The claim that “According to special relativity, the mass of an object is dependent on its velocity” is false. In fact it’s worse than false; it’s meaningless – because the velocity of an object is not something that exists except as relative to some observer.

What is true is that something which used to be called the “apparent mass”, or “relativistic mass”, of a body as seen by an observer is dependent on the velocity of the observer relative to the object (or of the object relative to the observer). However neither this apparent mass nor the velocity are properties of the object, since they depend also on its relationship to the observer.

In terms of any particular object and observer, there is indeed an absolute zero **relative** velocity. It corresponds to the situation where neither of them sees any change in the distance or direction of the other, and is absolute in the sense that any other inertial observer will perceive them as having the same velocity as one another (relative to it) and so as having zero relative velocity (relative to one another).

And the “apparent mass” as perceived by an observer at zero relative velocity, which **is** an inherent property of the object, is what was once called the “rest mass” but has for many decades been identified just as the mass of the object (without any qualifier).