does time move relative to space?
I guess you are saying that because you learned the basics of special relativity or space-time, and began wondering why you age while you stand still....
it turns out we have some default motion through time, but not through space... this is just the way time is, why we only move through time in 1 direction but not the other (like we do through one of the spatial dimensions) is a mystery... it is called the "arrow of time" problem if you want to research it
things move through time without moving through space, but can't move through space without affecting their motion through time... if this seems bizarre just think about how the photon feels who moves only through space at full speed but doesn't move through time.
time does not move, space does not move, space does not bend, time does not bend, space-time bends because of mass... you move through space-time
Just to clarify, in its own frame the photon is located simultaneously at all spatial points along its path. That is, of course, because its time is the same all along its path.
It would seem to me that this could easily be a question of syntax or rather defining the terms, ie; does time (distance x velocity) move relative to space (?). Time and motion are never separate as you cannot make a definitive statement about one without reference to the other. To assume that a photon is in motion without reference to time would put it at infinite velocity rather than the (roughly) 300,000 km/s, which would be at least in error as the difference is quite substantial. Time then would be an aspect of motion (below infinite velocity) and by my understanding (or lack of understanding) of the special theory of relativity, time moves relative to velocity and space (?) is little more than the embankment or reference medium. The simple questions of time and space become profound when considering the vast distances involved in astrophysics and the finite velocities involved in exploration. I haven't made an attempt to address the question so much as to ask that the question be further defined as simple questions about complex subjects rarely meet up with simple answers.
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