Suppose we want to send a spaceship to Alpha Centauri and calculate the minimum possible time it will take for us here on Earth to have the spaceship back. We are not interested in how fast the time will pass for the people in the spaceship, but rather how long it will take for us here on Earth to have the spaceship back. Increasing the speed of spaceship will decrease the time of the roundtrip journey as measured by us waiting on Earth, but after the spaceship passing a certain fraction of the speed of light time dilation will start to be relevant. Is there a minimum time possible time for the spaceship to do the roundtrip journey (again, using Earth as reference)? As the spaceship accelarates, at which point the time dilation added due to the incrase of speed starts to increase the total time of the journey measured on Earth?
Space Travel – Minimum Time to Send and Return a Spaceship to Alpha Centauri
observersreference framesrocket-sciencespace-travelspecial-relativity
Best Answer
Never. If the ship can accelerate, it will reduce the time measured on earth. There are diminishing returns, but it is never zero.
The limit of this process is exactly the time observed on earth by light to make the round trip. A massive object with no restrictions on its ability to accelerate can get arbitrarily close to that limit.