  Suggested modification of the Einstein-Maxwell system, such that Maxwell
equations become non-gauge and nonlinear. The theory is based on assumption
that observable (i.e., felt by particles) metric is $ {\tilde{g}}_{ab} = g_{ab}
- l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations),
$A_a$ is electromagnetic potential, and $l$ is fundamental constant of the
theory. Specific model of the mass and charge densities of a fundamental
particle is considered. As a result, one obtains solutions corresponding to
quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} =
-{(2n+1)\over3}e$, where $n = 0, 1, 2, ...$ Theory predicts Coulomb interaction
between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$)
describe masses and electrical charges of two particles respectively, then
energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' -
\sqrt k(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$,
contributes negative electrical charge, $Q_E = - \sqrt k M_E$, which explains
why primary cosmic rays consist mainly of positively charged particles. One may
attribute the fairweather electric field at the Earth's surface to the charge
$Q_E$.
