In the same way that space is nothingness, so is time. Distances in space can only be measured using the objects that occupy space. The passage of time can only be measured by noting the events that happen to the objects that occupy space. Time is the measure of something being different from one moment to a succeeding moment.

Being nothingness, time doesn't dilate. Objects can accelerate or decelerate. Processes and mechanisms can accelerate or decelerate. When objects and processes and mechanisms are accelerating or decelerating, time is not dilating. It is merely that the objects, processes, or mechanisms are going faster or slower relative to other objects, processes or mechanisms.

Since time doesn't dilate, there is no relativistic Doppler colourshifting. Such effects are claimed to have been detected but these detections are a misinterpretation of the data in the light of the current paradigm.