We postulate that all the presently known kinematic effects on physical quantities related to a material particle (e.g., masss increase) are due to its velocity relative to surrounding matter, and not to the observer's reference frame. The minimal velocity (i.e., the velocity that minimizes these quantities) relative to a single large body being a function of the distance to and mass of the body. In consequence, the minimal velocity is a function of position, and the reference frame associated to this velocity is strictly of local validity. We further assume that, at any given point, light propagates isotropically solely in the minimal-velocity local frame existing at the point. We obtain the following results: (i) After showing the compatibility of the gravitational field eqs. with our assumptions, we find the functional dependance of the minimal velocity on the distance to and mass of a single large body. (ii) A permanent gravitational field is the convective rate of change of the minimal velocity field. (iii) A Lorentz transformation connects the values of quantities related to a particle, for two different velocities of the particle relative to its minimal-velocity local frame. However, a Lorentz transformation does not connect this frame with any other moving uniformly with respect to it. (iv) The experimentally detected effects of kinematic, as well as gravitational, mass increase and time dilation are derived. This is, they all are due to the presence of the nearby (single) large mass. (v) Fizeau's experiment, Michelson's experiment, aberration of fixed stars are taken account of. (vi) Michelson's experiment performed from an vehicle orbiting the earth, or the sun, should detect the orbital velocity of the vehicle.