## What's your solution to the twin paradox?

According to Special Relativity, a moving clock runs slower, so a person in a high speed moving vehicle will grow older slower.

Suppose E(arth) and T(raveler) are twins on Earth. At the age of 20, T starts a space trip. When he returns to Earth 10 years later, T will be 30 and E will be much older, let's say 40. The reason is that the high speed motion makes time pass slower in the spaceship, thus T can be much younger than E.

But the conclusion can also be the reverse.

From the standpoint of T, E is in a high speed motion relative to him, thus the clock on Earth should run slower, and E should be much younger.

This is the twin paradox.

One clever solution to this paradox is that E's conclusion is right, because one of special relativity's conditions is a uniform motion. The spaceship needs acceleration and deceleration, thus T's conclusion is not right.

But this solution has a little problem. Just let T travel more and we will see.

Suppose T travels double the distance at the same speed. How old will E and T be?

Following the original thought, T will be 40 and E will be 60, because both of their clocks would have passed double amount of time.

But here is another thought, let's call it thought B.

T's new journey can be thought of as the old journey plus an extra journey in a uniform motion. For this extra part of the journey, E and T are in exactly the same kind of relative state, so their clocks should not add any difference during this part. This will give us a different result: T will always be 10 years younger than E, no matter how much longer he travels further.

Let's continue thought B in another direction. Instead of traveling longer, let T travel shorter this time, so that all the uniform motion part is cut out. Due to the same reason, this cut-out should not cause any time difference. T will still be 10 years younger than E, even if the acceleration and deceleration causes T only 10 hours!

So, the clever solution does not work.

You may have seen other solutions to this paradox. If in any such solution, you saw the Earth reference frame was treated as something special, you can safely ignore it. Because since the day it is removed from the center of the universe, the Earth is not special any more.

Someone explained this paradox using General Relativity. A conclusion based on Special Relativity has to be explained by General Relativity! That's wonderful imagination!