The present work is aimed to explain why we started to consider Vibrating Rays Theory (VRT) as a viable representation of nature, and to elaborate some of its consequences. We first note that we have kept the probably unsuitable term "vibrating rays" as homage to its insightful introducer: Michael Faraday. Certainly, the image of rays or "protrusions" emanating from an electric charge is not a very palatable one for a contemporary physicist. The term is used in this work only as a reference to a complex, and as yet not studied, possible means of interaction among particles. In 1846 Faraday [1] introduced the concept of vibrating rays, in which an atom is conceived as having rays that extend to infinity and move with it. According to this point of view, electromagnetic radiative phenomena correspond to vibration of these rays, which propagate at speed c relative to the rays (and the atom). Although a discussion on this subject might seem to be out-of-date, there are many reasons that justified this work. The first reason is based on the fact that the constancy of the speed of light, irrespective of the source movement, has not been demonstrated experimentally in a conclusive way. In fact, only ballistic emission theories (see, for example, Ritz theory [2]) can be discarded by the experimental results (for example, Brecher [3] or Alvager et al.[4] both compare their results against a ballistic theory). The second reason is based on the fact that study of radiometric data from spacecrafts indicates the existence of different kinds of anomalous Doppler residuals. In 1998 Anderson et al. [5] reported an anomalous acceleration towards the Sun obtained from the analysis of the Doppler data of the Pioneer 10/11 spacecraft. The anomaly was inferred from a small, blueshift Doppler residual obtained as the difference between measured and modeled values. Besides this term (that may be a thermal effect) there is an annual term, and in a much shorter time scale, there is a diurnal term. Also, for the Pioneer 11 there was a fast increase in the anomaly right at Saturn encounter. More recently the Doppler frequency data of different spacecrafts before and after the closest approach to Earth have shown an unexpected frequency shift, which had been called flyby anomaly [6]. Further, a range disagreement has been measured between active and passive reflection [7]. We will show that the above mentioned anomalies exhibit a signature of VRT. The third reason is related to the time definition in a rotating frame. According to Special Relativity (SRT) there is not a unique way to assign a time, whereas under VRT no contradictions are present. And finally, that VRT is compatible with all known experiments on electromagnetism and light propagation. In the present work we will (1) explain how VRT should be interpreted, and why past experiments were misinterpreted (for example, by the use of the motion of a mirror image as if it were a real source, when according to SRT itself both produce different results), (2) show the characteristics ...