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Old 2013-10-08, 19:41   #1
davar55
 
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Default 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?
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Old 2013-10-08, 20:54   #2
kladner
 
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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.
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Old 2013-10-08, 21:13   #3
chalsall
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Quote:
Originally Posted by davar55 View Post
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.)
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Old 2013-10-09, 18:59   #4
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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.
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Old 2013-10-09, 19:05   #5
chalsall
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Quote:
Originally Posted by davar55 View Post
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?
You have read Einstein? Newton?
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Old 2013-10-09, 19:36   #6
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Quote:
Originally Posted by chalsall View Post
You have read Einstein? Newton?
total velocity = total displacement / time

in a round trip, total velocity is zero
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Old 2013-10-09, 19:56   #7
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Quote:
Originally Posted by davar55 View Post
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....
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Old 2013-10-09, 20:00   #8
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Quote:
Originally Posted by chalsall View Post
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.
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Old 2013-10-09, 20:10   #9
chalsall
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Quote:
Originally Posted by davar55 View Post
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....
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Old 2013-10-09, 20:19   #10
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Quote:
Originally Posted by chalsall View Post
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 ...
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Old 2013-10-09, 20:25   #11
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Quote:
Originally Posted by davar55 View Post
Or tensor ...
Please explain a tensor.
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