On the instability of classical dynamics in theories with higher derivatives

TL;DR

This paper investigates the instability issues in theories with higher derivatives, using the Pais-Uhlenbeck oscillator model with added friction to demonstrate how energy unboundedness leads to physical instabilities.

Contribution

It provides a detailed analysis of the instability mechanisms in higher-derivative theories through a specific oscillator model with external friction.

Findings

Higher derivatives cause energy unboundedness from below.

External friction reveals the physical implications of these instabilities.

The model demonstrates the development of instability in higher-derivative dynamics.

Abstract

The development of instability in the dynamics of theories with higher derivatives is traced in detail in the framework of the Pais-Uhlenbeck fourth oder oscillator. For this aim the external friction force is introduced in the model and the relevant solutions to equations of motion are investigated. As a result, the physical implication of the energy unboundness from below in theories under consideration is revealed.