Re: Variation of Twins Problem

From: Sylvain Croussette (NO_SPAM_sylvaincroussette_at_yahoo.ca)
Date: 08/18/04 

Date: Wed, 18 Aug 2004 18:30:17 -0400

seppala51@sbcglobal.net dixit:

>Can anyone please explain the following twins (clock) problem. There
>are two parts to this problem.
>
>Two identical twins (clocks) are traveling toward each other in
>identical spacecrafts along the x-axis. Their relative velocity is
>V=0.866c. When they meet at x=0, they verify they are indeed
>identical and the same age. They set both of their clocks to zero at
>this meeting point. They also press a deceleration button on each of
>their respecitve spacecrafts which causes their crafts to change
>velocity. When the deceleration ends, their relative velocity is V=0.
> Here's what I don't understand. When they meet, both twins are the
>same age and the clocks are set to zero, and when they have zero
>relative velocity both twins are the same age and both of their clocks
>show the same time (and are now running at the same rate). If the
>clocks start at zero, and then show the same time when they have zero
>relative velocity, doesn't that imply that the clocks ran at the same
>rate when they had relative motion? If spacecraft A observers say

I think the above is where there is an error in your reasoning.

As the twins move away while decelerating each thinks the other's
clock is ticking slower than his own. Ok so far. But when they reach
relative v=0, their clocks are not synchronized anymore. It's true
that the clocks will tick at the same rate from now on, but they won't
show the same time has passed since synchronization , both twin will
see the other's clock as having counted fewer ticks than his own
clock. So they don't see each other as having the same age. So the
comparison of ages is meaningless. It's only if they were reunited at
the same event that they could compare ages, but that's the usual
paradox.

But I'm not an expert, so maybe I'm wrong here.

>that craft B's clock ran at a slower rate during some part of the
>deceleration, then during some part of the deceleration craft's B
>clock must have run a faster rate also otherwise they would not show
>the same time when they have zero relative velocity. Observers in
>craft A cannot say that craft B stopped decelerating before craft A
>stopped and they cannot say that craft B stopped decelerating as each
>of these can be experimentally shown to be false. Please explain how
>this is resolved with Einstein's notion of time.

Quantcast