On 3/6/2014 9:01 AM, Jesse Mazer wrote:
On Thu, Mar 6, 2014 at 11:02 AM, Edgar L. Owen <edgaro...@att.net
<mailto:edgaro...@att.net>> wrote:
Liz,
Sure, but aren't the different lengths of world lines due only to
acceleration and
gravitational effects? So aren't you saying the same thing I was?
Isn't that correct my little Trollette? (Note I wouldn't have included this
except
in response to your own Troll obsession.)
Anyway let's please put our Troll references aside and give me an honest
scientific
answer for a change if you can... OK?
It would be nice to get an answer from Brent or Jesse as well if they care
to chime
in......
In the case of the traditional twin paradox where one accelerates between meetings while
the other does not, the one that accelerates always has the greater path length through
spacetime, so in this case they are logically equivalent. But you can have a case in SR
(no gravity) where two observers have identical accelerations (i.e. each acceleration
lasts the same interval of proper time and involves the same proper acceleration
throughout this interval), but because different proper times elapse *between* these
accelerations, they end up with worldlines with different path lengths between their
meetings (and thus different elapsed aging)...in an online discussion a while ago
someone drew a diagram of such a case that I saved on my website:
http://www.jessemazer.com/images/tripletparadox.jpg
In this example A and B have identical red acceleration phases, but A will have aged
less than B when they reunite (you can ignore the worldline of C, who is inertial and
naturally ages more than either of them).
Right. And you could also replace A's path with the broken line path formed by two clocks
passing one another in opposite directions and just handing off the time reading (as in
the diagram I posted earlier) so that there was no acceleration involved at all, yet the
path would still have less proper time elapse than B's.
Brent
You can also have cases in SR where twin A accelerates "more" than B (defined in terms
of the amount of proper time spent accelerating, or the value of the proper acceleration
experienced during this time, or both), but B has aged less than A when they reunite,
rather than vice versa. As always the correct aging is calculated by looking at the
overall path through spacetime in some coordinate system, and calculating its "length"
(proper time) with an equation that's analogous to the one you'd use to calculate the
spatial length of a path on a 2D plane.
Jesse
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