Snickers said:
o what I was trying to convey is that if I were able to observe some time measurement somewhere else from where I am it would appear different. Know what I mean? IF time were stretched and I were able to able to observe that other clock in that other place it would appear to measure time differently than my clock.
Think about exactly what you're asking for when you speak of observing the other clock: You are making an observation that permits you to say something along the lines of "
At the same time that my wristwatch reads X the other clock reads Y". For example, if the remote clock is ten light-minutes away and at 3:10 PM you observe (really powerful telescope?) that it reads 2:30, you will conclude that the remote clock read 2:30 PM
at the same time that your clock read 3:00 - the remote clock was 30 minutes behind yours and then it took ten minutes for the light to get to you.
The key phrase here is "
at the same time". Observers who are in motion relative to one another will not agree about which spatially separated events happen at the same time; this is the relativity of simultaneity (google for "Einstein train simultaneity"), absolutely essential for understanding relativity.
We can compare how much time passed for two clocks that start together, separate and follow different paths through spacetime, then come back together because they're colocated when we compare them.
But anything you say about whether one clock is running slower than anpother when they're not colocated is going to depend on an "
at the same time" assertion. Your clock reads 3:00
at the same time that the remote clock reads 3:00; later,
at the same time that your clock reads 3:40, the remote clock reads 3:20; you will be tempted to say that the remote clock is running slow and measuring time differently from yours. But that's not what's going on. Instead, you're using a definition of
at the same time that makes it come out that way. In fact, if the two clocks are moving relative to one another, someone at rest relative to the remote clock will find that
at the same time the remote clock read 3:20 your clock read 3:10 so yours is the slow one. They're both right.