  (Abridged) The ammonia method, which has been proposed to explore the
electron-to-proton mass ratio, mu = m_e/m_p, is applied to nearby dark clouds
in the Milky Way. This ratio, which is measured in different physical
environments of high (terrestrial) and low (interstellar) densities of baryonic
matter is supposed to vary in chameleon-like scalar field models, which predict
strong dependence of both masses and coupling constant on the local matter
density. High resolution spectral observations of molecular cores in lines of
NH3 (J,K) = (1,1), HC3N J = 2-1, and N2H+ J = 1-0 were performed at three radio
telescopes to measure the radial velocity offsets, DeltaV = V_rot - V_inv,
between the inversion transition of NH3 (1,1) and the rotational transitions of
other molecules with different sensitivities to the parameter dmm = (mu_obs -
mu_lab)/mu_lab. The measured values of DeltaV exhibit a statistically
significant velocity offset of 23 +/- 4_stat +/- 3_sys m/s. When interpreted in
terms of the electron-to-proton mass ratio variation, this infers that dmm =
(2.2 +/- 0.4_stat +/- 0.3_sys)x10^{-8}. If only a conservative upper bound is
considered, then the maximum offset between ammonia and the other molecules is
|DeltaV| <= 30 m/s. This gives the most accurate reference point at z = 0 for
dmm: |dmm| <= 3x10^{-8}.
