A model of extended mechanics and nonlocal hidden variables for quantum theory

Newton’s physics describes macroobjects sufficiently well, but it is not appropriate for describing microobjects. A model of extended mechanics for quantum theory is based on an axiomatic generalization of Newton’s 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 secondorder ones and follows from Mach’s principle. In this case, the Lagrangian depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if the nth derivative of the body coordinate with respect to time is a constant (i.e., finite). First, the kinematic state of a free body is postulated to be an invariant in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the nth order derivative of the coordinate with respect to time, then the body dynamics is described by a second-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 a fourth-order differential equation in a uniformly accelerated reference frame.