Abstract

The problem of propagation of acoustic waves in a linear infinite crystal is solved. When time is continuous, the solution of the equation of motion leads to strange results, in regard to the wave speed and the capacity of waveforms to propagate. The conundrum needs resolution. Discontinuous time is posited and Newton’s Law of Motion becomes inoperable. A nanomechanical equation of motion, based on temporal discontinuity, is proposed and solved with the following natural physical outcomes. The wave speed depends only on the bond strength, atomic mass and interatomic distance. All initial atomic configurations propagate, at the same speed.

Keywords:Crystal acoustic waves; Acoustic wave speed; Newton’s law challenge; Discontinuous time

HighlightsThe problem of propagation of acoustic waves in a linear infinite crystal is solved. When time is continuous, the solution of the equation of motion leads to strange results, in regard to the wave speed and the capacity of wave forms to propagate. Discontinuous time is posited and Newton’s Law of Motion becomes inoperable. A nanomechanical equation of motion, based on temporal discontinuity, is proposed and solved with the following natural physical outcomes. The wave speed depends only on bond strength, atomic mass and interatomic distance. All initial atomic configurations propagate, at the same speed.