Volume 6, Issue 4, pages 114-132
A hidden variables matrix mechanics model of the harmonic oscillator is presented as a counter-example in examining fundamental assumptions of quantum mechanics. Solutions are obtained which can be interpreted as describing continuous motion of a particle at all times located at points in space. While this is contrary to the basic postulate of Heisenberg, the experimental results of the standard matrix mechanics treatment are nevertheless reproduced. The proposed model is motivated by the foundational issues raised by Bell. Inequalities violation is however, attributed to the mathematical representation of outcome quantities as metric variables rather than the consensus assumption of local causality. Examining the consequence of this alternative conclusion on an actual quantum system creates an overlapping between Bell inspired foundational issues and the original postulates of Heisenberg and Born. Heisenberg’s basic postulates – randomness of transitions and treating the system as an ensemble – are critical. Bohr’s assumption that transitions occur instantaneously, together with Heisenberg’s non-path postulate where the particle can be measured at spatially separated locations without continuous movement between locations, are discarded. Heisenberg’s measurable-only quantities are interpreted as arising from a substructure of periodic endogenous motion of the system.