Re: Unanswered S.R. Paradoxes
Re: Unanswered S.R. Paradoxes
Source: http://sci.tech−archive.net/Archive/sci.physics/2005−04/msg00187.html
• From: "Paul Cardinale"
• Date: 30 Mar 2005 14:36:22 −0800
mkolchins wrote:
[snip]
> QUESTION 1.
>
> Professor Wolfson used an example of an earth and star frame of
> reference at rest with respect to each other and a spaceship
> traveling at 0.8 "c" past an observer on earth toward the star
that
> was 10 light years from earth in the earth/ star frame of reference.
> In the lecture Professor Wolfson noted an observer on the space ship
> and on earth would both see themselves as stationary an the other as
> moving and therefore distance and time for the other would appear to
> be shorter and slower in both cases however this paradox could be
> explained away by the relativity of simultaneity, whereby a clock on
> the star that was synchronized with a clock on earth in their frame
> of reference would seem out of synchronization with the earth clock
> in the space ships frame of reference.
>
> I was wondering though what if the space ship passed by the observer
> on earth close enough so that both observers could hold up signs
> indicating to the other observer how far away the star was in their
> respective frames of reference. Assuming the spaceship observer held
> his sign up in a window and they could both find a way to read the
> signs which observer would indicate the greater distance and which
> the lesser distance according to S.R.?
>
The Earthbound observer indicates the greater distance.
[snip]
> QUESTION 2.
>
> I am assuming that if the laws of physics are the same in all frames
> of reference that includes the predictive abilities of SR. If we take
> my original example of a spaceship passing an observer on earth at
Re: Unanswered S.R. Paradoxes 1
Re: Unanswered S.R. Paradoxes
0.8
> c relative to the earth frame of reference the earth observer will
> predict that the spaceship observer will view the star to be closer
> than he observes it to be
OK.
> but because the spaceship observer views
> his frame of reference to be at rest and the earth to be moving he
> will predict that the earth observer will view the star to be closer
> than he observes it to be.
No, that is not what SR predicts. That is the 'comic−book'
interpretation of SR.
[snip]
> Are the predictive powers of
> SR right in both frames of reference?
Yes, it is right, but is does not agree with your misinterpretation of
SR.
>
> QUESTION 3
>
> If we consider the traditional twin paradox whereby one of two twins
> on earth takes off in a spaceship journeys to a nearby star turns
> around and comes back to earth, according to S.R. the fact that the
> twin who flew in the spaceship experienced accelerated motion when it
> turned around means it broke the symmetry of each twin thinking he
was
> at rest and the other was moving and this is how he becomes the
> younger twin upon arrival back on earth.
>
> I was wondering though what if just before the twin who flew to the
> star was due to arrive back on earth the twin on earth took off in
> another spaceship, orbited the earth a few times, rendevued with his
> brothers ship and they both landed back on earth at the same time.
> Who is older and who is younger?
Same as before the orbiting: the Earthbound twin is older.
> The purpose of the question is to
> inquire about what happens when both twins experience accelerated
> motion prior to re−uniting.
The relationship between acceleration and aging is rather like the
relationship between turning the steering wheel on your car, and the
distance traveled: how much effect it has depends upon other factors.
Re: Unanswered S.R. Paradoxes 2
Re: Unanswered S.R. Paradoxes
> Another versions of this could include
> the twin on earth flying a spaceship in accelerated motion at the
> same time his twin in turning around.
See above.
> One last version I thought of
> involves the observer in the spaceship and the earth observer from my
> first two questions. What if the spaceship turns around at the star
> comes back past earth however shortly before he does the earth
> observer takes off in another spaceship accelerates up to the same
> speed as the first ship such that they meet each other and join
> together. When the two observers compare the time elapsed since they
> passed each the first time who will have experienced greater time
> lapse?
>
Same as before: the Earthbound twin is older.
In any case, the amount of elapsed proper time on a clock is equal to
the integral of the spacetime interval along the path. That value is
the same in all frames of reference.
Paul Cardinale
.
• References:
♦ Unanswered S.R. Paradoxes
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