Isn’t it the opposite - time slows down for you when you move at relativistic speeds, and hence you end up getting to alpha Centauri in 5years w.r.t clocks at Centauri or earth?
An object's relative speed to itself is always 0 (by definition) and so the passage of time is always constant for every object. As you can guess by the name of the theory there is also no "universal clock" or "0 speed" in the universe to compare against, it's only possible to measure speed and the flow of time relatively between objects.
For these reasons "time slows down for you when you move at relativistic speeds" is really a bad way to think of it (and not how the math of the theory actually works). It's much more proper to say things in the form "To <observer a> it appeared as if the clock of <observer b> was <sped up|slowed down>". E.g.:
To the traveler it appeared as if the clock of Alpha Centauri was sped up.
To Alpha Centauri it appeared as if the clock of the traveler was slowed down.
It's pretty confusing but essentially, as you travel faster, your clock slows down arbitrarily. In the most extreme case, at the speed of light, your clock stops. For a photon, it emerges and appears at its final location instantly, even if those distances are millions of lightyears apart.
So if you travel to Centauri from Earth, the fastest you get can get there is 5 years as seen from Earth but to the actual spaceship, it could perceive any arbitrarily small change in time.
zamadatix|6 years ago
For these reasons "time slows down for you when you move at relativistic speeds" is really a bad way to think of it (and not how the math of the theory actually works). It's much more proper to say things in the form "To <observer a> it appeared as if the clock of <observer b> was <sped up|slowed down>". E.g.:
To the traveler it appeared as if the clock of Alpha Centauri was sped up. To Alpha Centauri it appeared as if the clock of the traveler was slowed down.
dumbfoundded|6 years ago
So if you travel to Centauri from Earth, the fastest you get can get there is 5 years as seen from Earth but to the actual spaceship, it could perceive any arbitrarily small change in time.