  We study the causality violation in the non-local quantum field theory (as
formulated by Kleppe and Woodard) containing a finite mass scale $\Lambda $. We
use $\phi ^{4}$ theory as a simple model for study. Starting from the
Bogoliubov-Shirkov criterion for causality, we construct and study combinations
of S-matrix elements that signal violation of causality in the one loop
approximation. We find that the causality violation in the exclusive process
$\phi +\phi \to \phi +\phi $ grows with energy, but the growth with energy,
(for low to moderate energies) is suppressed to all orders compared to what one
would expect purely from dimensional considerations. We however find that the
causality violation in other processes such as $\phi +\phi \to \phi +\phi +\phi
+\phi $ grows with energy as expected from dimensional considerations at low to
moderate energies. For high enough energies comparable to the mass scale
$\Lambda $, however, we find a rapid (exponential-like) growth in the degree of
causality violation. We generalize some of the 1-loop results to all orders. We
present interpretations of the results based on possible interpretations of the
non-local quantum field theory models.
