You might find it helpful to have a read of chapter 7 of Benjamin Crowell's online textbook
Simple Nature. I always had a hard time understanding it too, but reading this when where it started to make sense for me.
http://www.lightandmatter.com/html_books/0sn/
dangerflow said:
Say for example nothing else exists in the universe except for two people "A" and "B" . Relative to themselves they are traveling at 0mph but to each other 10,000 kmps away from each other for many years. Would one experience time more slowly then the other and age differently? If so why?
If they always travel at the same velocity relative to each other, the situation is perfectly symmetrical. Each person will see the other's clock ticking slow compared to their own: A will see B's clock slow, B will see A's clock slow.
Say A moves away from B at a constant velocity of 10 000 km per second, about three hundredths of the speed of light in a vacuum--or we could just as well describe this situation as B moving away from A at the same speed in the other direction. When 10 years have past according to a spacetime coordinate system in which A is not moving, then in that coordinate system, 9 years and 363 days will have passed for B. Likewise, when 10 years have passed according to a spacetime coordinate system in which B is not moving, then in that coordinate system, 9 years and 363 days will have passed for A.
What do I mean by "for B" and "for A"? When, for example, A wants to measure how much time has passed on a clock carried by B over the course of 10 years, A needs some way of defining simultaneity: which events in the universe happen at the same time as each other. In other words, given an event at A's location, which event at B's location should A think of as happening at the same time as the first event? The natural way to decide which events are simultaneous is to make use of the constancy of the speed of light. If A sees two stars at the same distance explode simultaneously, A judges the explosions to have been simultaneous with each other. If A sees a star 100 light years away explode 100 years before a star that's 200 light years away, then A considers these two stars to have exploded simultaneously, and so on. This is the method A uses to compare readings on A's own clock with readings observed on B's clock. (A takes into account the time to takes for the image of B's clock to arrive; after 10 years, at this speed, they'll be about a third of a light year apart.)
Obviously if two events happen in the same place at the same time in one coordinate system, they must happen at the same time in all reasonable coordinate systems, or there'd be a contradiction. Weirdly though, events that happen far enough apart in space and close enough together in time, so that light leaving one event doesn't have time to reach the other event, can happen in a different order according to coordinate systems moving at different velocities. No contradictions arise because such events can't effect each other, since nothing can travel faster than light and even light can't travel fast enough to get from one event to the other. In other words, given some event, i.e. a point in spacetime, each coordinate system defines its own "now", its own set of events elsewhere in the universe which are happening at the same time as that event. But from the perspective of a coordinate system moving at some other velocity, a different set of events are simultaneous with that event. There's no natural (non-arbitrary) way of chosing one absolute present moment that everyone can agree on no matter where they are or what velocity they're traveling with.
The idea that even simultaneity is relative might seem even more confusing than relativity of time and spatial distance, but all three are necessary if the velocity of massive objects is relative and the speed of light the same for all observers, no matter what velocity they have relative to other observers. The easiest way to see how it all works out is to get stuck into the algebra. Read up on the basics and try out some examples. Spacetime diagrams--Minkowski diagrams are most widely used--are a good way to visualise it geometrically.
