Can Wormholes Enable Time Travel Without Space Displacement?

[Starlover]

Hello, All!

Could a wormhole take us to a different time, but the same place? (Meaning, is it possible for the two mouths of a wormhole to be separated only by time, and not by (significant) space?

Thank you very much!

 

[Lamdbaenergy]

Maybe, but a person needs to know how to keep the thing opened in the first place; I'm not too sure how one'll be able to manipulate where a wormhole will take you in time and or space—probably never going to bring you into the past, but more likely into the future, I'd say.
As for traveling through space, that's much more probable.

 

[Matterwave]

It's very hard in General Relativity to try to specify "the same place", and care must be taken whenever you try to invoke this concept. What constitutes "the same place" is different to different people. So what do you mean by "the same place"?

 

[DrStupid]

So what do you mean by "the same place"?

I think he means a wormhole with a time-like distance between its ends. In that case there would be frames of reference where they are at the same place at different times.

 

[Matterwave]

I think he means a wormhole with a time-like distance between its ends. In that case there would be frames of reference where they are at the same place at different times.

If a wormhole is to be traversible, it must mean that the two ends are connected by time-like curves...so wouldn't that be every (traversible) wormhole?

EDIT: added word

 

[WannabeNewton]

Could a wormhole take us to a different time, but the same place?

Did you mean to say "the same time"? If so then yes. See Morris et al (1988). The conclusion of the paper is that if one has a traversible wormhole wherein one mouth is moving with respect to the other then closed timelike curves form in the wormhole. If not then it would seem the question is trivial as matterwave pointed out.

 

[DrStupid]

If a wormhole is to be traversible, it must mean that the two ends are connected by time-like curves

Both outside and inside?

 

[stevebd1]

Could a wormhole take us to a different time, but the same place? (Meaning, is it possible for the two mouths of a wormhole to be separated only by time, and not by (significant) space?

You might want to take a look at a popular science book called Black Holes, Wormholes and Time Machines by Jim Al-Khalili which looks at this sort of thing.

These two articles also look at the possibility of wormholes as time machines-
Time Travel and Wormholes: Physicist Kip Thorne's Wildest Theories
http://web.mit.edu/asf/www/Wilfred_Wormhole/wormhole.pdf

Taken from the first link-

When Thorne began to consider the likelihood that wormholes could be used for space travel, he realized that they could also be used for time travel.

In his 1994 book "Black Holes and Time Warps" (W.W. Norton & Co. 1994), Thorne proposes a thought experiment: Say he obtains a small wormhole, which connects two points in space as if they were not separated by any distance at all.

Thorne takes his wormhole and puts one end in his living room, and the other aboard a spaceship parked in his front yard. Thorne's wife, Carolee, hops aboard the spaceship to prepare for a trip. The two don't have to say goodbye, though, because no matter how far away Coralee travels, they can see each other through the wormhole. They can even hold hands, as if through an open doorway.

Carolee starts up the spaceship, heads into space and travels for six hours at the speed of light. She then turns around and comes back home traveling at the same speed — a round trip of 12 hours. Thorne watches through the wormhole and sees this trip occur. He sees Coralee return from her trip, land on the front lawn, get out of the spaceship and head into the house.

But when Thorne looks out the window in his own world, his front lawn is empty. Coralee has not returned. Because she traveled at the speed of light, time slowed down for her: What was 12 hours for her was 10 years for Thorne back on Earth.

Now, as Thorne and Coralee hold hands through the wormhole, they are each traveling in time. Coralee has landed on Earth 10 years after she left, and there she will meet Thorne, 10 years older. But she can still reach through the wormhole and find Thorne, who is only 12 hours older. Thorne can step through the wormhole and find himself 10 years in the future, or his future self can step back 10 years into the past.

 

[Matterwave]

Both outside and inside?

So you want to rephrase the OP question to "Is it possible for 1 mouth of the wormhole to be in the chronological future of the other mouth of the wormhole, where causal structure is determined in the absence of the wormhole?" I think this is possible. I'm not sure how rigorous you could make this statement, but at face value, I don't see why not.

But of course, if you modify it this way, I doubt you are staying within the spirit of the OP. There are time-like curves from here to Andromeda...or to a distant quasar. After all, I would simply have to send a particle there to prove there is a time-like curve connecting these objects' world tubes to the Earth's world tube. I don't know if the OP would consider here and Andromeda to be "the same place" that he means in his question.

 

[DrStupid]

I don't know if the OP would consider here and Andromeda to be "the same place" that he means in his question.

He just need to chose an appropriate frame of reference.

 

[PeroK]

I think he means a wormhole with a time-like distance between its ends. In that case there would be frames of reference where they are at the same place at different times.

