Question

1. Is it possilbe for you to travel for enough and fast enough so that when you return home from a trip you are younger than your stay at home sister, who was born 5.0 yr after you?

2. Suppose you fly on a rocket with a speed of v=0.99c for 1 yr. according to the ship's clocks and calendars. How much time elapses on earth during your 1 year trip?

3. If you were 22 when you left home and your sister was 17, what are your ages when you return home?

Answer 1

a) Yes, that is possible because all clocks, including your biological clock which determines how fast you get old, slow down if you move fast enough close to the speed of light which is c = 3.0E+08m/s.
The relevant formula to be used is apparent time = proper time / [square root of (one - v*v/c*c)], where v is the speed of the moving object and proper time is the time measured by a clock moving with the object. Since c is the maximum speed possible (no object can move faster than light), v*v/c*c is less than one so that the apparent time is larger than the proper time.
b) Flying on a rocket with a speed of 0.99c for 1 y, according to the ship's clock and calendar, we find that v*v/c*c = (0.99)(0.99) = 0.9801 so that 1 - v*v/c*c = 0.0199 and square root (1 - v*v/c*c) = 0.1411. Therefore, one year of proper time gives an apparent time of 7.1 years. About 7 years elapses on earth during the one year trip inside the moving rocket.
c If you were 22y old when you left home, one year travel time inside the rocket makes you 23y old at the end of the trip while your 17y-old sister when you left will be (17y + 7y) = 24y old when you return.