Field theories based on non-commutative spacetimes exhibit very distinctive
non-local effects which mix the ultraviolet with the infrared in bizarre w
ays. In particular if the time coordinate is involved in the non-commutativ
ity the theory seems to be seriously acausal and inconsistent with conventi
onal hamiltonian evolution. To illustrate these effects we study the scatte
ring of wave packets in a field theory with space/time non-commutativity. I
n this theory we find effects which seem to precede their causes and rigid
rods which grow instead of Lorentz contract as they are boosted. These fiel
d theories are evidently inconsistent and violate causality and unitarity.
On the other hand open string theory in a background electric field is expe
cted to exhibit space/time non-commutativity. This raises the question of w
hether they also lead to acausal behavior. We show that this is not the cas
e. Stringy effects conspire to cancel the acausal effects that are present
for the non-commutative field theory.