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I did a search for "crackpot physics" and found https://www.physicsforums.com/showthread.php?t=111647 and then this forum.

A friend of mine found some strange twins paradox on the net but he can't remember where.

Neither of us can figure out the solution, but it must be crackpot.

So, here is the strange twins paradox.

1) Assume T1 and T2 are in the same frame.

2) T2 instantly acquires some v.

3) Both remain in relative motion for some time t in the T1 frame.

4) After t elapses in the T1 frame, T1 also acquires the same v.

5) Both twins think each are time dilated. So, they conduct Einstein's clock synchronization method to compare their clocks.

6) After they compare, they have exact time values from the comparison. So, either t1<t2, t2 >t1 or t1=t2. Since these are actual time values, they are real numbers and must obey the law of trichotomy.

7) Yet, relativity says t2>t1 and t2<t1.

8) This violates the law of trichotomy of real numbers.

This must be wrong because relativity is always right.

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# Strange Twins Paradox

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