I've noticed that spacetime diagrams are often used to explain certain situations in special relativity such as the Twin's Paradox, for example:
In describing these diagrams, people will often say things like "the stationary twin's world line is along the y-axis; his position is constant in space, moving only in time." Of course, this is all relative, the twin could still be moving but he isn't in his frame of reference. My question, however, has to do with the statement "moving only in time." Lets say an object is truly stationary with respect to the three dimensions of space, why must the object be moving through time as the statement seems to imply? Does an object need to be moving to exist or can we not experience time without motion?
I've also heard people ask "if gravity is induced by the curvature of spacetime, how can an object experience gravity if it isn't moving through space?" In response to this, I hear arguments similar to that above "a still object is still moving through time and so will still experience gravity." Is this to imply all objects are moving through time even if they aren't moving through space? And if an object doesn't move with respect to space or time will it not experience gravity and will it even exist? I guess I am confused by what it means to be "moving" through time, is this the same as moving through the three dimensions of space and is it possible to not move through time?
Appreciate any responses. I realize this question is a bit informal, I'm just hoping to get a better concept of what is actually going on and not get lost in all the formality.