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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?

See The Solution Submitted by Tristan    
Rating: 3.6667 (3 votes)

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Some Thoughts re(3): Some thoughts | Comment 5 of 10 |
(In reply to re(2): Some thoughts by Sir Percivale)

I don't know enough about this to provide very satisfactory answers, but here are my 2 cents anyway.

i) I don't think a resolution of the Twin Paradox requires General Relativity, although I think it provides a different and perhaps better explanation than Special Relativity.  However, Special Relativity can account for this apparent "paradox" all by itself.

ii) This is the tricky part.  It would seem that at all points the two twins are travelling symmetrically with respect to each other.  However, the actual act of acceleration changes the moving twin's reference frame.  The simplest way I remember to explain it is that the moving twin "feels" the acceleration.  It may appear that the twin on earth is accelerating in reference to the moving twin, but the twin on earth never actually experiences the sensation of acceleration, while the twin on the spaceship actually does.  It is at this point that the time dilation effects are noticed.

As a matter of fact, I think the time dilation that accounts for their different ages takes place very quickly.  For example, say twin A sits on earth while twin B travels away near the speed of light.  During this outward bound trip, the effects of time dilation won't seem that pronounced - however, when twin B accelerates the ship to turn around and return to earth, she would all of a sudden notice very rapid aging in twin A (if she could see her twin, of course).

In other words, say that twin A on earth ages ten more years than twin B in the ship - the instant that twin B is turning the ship around will account for most of those ten years of aging.  Before turning the ship around, twin A might only appear 1 year older to twin B, but immediately upon completing the turn and returning to earth, twin B would observe twin A to be 9 years older.  I just made up those numbers, of course, but I think that's the idea.

Any confirmation if I'm at all on the right track?

  Posted by tomarken on 2006-05-24 19:28:13

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