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 2013-10-08, 19:41 #1 davar55     May 2004 New York City 2·2,099 Posts Relativistic Twins Two guys, identical twins, decide to challenge Einstein. On their twenty-fifth 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 turn-around 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?
 2013-10-08, 20:54 #2 kladner     "Kieren" Jul 2011 In My Own Galaxy! 999610 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 fly-guy 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/sec2. 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 "fly-guy" does return to Earth and marry his great grand-niece, but that only raises questions of consanguinity, not paradox.
2013-10-08, 21:13   #3
chalsall
If I May

"Chris Halsall"
Sep 2002

2×4,643 Posts

Quote:
 Originally Posted by davar55 How would you explain the apparent paradox?
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 2013-10-08 at 21:44 Reason: Edit: I was advised to add the "illusion" part.... (Some might find it funny.)

 2013-10-09, 18:59 #4 davar55     May 2004 New York City 2×2,099 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 round-trip of fly guy just a zero-total-force 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.
2013-10-09, 19:05   #5
chalsall
If I May

"Chris Halsall"
Sep 2002

2·4,643 Posts

Quote:
 Originally Posted by davar55 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?

2013-10-09, 19:36   #6
davar55

May 2004
New York City

101468 Posts

Quote:
 Originally Posted by chalsall You have read Einstein? Newton?
total velocity = total displacement / time

in a round trip, total velocity is zero

2013-10-09, 19:56   #7
chalsall
If I May

"Chris Halsall"
Sep 2002

2×4,643 Posts

Quote:
 Originally Posted by davar55 total velocity = total displacement / time in a round trip, total velocity is zero
Incorrect.

In such cases Work == 0.

If Distance traveled was > 0, then Velocity (and thus Acceleration) must have been > 0 half the time.

Do please try to keep up....

2013-10-09, 20:00   #8
davar55

May 2004
New York City

2·2,099 Posts

Quote:
 Originally Posted by chalsall Incorrect. In such cases Work == 0. If Distance traveled was > 0, then Velocity (and thus Acceleration) must have been > 0 half the time. Do please try to keep up....
Sorry, you are in error.

Distance is a scalar. Displacement is a vector.

2013-10-09, 20:10   #9
chalsall
If I May

"Chris Halsall"
Sep 2002

2·4,643 Posts

Quote:
 Originally Posted by davar55 Distance is a scalar. Displacement is a vector.
It's so cute to watch, isn't it?

Those who think they understand the "big words" like scalar and vector.

But don't....

2013-10-09, 20:19   #10
davar55

May 2004
New York City

2×2,099 Posts

Quote:
 Originally Posted by chalsall It's so cute to watch, isn't it? Those who think they understand the "big words" like scalar and vector. But don't....
Or tensor ... or matrix ... or monoid ...

2013-10-09, 20:25   #11
chalsall
If I May

"Chris Halsall"
Sep 2002

2·4,643 Posts

Quote:
 Originally Posted by davar55 Or tensor ...

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