#8
January 1st 13, 11:35 PM posted to sci.physics.relativity,sci.physics,sci.astro,sci.math
 Koobee Wublee external usenet poster Posts: 815
What is or is not a paradox?

On Jan 1, 11:46 am, Tom Roberts wrote:

OK, consider the case in which "home" is at rest in an inertial frame; one twin
stays at home in a centrifuge, spinning at a few tens of meters per second with
a proper acceleration of 1g; the other twin blasts off in a rocket accelerating
at 1g for a year on his clock, turns around with a maneuver that maintains the
1g acceleration, and returns home executing another maneuver that beings him to
rest at home (the trip takes 4 years on the rocket twin's clock: 1y speed up
headed out, 1y slow down, 1y speed up headed back, 1y slow down, stop). The
rocket twin is unequivocally younger when they meet again, because his average
speed relative to the inertial frame of home is much greater than that of the
centrifuge twin, even though their proper accelerations are equal.

Just as Koobee Wublee has predicted:

** Divine visions of showing no paradox to
** Euphoria of rejoicing no paradox to
** Careful examination of these divine visions to
** “what the fvck was I thinking?” rude awakening to
** Desperation once again and the cycle repeats.

shrug

The divine visions a

1) Acceleration breaking the symmetry by Born
2) Spacetime time diagram of a few lines
3) Mathemagic trick by paul andersen and others
4) Coordinate time as projection of proper time

The last time, Tom was in 4) so happy with the projection thing.
Apparently, he had gone through the rude awakening stage and more
desperation. Now, he is back to the first one. That is the life of a
self-styled physicist. Koobee Wublee thinks that is a fvcked up life
style, but what does Koobee Wublee know? Perhaps, Tom enjoys stuck in
these cycles chasing his own tail. shrug

Anyway, one can simply redesign the scenario to have both twins
traveling where each twin will experience the same acceleration
profile and thus nullifying the effect of acceleration. Given an
arbitrary amount of time to allow both twins coasting with null
acceleration but with a significant speed between them, the mutual
time dilation building up will obviously never be rectified. Thus,
showing the paradox is very real. shrug

Bottom line: here it is speed relative to the inertial frame of home that
matters, not acceleration. The actual computation involves integrating the
metric over the path followed by each twin between meetings, and comparing the
results; when written in terms of home's inertial coordinates, this integral
involves only speed, not acceleration, not position, and not direction.

Remember that in SR (no gravity) it simply is not possible for
two twins that both move inertially to separate and rejoin.

Tom, care to show some math to back up your babbling? shrug