  Assuming that the energy of a gas depends non-locally on the logarithm of its
mass density, the body force in the resulting equation of motion consists of
the sum of density gradient terms. Truncating this series after the second
term, Bohm's quantum potential and the Madelung equations are obtained, showing
explicitly that some of the hypotheses that led to the formulationb of quantum
mechanics do admit a classical interpretation based on non-locality. Here, we
generalize this approach imposing a finite speed of propagation of any
perturbation, thus determining a covariant formulation of the Madelung
equation.
