From: hinson@maxwell.physics.purdue.edu (Jason W. Hinson)
Newsgroups: rec.arts.startrek.tech
Subject: Re: Twin Paradox
Date: 19 Aug 92 14:39:39 GMT
Organization: Purdue University Physics Department

In article <XskqPB15w165w@west.darkside.com> max@west.darkside.com (Erik Max Francis) writes:
>tm@jyu.fi (Timo Mannikko) writes:
>
>> As I see it now, the difference between A and B is that B makes a turn.
>
>You have it, but you might say that "If he [B] just _moves_ away from 
>earth . . ." instead of that he accelerates.  The confusion with the twin 
>paradox is that it _cannot be explained_ by special relativity.  Special 
>relativity is a simplification of the Universe where things only travel 
>at constant (relative) velocities.  Since B is obviously accelerating 
>(quite powerfully!) to turn around and arrive back at A within some human 
>timeframe, we have acceleration and thus special relativity is invalid.  
>You have to look at accelerating frames of reference -- that is, general 
>relativity.

Actually, you can use integartion over the formulas in special relativity
in order to come out with what happens for accelerations.  General
relativity comes into play with gravitational fields.  There is a
difference between a gravitational field and a simple acceleration, because
no matter what mass creates a gravitational field, the acceleration felt
closer to the mass is stronger than that felt far away from the mass. on
an infintesimal level they are the same, but in the big picture gravity
creates a gradient --> a direction in which the acceleration felt becomes
larger.  General relativity deals with these warpings of space-time.

Another way of dealing with the twin paradox using special relativity
is to have 3 observers: 
   It would look like this:
   B passes A   |     C and B pass   | A and C pass
                |                    |
         -v<--C |      <--C          |-C
 A              | A                  | A
 B-->v          |         B-->       |              B-->

     Observer B (traveling at a constant velocity v with respec to 
observer A) passes observer A. At that point they synchronize swatches
(no mater what their velocities, two observers can always synchronize their
clocks the moment they are right next to one another).
     Now, abserver C is traveling from a far distance away at a velocity
-v w/r/t A (he is traveling at the same speed as B, but he is traveling
towards A)
     When B and C pass, C syncronizes his clock with B's.
Finally, A and C meet, and no matter which observer you start with, ALL
observers will find that C's clock has registered less time than A's clock 
(though the calculations can be tricky).


(Stuff Deleted  >>  Sorry, I don't know the history of the twin paradox)

>The situation used to illustrate the twin paradox can also be used to 
>explain some elements of general relativity.  For instance, according to 
>general relativity, a clock ticks slower in a stronger gravitational 
>field than in a weaker one.  This works out as follows:  B is present 
>accelerating at turnover, to turn around and return to A.  From his point 
>of view (in an accelerating frame of reference), B is moving at high 
>velocity with respect to him, and thus A's clock must be running faster 
>than B's.
>
>But according to the principal postulate of special relativity, there is 
>_fundamentally no way of discerning_ between acceleration due to thrust 
>and acceleration due to gravity.  Thus the Universe treats B's enormous 
>acceleration -- to turn around, applied by its engines -- as if it were 
>very near to a large mass; that is, in a high gravitational field.  Since 
>A is far away, A is in the weaker field.  Thus, clocks tick slower in 
>high gravitational fields than in low ones.
>
>There are similar arguments for other aspects of general relativity, such 
>as the bending of light rays in a gravitational field.  I'd be glad to 
>share them if anyone is interested.


These arguments are ok for a general understanding, but again there is 
a difference between a gravitational field and an acceleration.

-Jay
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