Wormhole and relative motion

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Consider a wormhole. Suppose its two mouths have no relative motion with each other.

Therefore no time difference exists across its ends. It provides a mean to travel faster

than "light in normal space". Imagine this wormhole to be at rest in frame "S"

(say). If there is another frame "W"(say) in relative motion (much closer to the speed of

light) w.r.t. frame "S". An observer in frame "W" will view the wormhole (rest in frame "S")

as a time tunnel. Therefore accelerating another end of wormhole is not the only way to

convert a wormhole to a time tunnel. Uniform Relative motion is just enough to create

such a scenario.
 

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  • #2
pervect
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It depends on what you mean by time travel. Usually people mean closed timelike curves exist, and this won't happen in your example. If there are no closed timelike curves in S, there will be no closed timelike curves in S'.
 
  • #3
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Consider a wormhole. Suppose its two mouths have no relative motion with

each other. Therefore no time difference exists across its ends. It provides a

mean to travel faster than "light in normal space". Imagine this wormhole to be

at rest in frame "S"(say). If there is another frame "W"(say) in relative motion

(much closer to the speed of light) w.r.t. frame "S". An observer in frame "W"

will view the wormhole (rest in frame "S") as a time tunnel. If there is a similar

wormhole, of equal or greater length in frame "W", then at a certain relative

velocity a closed time loop does form. This is called a "Roman ring".
 
  • #4
George Jones
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According to Matt Visser, a Roman ring is a configuration of *several* wormholes such that the whole configuration is a time machine, but such that no pair of mouths for a single wormhole is a time machine.

As in your example, in all frames, there is a spacelike identification between mouths of each individual wormhole, so each individual wormhole is not a time machine. In order for a single wormhole to be a time machine, the identification between mouths has to be timelike. See the second link I give in post #3 of this thread.
 
  • #5
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Roman ring

So the configuration outlined above does form a time machine. i.e. Whenever

two wormholes of equal length are in uniform relative motion (close to speed

of light)and are sufficiently close to each other, such a configuration will form

a closed time loop. A signal starting from any mouth of wormhole can easily

loop back to a time long before it was sent.
 
  • #6
George Jones
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Yes, it's possible two create a time machine with two wormholes that all have mouths moving inertially, but in your previous two posts you said explicitly that it could be done with only one wormhole that had mouths moving inertially.
 
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You are correct, only the configuration consisting of two wormholes having uniform relative motion with each other and sufficiently close, can form a time machine. This example clearly shows how much problematic is the idea of wormholes with relationship to causality.
 
  • #8
George Jones
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This example clearly shows how much problematic is the idea of wormholes with relationship to causality.
How does one deal with the paradoxes associated with time travel? Matt Visser has written interesting stuff about this. He talks about four possibilies:

1. Radically rerwite physics from the ground up;

2. Permit time travel, but also invoke consistency constraints;

3. Quantum physics intervenes to prevent time travel;

4. the Boring Physics Conjecture, where we assume (until forced not) that our particular universe is globally hyperbolic, and thus doesn't have closed timelike curves.

In the past 4. was often assumed, but since global hyperbolicity is a very strong global condition and Einstein's equations are (local) differential equations, many physicists have moved to 2. and 3. Stephen Hawking likes 3., for example, and has formulated the Chronology Protection Conjecture, "It seems that there is a Chronology Protection Agency wich prevents the appearance of closed timelike curves and so makes the universe safe for historians."

This roughly states that near a chronology horizon (horizon at which spacetime becomes causally ill-behaved), expectation values of stress-energy tensors for quantum fields blow up, thus preventing (by wall-of-fire barriers) physical objects from crossing chronology horizons. There seems to be some semi-classical evidence for this conjecture, but a more refined analysis by Kay, Radzikowski, and Wald muddies the picture a bit. Their analysis shows that the semi-classical stress-energy tensor is ill-defined, but not necessarily infinite, at a chronology horizon.

This may be just an indication that the semi-classical theory breaks down at chronology horizons, and that full quantum gravity is needed for definitive predictions.
 
  • #9
Ich
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Isn't it enough to assume that suitable energy condition holds?
 
  • #10
is mathematical equation always correct
 
  • #11
pervect
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Isn't it enough to assume that suitable energy condition holds?
It appears to be difficult to do this, though.

From http://www.mcs.vuw.ac.nz/~visser/research.shtml (this may be slightly outdated as the webpage warns)

visser said:
In the interface region between quantum field theory and general relativity I (ed: Visser, not me!) have been heavily involved in trying to get a deeper understanding of the energy conditions and the extent to which they should be trusted. (Not only do one-loop quantum effects violate all the energy conditions, but even certain quite seemingly sensible looking classical systems violate all the energy conditions.) The implications are potentially disturbing.
The usual example of the problem of believing that the energy conditions always hold is the Casimir effect. Other examples include the space-time outside but near the event horizon of a black hole. If it didn't have negative energy density, hawking radiation would be impossible. We don't have any experimental confirmation of Hawking radiation, of course, but we do have experimental confirmation of the Casimir force.

I'm not sure what Visser means by "sensible looking classsical systems" violating the energy condition, though.
 
  • #12
George Jones
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Ich said:
Isn't it enough to assume that suitable energy condition holds?
As far as I know, any traversable wormhole violates at least one of the energy conditions.

I'm not sure what Visser means by "sensible looking classsical systems" violating the energy condition, though.
He means classical scalar fields.

According to Barcelo and Visser's Twilight for the energy conditions?, the trace energy condition is forgotten, the null, weak, and dominant energy conditions are all moribund, and the strong energy condition is dead.
 
  • #13
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I believe (3) may hold in the end. i.e. A correct theory of Quantum Gravity may prevent a wormhole to become traversable in the first place. If there is no travel possible through wormhole, no space like intervals appear in any frame of reference thus effectively excluding the possibility of closed time like curves.
 
  • #14
Ich
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George Jones said:
As far as I know, any traversable wormhole violates at least one of the energy conditions.
pervect said:
It appears to be difficult to do this, though.
Ok, I'm not able to contribute much. I have read that negative energy in all known forms seems to be unable to produce time travel possibilities. My guess is that this will hold in a TOE, too. Some cool equation will appear there to prove it.
 

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