"PD" <TheDraperFamily@gmail.com> wrote in message
news:1149168315.005684.230870@i40g2000cwc.googlegroups.com...

> Koobee Wublee wrote:
>> Consider two identical spaceships with a pair of twins (what a
>> surprise) face to face originailly.  They propose an identical plan
>> which each promises to execute with due dilligence.  The plan is to
>> apply a certain power to his spaceship in the exact opposite direction
>> of the other for a predetermined amount of time.  Then, the power is
>> cut off.  After another predetermined amount of time, the power is
>> applied in the other direction.  Then, power off.  Then, power again in
>> the origninal direction.  So, after sometime far in the future, the
>> twins reunite again face to face.  Now, in the scenario, you cannot
>> cheat (as Einstein did his swindle to the world) with GR because both
>> twins go through the same acceleartion.  Please note there is a large
>> period of time the twins are just flying apart or coming back together
>> without any acceleration.  What would then each twin report his own
>> passage of time relative to the other?
>
> [...]
>
>> dt' = (dt - v dx / c^2) / sqrt(1 - v^2 / c^2)
>> dt = (dt' + v dx' / c^2) / sqrt(1 - v^2 / c^2)
>>
>> With dx = 0, dx' = 0, we have
>>
>> dt' = dt / sqrt(1 - v^2 / c^2)
>> dt = dt' / sqrt(1 - v^2 / c^2)
>
> No, but you seem to be misapplying this one. This compares the dt in
> one inertial frame to the dt' measured in another (single) inertial
> frame. Now, for the spaceship-bound twin, what single inertial frame
> exhibits dx' = 0?

Have you not read and understood the thought experiment I came up with?
 There is no earthbound twin.  The event experienced by both twins are
exactly identical.

Lorentz Transform is a tale of 3 points.  One (Point Primed) uses
coordinate dt', dx'; one (Point Unprimed) uses dt, dx; the other one
(Point Target) is observed by both observers.  dt' is the incremental
elapsed tiime of the event taking place by Point Target as observed by
Point Primed using Point Unprimed's measurement system.  In our case,
the Target is each of the twin himself.  Thus, dx = dx' = 0.  Again,
both twins are identical and undergo identical events.  The only thing
different is v which is (- v) from the other one's point of view.
Since the only other parameter that affects the incremental elapsed
time is the gamma factor (1 / sqrt(1 - v^2 / c^2)), from each twin's
point of view the gamma factor is identical due to (v^2).  The overall
elapsed time is just the integration of time of the other twin's.
Since both twins start out and end face to face, the boundary of the
integral is well defined.