What is Uncertainty Principle

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore, the well-known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and they consider the application in electromagnetism. This chapter is an enhanced version of a published work. It proves the existence of particular relativistic error condition in classical mechanics, potentially significant on experiments of light propagation in matters. The work includes a discussion of applications potentially correlated with the found particle motion error condition.