20131008, 19:41  #1 
May 2004
New York City
4227_{10} Posts 
Relativistic Twins
Two guys, identical twins, decide to challenge Einstein.
On their twentyfifth birthday, one arranges to stay home for ten years, The other goes from their home to a spacepad, boards a spaceship, and takes a trip that starts with a quick acceleration to near c (say 0.999c), a steady straight run, then a turnaround and return trip back to their home planet, landing, and a walk home. The paradox is that while homebound guy's clocks have progressed ten years, fly guy's have progressed much less (according to relativity), hence fly guy has apparently aged less. There have been tests of this paradox, in planes traveling fast and resulting clocks being a little slowed. But the differences are slight, not as in the above example. How would you explain the apparent paradox? Isn't acceleration more important than simply the high (near c) velocity? 
20131008, 20:54  #2 
"Kieren"
Jul 2011
In My Own Galaxy!
9850_{10} Posts 
This is the premise of the Heinlein juvie novel Time for the Stars.
I am not sure what effect acceleration is supposed to have which compares with relativistic speed. Of course, getting to even a small fraction of C quickly would involve lethal acceleration, so flyguy would not age at all, unless one postulates some disconnect between acceleration and apparent gravity on the passenger. On the other hand, even prolonged 1 G acceleration, which would get you going very fast pretty quickly, supposes technology currently beyond our means. I have not done the calculation of how long it would take to reach a significant fraction of C at 9.81 m/sec^{2}. So let us leave aside the "how" part, including how a vessel and its contents would withstand the high energy bombardment which would be experienced at such velocities. You have pointed out that airplane experiments have shown small relativistic effects. GPS satellites do an even better job, but they are still terribly slow, so the effect is small. Why should we suppose that the formulae should fail at higher velocities? If they continue to apply, where is the paradox? This is not an "I'm My Own Grandpa" situation, as the arrow of time continues in the same direction. I do note that Heinlein's "flyguy" does return to Earth and marry his great grandniece, but that only raises questions of consanguinity, not paradox. 
20131008, 21:13  #3 
If I May
"Chris Halsall"
Sep 2002
Barbados
8994_{10} Posts 
There isn't actually any paradox. It is all an illusion...
If either of the two brothers had traveled backwards in time, on the other hand, then this would be a very different discussion..... Last fiddled with by chalsall on 20131008 at 21:44 Reason: Edit: I was advised to add the "illusion" part.... (Some might find it funny.) 
20131009, 18:59  #4 
May 2004
New York City
3·1,409 Posts 
It may not be a paradox in respect to relativity's axioms,
but if two friends aged at different rates simply because one traveled and the other didn't that's an apparent paradox. But isn't the traveled roundtrip of fly guy just a zerototalforce incident, since f=ma and a is a vector too? How can one explain the timing difference as a consequence of time dilation, which is a function of velocity, when the total velocity for the trip is zero? As I said, the acceleration is more important to consider in dissolving this paradox. 
20131009, 19:05  #5 
If I May
"Chris Halsall"
Sep 2002
Barbados
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20131009, 19:36  #6 
May 2004
New York City
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20131009, 19:56  #7 
If I May
"Chris Halsall"
Sep 2002
Barbados
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20131009, 20:00  #8 
May 2004
New York City
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20131009, 20:10  #9 
If I May
"Chris Halsall"
Sep 2002
Barbados
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20131009, 20:19  #10 
May 2004
New York City
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20131009, 20:25  #11 
If I May
"Chris Halsall"
Sep 2002
Barbados
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