The significance of the energy-momentum conservation laws, as consequences of the general invariance principles, is much enhanced if the momentum, and hence the energy, can be coupled, still by means of the invariance principles, to some directly observable quantity. If the positions of particles can be measured in the quantum-mechanical sense, and if the corresponding operator satisfies the obvious invariance requirements, the velocity can also be ascertained and its relation to the momentum four-vector can easily be derived from the displacement invariances. Serious doubts have been cast, however, on the measurability of the position. Hence, a more primitive method of measuring the velocity, by means of « traps » is described; it is essentially the experimental method. The connection between momentum and velocity is then derived, for the velocity measured in this way, from the displacement invariance principle.