The harmonic oscillator provides a unique opportunity to study with simple mathematics the properties acquired by a mechanical system in permanent contact with the zeropoint field, and to assess with a specific example the merit of the assumption that the classical particle becomes through this interaction a quantum object. Of course, due to its linearity the oscillator is far from being a fair representative of the general quantum system, but nevertheless the importance of getting a concrete expression of the relationship between quantum theory and SED can hardly be overestimated.