Classical and Quantum-Mechanical Axioms with the Higher Time Derivative Formalism

TL;DR

This paper explores a formalism incorporating higher time derivatives into classical mechanics, providing a framework that aligns with quantum mechanics and extends the description of physical systems in non-inertial frames.

Contribution

It introduces a higher derivatives formalism for classical mechanics that bridges to quantum mechanics and describes extended bodies in vibrational reference frames.

Findings

Higher derivatives formalism aligns with quantum mechanics.

Describes extended bodies in non-inertial frames.

Provides a unified classical-quantum description.

Abstract

A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general description (known as the higher derivatives formalism) consists in taking into account the infinite number of the higher order temporal derivatives of the coordinates in the Lagrange function. Such formalism describes physical objects in the infinite dimensional space does not contradict quantum mechanics and infinite dimensional Hilbert space.