Abstract
This chapter discusses Lorentz invariant computations. It focuses on the arithmetic modeling and analysis of a harmonic oscillator, typical of which is an electron in an atom. Before discussing such an oscillator, however, the chapter presents the proof of a fundamental result about the related calculations, that is, that the computations in the lab and the rocket frames will be related by the Lorentz transformation. An oscillator is a particle of whose motion is back and forth over all, or part, of a straight or curved path. The most well-studied oscillator is the harmonic oscillator, whose motion is along a straight line, whose energy is conserved, and the force on which is directly proportional to its distance from fixed point, usually taken as the origin. The chapter shows the way to formulate and analyze a Newtonian harmonic oscillator using only arithmetic. It also describes an arithmetic, relativistic harmonic oscillator and presents a comparison of the two models.
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