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
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.
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
.