Exact Description of Rotational Waves in an Elastic Solid

TL;DR

This paper derives an exact nonlinear equation describing rotational waves in an elastic solid, using Dirac bispinors, linking classical elasticity with relativistic quantum mechanics.

Contribution

It introduces a novel exact nonlinear model for rotational waves in elastic solids, extending beyond traditional small-gradient approximations.

Findings

Derivation of a nonlinear wave equation using Dirac bispinors

Classical interpretation of relativistic quantum dynamics

A new Lagrangian formulation for rotational waves

Abstract

Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a restricted class of rotational waves in an ideal isotropic elastic solid. The result is a nonlinear equation expressed in terms of Dirac bispinors. This result provides a simple classical interpretation of relativistic quantum mechanical dynamics. We construct a Lagrangian of the form L=-E+U+K=0, where E is the total energy, U is the potential energy, and K is the kinetic energy.