper analyzes gravitational wave bursts in plane wave spacetimes,
deriving memory effects on timelike and null geodesics, massless scalar fields,
and massless spinning particles whose motion is described by the spin Hall
equations. All associated memory effects are found to be characterized by four
``memory tensors,'' three of which are independent. These tensors form a
scattering matrix for the transverse components of geodesics. However, unlike
for the ``classical'' memory effect involving initially comoving pairs of
timelike geodesics, one of our results is that memory effects for null
geodesics can have strong longitudinal components. When considering massless
particles with spin, we solve the spin Hall equations analytically by showing
that there exists a conservation law associated with each conformal Killing
vector field. These solutions depend only on the same four memory tensors that
control geodesic scattering. For massless scalar fields, we show that given any
solution in flat spacetime, a weak-field solution in a plane wave spacetime can
be generated just by differentiation. Precisely which derivatives are involved
depend on the same four memory tensors. These effects are illustrated for
scalar plane waves and higher-order Gaussian beams. Furthermore, we also
present a numerical comparison between the dynamics of localized wave packets
carrying angular momentum and the spin Hall equations.
