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The Paradox of Relativity (Posted on 2006-05-24) Difficulty: 4 of 5
This is a classic thought experiment relating to the Special Theory of Relativity.

Two twins of the same age start on planet Earth. Twin A stays on Earth while twin B travels far, far away and back at near the speed of light.

Because of Special Relativity, A looks at B's clock, and it moves slower than his own. So at the end of B's journey, A is much older than B.

However, B's frame of reference is equally valid. According to B, A's clock is moving slower than his own. So at the end of the journey, B is older than A.

What faulty reasoning leads to this apparent contradiction?

  Submitted by Tristan    
Rating: 4.3333 (3 votes)
Solution: (Hide)
This thought experiment is most often called "The Twin Paradox."

The mistake lies in the fact that B actually changes his own frame of reference when he reverses direction, changing his velocity. There are not two but three separate frames of reference.

On the first half of B's journey, B would in fact see A's clock moving slower relative to his own. But if he were to "look" at his future self, he would see that his own clock is moving even slower than A's clock. Similarly, on the second half of his journey, if he "looked" at his past self, he would see it moving even slower than A's clock. At the end of the journey, A would be older than B.

Some people say that this paradox requires taking into account General Relativity, because acceleration is involved. However, perhaps twin B, rather than turning around, crossed the path of twin C, who is the same age, and going in the opposite direction. Even though there is no acceleration in this alternative situation, the results should be the same.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2019-07-26 15:11:40
Solutionre(2): Some thoughtsKen Haley2006-05-29 02:02:31
re(2): Some thoughtsFederico Kereki2006-05-28 20:37:50
re: Some thoughtsTristan2006-05-26 16:37:07
The TwinsGina Ernyey2006-05-26 13:15:59
Some Thoughtsre(3): Some thoughtstomarken2006-05-24 19:28:13
re(2): Some thoughtsSir Percivale2006-05-24 19:05:13
Solutionre: Some thoughtse.g.2006-05-24 17:41:12
How I understand it...Eric2006-05-24 17:25:58
SolutionSome thoughtstomarken2006-05-24 17:15:40
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