# Randomness in Classical Mechanics and Quantum Mechanics - Quantum Physics

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Abstract: The Copenhagen interpretation of quantum mechanics assumes the existence ofthe classical deterministic Newtonian world. We argue that in fact the Newtondeterminism in classical world does not hold and in classical mechanics thereis fundamental and irreducible randomness. The classical Newtonian trajectorydoes not have a direct physical meaning since arbitrary real numbers are notobservable. There are classical uncertainty relations, i.e. the uncertaintyerrors of observation in the determination of coordinate and momentum isalways positive non zero.A -functional- formulation of classical mechanics was suggested. Thefundamental equation of the microscopic dynamics in the functional approach isnot the Newton equation but the Liouville equation for the distributionfunction of the single particle. Solutions of the Liouville equation have theproperty of delocalization which accounts for irreversibility. The Newtonequation in this approach appears as an approximate equation describing thedynamics of the average values of the position and momenta for not too longtime intervals. Corrections to the Newton trajectories are computed. Aninterpretation of quantum mechanics is attempted in which both classical andquantum mechanics contain fundamental randomness. Instead of an ensemble ofevents one introduces an ensemble of observers.

Author: ** Igor V. Volovich**

Source: https://arxiv.org/