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This work shows that in the frame of the stochastic generalization of thequantum hydrodynamic analogy (QHA) the uncertainty principle can be derived bythe postulate of finite transmission speed of light and information . Thetheory shows that the measurement process performed in the large scaleclassical limit of stochastic QHA (SQHA), cannot have a duration smaller thanthe time need to the light to travel the distance up to which the quantumnon-local interaction extend itself. The product of the minimum measuring timemultiplied by the variance of energy fluctuation due to presence of stochasticnoise shows to lead to the minimum uncertainty principle. The paper also showsthat the uncertainty relations can be also derived if applied to theindetermination of position and momentum of a particle of mass m in a quantumfluctuating environment.

The Uncertainty Principle derived by the finite transmission of light and information