Wormhole Causality

[Butters]

I have a speculative idea about wormholes. Let's say that a person (or anything for that matter) was able to pass through one, traveling through space, but also through time. If the wormhole mouths were close together, this would obviously cause some problems in terms of causality. If they were on either side of a regular sized room, then it would be possible for the person to emerge in the very recent past and stop themselves from entering the wormhole in the first place, creating a paradox. I believe this is one reason that some theorists believe time travel is not possible.

 

But if the only reason for discounting time travel (specifically for a wormhole in terms of this post) is the possible disruption of causality, then I have another suggestion. What if there was a fixed relationship between the distance in space between two wormhole mouths and the amount of time shift that occurs from the POV of an observer traveling through it?

 

First, we accept that the speed of light is the speed limit of the universe. Let's say the time shift of our example wormhole was ten years into the past relative to the wormhole entrance. Then the distance between our two wormhole mouths in space must be at least slightly more than ten light years. Call it a law of nature, as yet unproven, that for that amount of time shift it is physically impossible for them to be closer in space.

 

No information from the future could be used to alter the past, because even if you sent a message it would arrive just after the event had occurred. It is conceivable that you could bring back technology but this still doesn't mean you've created a paradox as far as I can see. Then you're just however many light years from anywhere with future technology. Also, observing events through a telescope, no matter how powerful, has the same speed of light restriction on whatever observations you make.

 

So in short, my idea is that there is a direct correlation between distance in space and time shift of wormholes that allows time travel, but protects causality.

 

Please feel free to tell me what logic jumps I may have made and why this wouldn't be the case. Or link me to somebody who has hypothesised this already.

[Nigel]

It turns out that you are correct. There is a relationship between the separation of wormhole mouths and the maximum paradox-free time jump.

 

To avoid paradoxes, the exit mouth cannot be in the "past light cone" of the entrance mouth.

 

In other words, if you want the paradox-free time jump to be T years, the spatial separation between exit mouth and the entrance mouth must be greater than the distance that light can travel in T years.

 

However, according to the book I'm getting this from, that sort of time travel would not be considered "true" time travel. The reason is that there exist observers (moving at a particular velocity) for which your backward paradox-free time jump appears to be a forward time jump.

 

The only sort of time jumps for which there are no such observers are the paradox-generating jumps into your own past-light cone.

 

Source: The Physics of Stargates -- Parallel Universes, Time Travel and the Enigma of Wormhole Physics, by Enrico Rodrigo (Eridanus Press, New York 2010) p. 284

[Butters]

Interesting. I have been trying to come up with ways to trick it, but so far I cannot. It does of course mean that information can appear to travel faster than light, for example. If I was to enter the wormhole, see a star go supernova, and then return and tell astronomers to watch out in five years then they know something they should not. But of course, it's an illusion as I have not actually travelled faster than light, I have simply taken a shortcut through space at less than the speed of light. Still, even then, causality is preserved.