If the postulate of symmetry on which special relativity is built is rejected, a generalization of the relativistic notions of event and space-time can be proposed. The generalization leads to the notion of noumenon. The noumenon possesses a handedness; it is a seven-parameter entity obtained by associating with an event the angular momentum corresponding to a particular evolution of that event. The noumenon is defined in the complex extension C4 of space-time R4. The main purpose of the paper is to prove the acceptability of the new concepts when confronted with experimental results which are generally regarded as supporting the classical theory of relativity. The potential fruitfulness of the new concepts is shown by a short review of similar ideas developed independently by several authors in different fields of physics: A Maxwellian theory of gravitation is developed; interactions between gravitation and electromagnetism appear, which have common characteristics with weak interactions; and it is suggested that the extra degrees of freedom of the noumenon are related to the quantum numbers of elementary particles.