  We show that the generating functional describing the slow dynamics of spin
glass systems is invariant under reparametrizations of the time. This result is
general and applies for both infinite and short range models. It follows simply
from the assumption that a separation between short time-scales and long
time-scales exists in the system, and the constraints of causality and
unitarity. Global time reparametrization invariance suggests that the low
action excitations in a spin glass may be smoothly spatially varying time
reparametrizations. These Goldstone modes may provide the basis for an analytic
dynamical theory of short range spin glasses.
