I've already talked about that one futher up the page
, though I didn't talk about simultaneity of relativity up there...
Talking about it again, with a different focus... also, we won't look at the rocket accelerating or decelerating... just say it's been going at 0.98c forever, happens to pass Earth, we synchronise clocks, and then it happens to pass Alpha Centauri and then keeps going.
If a rocket travels from here to Alpha Centauri at 0.98c. To us, it looks like it takes about 4 years (I'll call it exactly 4 years, to make the description nicer). However, we see the clock on the spaceship running slow, and it only measures the time as about 9 and a half months (again, to simplify the explanation, I'll just call it 9 months, since the actual value doesn't matter). So according to us, "launch time plus 4 Earth-years", an event that happens on Earth, is simultaneous to "launch time plus 9 rocket-months", an event that happens on Alpha Centauri, is simultaneous to "the rocket arrives", an event that happens on Alpha Centauri.
In the rocket's frame, the universe is moving at 0.98c, and thus has length contraction... the distance to the star is measured as only 9 light-months. So, conveniently, it'll take us about 9 months to arrive. But we'll see the clock on Earth running slowly, by symmetry... according to us, when we arrive, 9 months later, only 2 months has passed on Earth. So, in the rocket frame, "launch time plus 2 Earth-months", on Earth, is simultaneous to "launch time plus 9 rocket-months", on Alpha Centauri, is simultaneous to "the rocket arrives", on Alpha Centauri.
So we both agree that the two latter events happen at the same time... since they happen at the same time and
at the same place, all observers will agree. But the time on Earth, we disagree on. Because we're talking about what's happening at the same time but in a different place
. And that is relative
. Neither the rocket's, nor Earth's, opinion about what events are simultaneous are wrong, and neither are absolute.