  In this paper, we extend our previous study of causality and local
commutativity of string fields in the pp-wave lightcone string field theory to
include interaction. Contrary to the flat space case result of Lowe,
Polchinski, Susskind, Thorlacius and Uglum, we found that the pp-wave
interaction does not affect the local commutativity condition. Our results show
that the pp-wave lightcone string field theory is not continuously connected
with the flat space one. We also discuss the relation between the condition of
local commutativity and causality. While the two notions are closely related in
a point particle theory, their relation is less clear in string theory. We
suggest that string local commutativity may be relevant for an operational
defintion of causality using strings as probes.
