dennis83704 said:
It is my understanding that all things travel through spacetime at the same speed.
I think you are thinking of Brian Greene's explanation of relativity, I posted the math behind it in [post=430613]this post[/post]--I've never seen any textbook that explains relativity this way though, and it has potential to create conceptual confusion.
dennis83704 said:
Additionally , I am told we are moving through space at some velocity.
Not in any objective sense--if you pick an
inertial reference frame we have some speed relative to that frame, but we have a different speed relative to other frames, and every inertial reference frame is considered equally valid. In any frame, if you take the square of your speed through space [tex]d\vec{x}/dt[/tex] and add it to the square of the rate that your clock is ticking relative to the time coordinate in that frame ([tex]d\tau / dt[/tex], what Greene calls your "speed through time"), multiplied by the speed of light squared, the sum of these terms is always equal to the speed of light squared, i.e. [tex](d\vec{x}/dt)^2 + c^2(d\tau/dt)^2 = c^2[/tex]. Greene uses the shorthand "your speed through spacetime is always c" to describe this fact, though like I said I think this has the potential to create some conceptual confusion.
dennis83704 said:
My question is this: If an object were made to travel in a direction opposite to our direction of motion , would that object not then be traveling through space at a slower speed? Wouldn't time pass faster for that object as it would be moving slower through space?
If we are using an inertial frame where your speed is nonzero, then an object moving at a lower speed in this frame (or at rest in this frame) will have its clock tick more quickly than your clock, relative to the time coordinate of this frame. But again it's all completely relative, you could analyze things from the point of view of the inertial frame where
you are at rest and then it would be
your clock ticking faster than the other clock.