By that definition the Bakerloo line on the London underground is a wormhole.

 

[bcrowell]

By that definition the Bakerloo line on the London underground is a wormhole.

But if you ride the train from one station to another, your wristwatch is still synchronized with the clocks outside, and if you ride the train in the opposite direction you don't end up in the past.

If there's an external frame of reference where the two mouths are at rest at the same place, at different times, then at some point the past mouth is either going to have to disappear or else it's going to be present at the creation of the future mouth.

 

[pervect]

My $.02

While the OP didn't specify a frame of reference or a coordinate system, there's an obvious choice to specify for him - cosmological coordinates, in which objects moving with the Hubble flow are said to be "in the same place". So let's just make that an explicit assumption in order to answer the question.

Going back to the original question - I don't think it makes sense to allow the two mouths of the wormhole to be in the same place at the same time (here I mean cosmological time), but it's certainly possible for the two different mouths to be in the same place at different times.

We also have to consider the connection between the mouths. The connection between the mouths can be in general different from a path through cosmological time, and while the connection through the interior path will be timelike, the connection through the exterior path may be spacelike or timelike in general. I see no reason why the connection cannot be such that you enter one of the mouths, and exit the other mouth at the same place at a different time, as long as you ensure that the two mouths are never at the same place at the same time on a cosmological space-time diagram.

I'm assuming there isn't any issue with wormholes becoming time machines or the existence of CTC's. If you wish to allow the chronological protection conjecture that CTC's are not allowed, the answer might be different.

 

[bcrowell]

I'm assuming there isn't any issue with wormholes becoming time machines or the existence of CTC's. If you wish to allow the chronological protection conjecture that CTC's are not allowed, the answer might be different.

You basically can't have wormholes without CTCs. You can't form a wormhole without also having CTCs, because topology change can't happen without CTCs. There's a theorem by Geroch on this, described here: http://arxiv.org/abs/gr-qc/9406053 . Any wormhole is also capable of being turned into a CTC: Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446.

 

[Matterwave]

You basically can't have wormholes without CTCs. You can't form a wormhole without also having CTCs, because topology change can't happen without CTCs. There's a theorem by Geroch on this, described here: http://arxiv.org/abs/gr-qc/9406053 . Any wormhole is also capable of being turned into a CTC: Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446.

This was my hunch, so I have been replying in this thread without regard for CTCs. I do; however, wonder if one can fix this partially by making the wormholes only 1-way traversible? (Surely there's a way to build such wormholes?)

 

[pervect]

You basically can't have wormholes without CTCs. You can't form a wormhole without also having CTCs, because topology change can't happen without CTCs. There's a theorem by Geroch on this, described here: http://arxiv.org/abs/gr-qc/9406053 . Any wormhole is also capable of being turned into a CTC: Morris, Thorne, and Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys Rev Lett 61 (1988) 1446.

While I agree that creating a wormhole classically requires a time machine, one of the references you cite, "Wormholes, time machines, and the weak energy condition," suggest that wormholes could be created from "quantum foam" without violating Geroch's theorem.

One can imagine an advanced civilization pulling a wormhole out of the quantum foam and enlarging it to classical size

Thus, as far as I know the non-classical (i.e. quantum) formation of wormholes is still thought to be possible without time machines, even though classical formation of wormholes does require them.

As far as turning wormholes into time machines go, there is a possibility and perhaps even a probability that quantum vacuum fluctuations could destroy a wormhole that attempted to become a time machine. My not-very-good understanding of this is from Kip Thorne's popular book, "Black Holes & Time Warps", pg 521

Every time machine is likely to self destruct (by means of circulating vacuum fluctuations) at the moment one tries to activate it

The literature reference where this is discussed is "Do Vacuum fluctuations prevent the creation of closed timelike curves", Kim and Thorne, 1991, the conjecture that they will prevent the creation of time machines is originally due to Hawking. Thorne seems to believe that this is not only possible but likely. Nobody knows for sure, as the calculation requires an understanding of quantum gravity, so the whole issue is poorly understood as Thorne is one of the first to point out.

 

[DrStupid]

I do; however, wonder if one can fix this partially by making the wormholes only 1-way traversible?

Take a second wormhole for the opposite direction and the problem returns.

 

[Matterwave]

Take a second wormhole for the opposite direction and the problem returns.

In a globally hyperbolic space-time (indeed, even in a strongly causal space time), there can be some notion of "forward in time" given by the "time coordinate" of the Cauchy surfaces which foliate the manifold. Given this notion, perhaps it becomes possible to define 1-way traversible wormholes that only allow travel "forward in time" was my thinking. Perhaps then, we can avoid CTCs. I don't know how to make this rigorous, nor do I know if this would fix any of the CTC problems however.