  This work shows that in the frame of the stochastic generalization of the
quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by
the postulate of finite transmission speed of light and information . The
theory shows that the measurement process performed in the large scale
classical limit of stochastic QHA (SQHA), cannot have a duration smaller than
the time need to the light to travel the distance up to which the quantum
non-local interaction extend itself. The product of the minimum measuring time
multiplied by the variance of energy fluctuation due to presence of stochastic
noise shows to lead to the minimum uncertainty principle. The paper also shows
that the uncertainty relations can be also derived if applied to the
indetermination of position and momentum of a particle of mass m in a quantum
fluctuating environment.
