  A number of gravitation-motivated theories, as well as theories with new
coloured fermions predict heavy particle towers with spectral densities
$\rho(m^2)$ growing faster than $e^{m}$, a characteristic of nonlocalizable
theories. It is shown that if a light scalar, like the Higgs boson, interacts
strongly with a heavy scalar particle tower with exponentially rising
degeneracy, then the local low-energy theory is equivalent to an effective
nonlocal scalar QFT. For energies approaching the nonlocality scale
$p^2\simeq\Lambda_{NL}^2$, the scalar propagator and scattering amplitudes are
modified by nonlocal factors of the form $e^{p^2/\Lambda^2_{NL}}$. The
double-Higgs production measurement at the LHC is proposed as a highly
sensitive probe of nonlocality at the electroweak scale.
