Instability Criterion and Uncertainty Relation

The main idea of I. Newton in Principia is a description of the laws of motion in Inertial Reference Frames by a second-order differential equation. The variation of the action functional S of stability trajectories equals to zero. The observational error is including the influence of the random fields’ background to the particle. Are we must to use a high-order differential equation for the description in the random fields background? The highorder derivatives can be used as additional variables accounting for the influence of random field background. Trajectories due the influence of the random fields’ background can be called instability random trajectories. They can be described by high order derivatives. Then the stability classical trajectories must be complemented by additional instability random trajectories. Quantum objects are described by the trajectory with neighborhoods. Quantum Probability can describe quantum objects in random fields’. The variation of the action functional S is defined by the Planck constant. For the common description of quantum theory and high-order theory, let us compare r -neighborhoods of quantum action functional with r -neighborhoods of the action functional of a high-order theory.