One of the pair of 25 year old twins take a round trip through space while the o

Question

One of the pair of 25 year old twins take a round trip through space while the other twin remains on Earth. The traveling twins move at a speed of 0.95c for a total of 39 years, according to Earth time. Assuming that special relativity applies for the entire trip. (neglect accelerations at the start, end, and turnaround)

Twins age when they return to earth?

On the round trip, how far did the traveling twin go according to the ttraveling twin?

on the round trip, how far did he go according to the earth twin?

which one is the proper length

This is the twin paradox. what is a resolution for this paradox?

Explanation / Answer

To travel for 39 years, we need to convert to seconds

39 years is 1.23 X 10^9 sec

Apply d = vt

d = (.95)(3 X 10^8)(1.23 X 10^9)

d = 3.51 X 10^17 m

Part A) - Trip distance according to traveling twin

L = L'(sqrt 1 - v^2/c^2)

L = (3.51 X 10^17)(sqrt (1 - .95^2)

L = 1.10 X 10^17 m

Part B)

According to the Eart Twin, the traveler when 3.51 X 10^17 m

Part C)

The 3.51 X 10^17 m is the porper length. Proper length is always based on stationary reference frame. In other words, from the stationary twins reference.

Part D)
The paradox is resolved by making sense in your mind that at relativistic speeds, time slows down and length contracts. Even though the twins may not understand, the traveling twin did indeed travel a smaller time then the stationary twin noticed. Both twins, in their respective reference frames are correct. Because the reference frames are different, you can not compare the two. If is mind boggling, but both twins are correct but can not be compared to each other through different reference frames when one is traveling near the speed of light. Remember, Newtonian Mechanics breaks down at relativistic Speeds and ideas we are used to, and take as fact, do not apply.

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