If we could travel at 99.9% the speed of light, it would take 4 years to get to Alpha Centauri. Would the people on the spaceship feel like they were stuck on board for 4 years or would it feel shorter for them?
The time dilation factor is (1 – f2 )0.5 , where f is the fraction of light speed.
(This means that the
experienced travel time time that passes inside the ship approaches 0 as f approaches 1. If you could travel arbitrarily close to light speed, you would experience the journey as effectively instantaneous.)
Here’s a calculator for it: http://www.emc2-explained.info/Dilation-Calc/
At .999c (99.9% light speed) it calculates that time is slowed down to 4.47% of the outside value. That means four years are experienced as approximately 65 days.
When they would reach Αlpha Centauri and send back signals, it would take 4 years to reach us, then it would take 4 years for our responding signals to reach them. To those individuals at Alpha Centauri, they experience the full 4 year delay the same as us, since they are no longer moving at a speed near the speed of light. The intense time dilation only occurs when moving at such speed. So, in fact, if you are moving at the speed of light, as per a photon, time doesn’t just slow down, it stops moving altogether. Photons experience literally no time passage from the moment they are produced to the moment they are absorbed.
Those travelling at 99% the speed of light would have only aged 0.17 years opposed to those on Earth, who would have aged 4 years in the same amount of time. That’s because the literal spacetime surrounding the space-travellers gets warped, almost like a stretched piece of fabric, literally making the rate that time passes (not just their perception of time) change for them.
If they return to Earth, you’re totally right, their lifespan would indeed have an extra 7-ish years relative to Earth-time, but to them, it would just be a normal lifespan since they only experienced 0.34 years on their travel there and their travel back.