Digitization of the harmonic oscillator in extended relativity

Extended relativistic dynamics (ERD) admits only solutions that have speed bounded by the speed of light c and acceleration bounded by an assumed universal maximal acceleration am. Here we explore the harmonic oscillator under ERD. For oscillators with small natural frequency ω, we recover the classical solutions, while for large ω, the solutions differ significantly from the classical one. The solutions for large ω are a 'digitization' of the standard signals of the classical harmonic oscillator. The spectrum of these signals coincides with the energy spectrum of the quantum harmonic oscillator. While for small ω, the thermal radiation is a wave type, for large ω, it becomes pulses of radiation. This provides a possible explanation for the difference in the blackbody radiation for small and large ω and is another indication of the validity of ERD. (paper)