  We discuss the importance of measuring $\rho= ReF/ImF$ at LHC to test the
forward dispersion relations and local QFT. It is pointed out that at LHC we
can reach a short distance domain that has not been pre-explored by QED. This
is in contrast with all previous tests of the dispersion relations. We argue
that the most likely property of QFT to fail is polynomial boundedness. In a
theory with `fundamental length', R, we study the consequences of having
exponential behavior in the amplitude of the form (exp$\pm i\sqrt{s}\;R)$, as
suggested by different models. We show that such a behavior makes a significant
and measurable contribution to $\rho$ even at energies where $(\sqrt{s}\;R)$ is
still small, O(0.1). Talk delivered at Les Rencontres de Physique de la Vallee
d'Aoste: Results and Perspectives in Particle Physics, La Thuile, Aosta, March
1994.
