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Journal of Physics Conference Series

Instability states and Ostrogradsky formalism

T. F. Kamalov

Published Jul 1, 2018• 4 citations
Publisher

Abstract

Contemporary physics, both Classical and Quantum, requires a notion of inertial reference frames. However, how to find a physical inertial frame in reality where there always exist random weak forces? We suggest a description of the motion in instability frames by means of inclusion of higher time derivatives. They may play a role of non-local hidden variables in a more general description complementing both classical and quantum mechanics.

DOI
10.1088/1742-6596/1051/1/012033

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Contemporary physics, both Classical and Quantum, requires a notion of inertial reference frames. However, how to find a physical inertial frame in reality where there always exist random weak forces? We suggest a description of the motion in instability frames by means of inclusion of higher time derivatives. They may play a role of non-local hidden variables in a more general description complementing both classical and quantum mechanics.
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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 (vibration) reference frames with the random initial conditions? One of the most generalized ways of descriptions (known as the higher derivatives formalism) consists in taking into account the infinite number of the higher temporal derivatives of the coordinates in the Lagrange function. Such formalism describing physical objects in the infinite dimensions space does not contradict to the quantum mechanics and infinite dimensions Hilbert space.
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.
This preprint presents a stability-based approach to higher-derivative dynamics in non-inertial reference frames. By imposing the non-negativity of the second variation of the action, a dynamically admissible subset of trajectories is selected within the Ostrogradsky formalism. The resulting extended Hamilton–Jacobi structure naturally contains an additional term that coincides with the Bohm quantum potential in the Madelung representation of the Schrödinger equation. The work is related to the author’s contribution to the BSM 2025 conference and is shared here to ensure early dissemination of the results.
Abstract The main idea of I. Newton in Principia is a description of the laws of motion by a second-order differential equation. Classical Newtonian physics can describe stability trajectories in Inertial Reference Frames and some Non-Inertial ones. 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. Can we use another description in the form of a high-order differential equation? The high-order derivatives can be used as additional variables accounting for the influence of random fields 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 to 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.