Why Do Total Cross Sections Grow with Energy?

By using exact inclusive sum rules we infer that the growth with energy of the total $\mathrm{pp}$ cross section is connected with the mechanism which is responsible for the appearance of a sharp peak near the kinematical boundary in the process $p+p\to p+\mathrm{anything}$. We discuss this mechanism in the context of Regge models and suggest tests of this idea which involve $K^{+}p$ scattering experiments.