In the light of relativity theory, we can say that our perception of absolute time is an illusion: beyond the scope of classical mechanics, empirical evidence does not support it any longer. The illusion arises due to restrictions prevailing in our environment: the relatively low speeds and short distances of physical objects in our everyday life, coupled with the limited accuracy of our senses and measurements. Similar applies to absolute space, and to the independence of space and time.
As soon as the restrictions are relaxed, we cease to perceive space and time as independent, absolute entities, and a unified, absolute spacetime appears instead. There is no such thing anymore as an observer-independent, globally passing time.
In a sense, everything, or rather, every property we perceive is an illusion and ceases to exist as soon as the horizon of our perception and measurements sufficiently broadens. (On a related note: is it due to causality that no signal can travel faster than light, or is it because nobody has ever seen a signal traveling faster than light that causality appears as a law of nature?)
Does then special relativity capture the real nature of space and time? Well, on the one hand it definitely does, in its own scope. But on the other hand it does not, for the real nature of space and time is that they, eventually, don't exist.