Time Dilation v-v Space Travel I have read two different explanations of time dilation in the context of space travel.
Given:  round trip v-v Alpha Centauri, assumed distance 4.37 light years one way.  Speed of the space craft:  0.9999C
Explanation 1:        From the reference plane of the space ship, the trip would take 8.7409 years.    From the reference plane of the earth, the space ship would have been gone 618.0888 years.     That's the one I learned in college in the 1960's.
Explanation 2:       From the reference plane of the space ship, the trip would appear instantaneous.   From the reference plane of the earth, the space ship would have been gone for 8.7409 years.
The implications of these two approaches is obvious:   #1 pretty much eliminates space travel for humans.   #2 makes space travel trivial; easier even than in STNG.
I was only a physics major for 2 years.........I'm hoping we have some PhD's on the site who can give me the reality on this.   Thanks in advance for your info.
 A: Let's consider just the 'going' part of the trip. In the reference frame of the earth, the ship is travelling at some speed $v = 0.9999c$ and has to travel a distance $L = 4.37 \, \text{LightYear}$. This means that for us, standing on earth, the trip would of course take
$$
t_{earth} = \frac{L}{v} \simeq 4.37044 \, \text{Years} 
$$
just a bit above the time light would take.
On the ship's frame, however, Alpha centauri is moving towards the origin(the sip, in this case) at a speed of $0.9999c$, but only has to travel a distance $\frac{L}{\gamma}$ where $\gamma = \frac{1}{\sqrt{1-(v/c)^{2}}}$ is the Lorentz's factor. (I am using space contraction as a given here, but it is easiliy verified through Lorentz's transformation). This gives a time observed by the spaceship
$$
t_{ship} = \frac{L}{\gamma v} \simeq 0.062 \, \text{Years}
$$
If we ignore acceleration effects that happen when the ship mask a u-turn to get back, the time for the whole travel is
$$
2\cdot t_{earth} \simeq 8.7408 \, \text{Years} 
$$
according to citizens on earth and
$$
2 \cdot t_{ship}  \simeq 0.12 \, \text{Years}
$$
for those on the ship.
Yes, interstellar travel is 'easy' on the travellers.
