02-13-2017, 01:41 AM
(02-12-2017, 05:55 PM)Bear Wrote: Okay...
A wormhole gets created. Then a linelayer takes one end of it and accelerates to some relativistic velocity where it traverses substantially less time (and more space) than the end that got left behind. Let's say it arrives 50 light years distant having traversed ten years less time than the end that stayed home. Now Alice can enter the end that was left behind, and emerge 10 years "earlier" but 50 light years away. Causality is not broken because neither space-time location is within the other's light cone (ie, there's no way for Alice to send a signal from 50 light years away to arrive before she leaves, even if it's sent after her arrival which is ten years "before" she leaves.).
OK. OA wormholes/metric technology have limitations that would prevent this exact situation from coming up, but correct in principle.
(02-12-2017, 05:55 PM)Bear Wrote: But there's absolutely no way for Alice to get back to the first wormhole mouth without giving up that ten years. She can either give it up by traversing the wormhole in the opposite direction (and arrive ten years after leaving) or travel via flat space (more than ten light years) or traverse some other wormhole.
Actually no. This isn't how wormholes work. The two frames of reference are both equally valid and independent of each other. While they may be years, decades, or eons apart in time within their own frames of reference, the wormhole connects those two points in both space and time in both directions. The only time that Alice with 'lose' in transiting the wormhole (in either direction) is the time it takes her to cross the distance within the wormhole itself. OA wormholes have internal transits measured in hundreds of AUs (if you count the entire structure of the wormhole). But for sake of our thought experiment that distance could be no more than the distance through a standard household doorway (ala Stargate SG-1 more or less).
To put it another way, if Alice goes thru the WH to a point 50 light-years away in distance and 40yrs away in time (taking 1 second to make the transit), spends a week there and then comes back through the wormhole - she will not be away from Earth for 10years, 1 week, and 2 seconds. She will be away for 1 week and 2 seconds. The 10 year differential between the two mouths of the wormhole doesn't have any effect on transits through the wormhole in either direction.
Since the 'constraint' you mention doesn't apply, it won't apply to the rest of your example either.
While different wormhole mouths can have a fair bit of time differential between them, the arrangement of the wormholes (such as is done in the Nexus - a treelike branching acyclic graph) can minimize or avoid this issue, as can moving wormohole mouths at lower speeds to reduce time dilation.
Attempting to create a time machine, either by moving a distant WH mouth back toward its origin or by setting up a network of wormholes will result in the destruction of the gateways (least stable first) to prevent a CTC from forming.
Moving to OA itself - linelayers are largely limited to speeds where time dilation is not really very significant (around .74c or so) since Lorentz contraction will cause WHs to destablize at higher speeds. This works out to time dilation that is equal to the distance crossed (50 light-year trip takes 50yrs ship-time). While there is certainly some amount of differential between the mouths in this situation, it isn't very large. Note also that most line-layers can't start/stop instantly and so will take years or decades to speed up and slow down, further reducing the time dilation effect. And a lot of line-layers don't travel at the max possible speed.
Void-ship linelayers can start/stop instantly and travel arbitrarily close to the speed of light - but because their interiors are 'at rest' in their frame of reference, no time dilation occurs inside them (a 50 ly trip will take 50yrs no matter how close to c the ship gets) and so there is not time differential between the two mouths. Void-ship linelayers are extremely rare however.
Todd