Model of Extended Mechanics and Non-Local Hidden Variables for Quantum Theory

Abstract

Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary reference frames postulating the description of body dynamics by differential equations with higher derivatives of coordinates with respect to time but not only of second order ones and follows from Mach principle. In that case the Lagrangian $L(t,q,\dot{q},\ddot{q},...,\dot {q}^{(n)},...)$ depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if n-th derivative of the body coordinate with respect to time is a constant (i.e. finite). First, kinematic state of a free body is postulated to invariable in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the n-th order derivative of coordinate with respect to time, then the body dynamics is describes by a 2n-th order differential equation. For example, in a uniformly accelerated reference frame all free particles have the same acceleration equal to the reference frame invariant, i.e. reference frame acceleration. These bodies are described by third-order differential equation in a uniformly accelerated reference frame.