Travelling through a wormhole in space

[Umbran]

Okay, let me try to address some points....

A long flashy tunnel or an instantaneous popover?

Popovers are not instantaneous. I mean, you need tie to make the batter, and then the things have to bake...

But seriously...

I don't think there's a "most likely" here. As far as I am aware, there's no particular theoretical constrain on how long the trip through the trip through the wormhole is. I would presume that, should the engineering allow it, folks would make wormholes with very short paths, but maybe that's not possible.

I'm sure Umbran will provide better info, but to my most recent reading about the subject in popular science literature, there isn't a theoretical way to travel as any wormhole collapses as soon as matter enters it (and wormholes have never been observed, of course - they're just a solution to an equation).

Yes, they are a solution to an equation, and none have ever been observed. There is, to date, no practical way to create or travel though such a thing. But, as for theoretical ways, yes, there are ways that work, in theory.

Einsteinian relativity allows for space to be shaped such that it has a "shortcut" through it. The problem is that all such solutions are not stable to small perturbations - which means that even small changes in gravitational fields in or near the wormhole tend to collapse it. However, Kip Thorne and others have come up with various ways to stabilize wormholes against these small perturbations. They all require application of materials or energies with unusual properties that, again do not seem to be prohibited by the Universe, but we have never observed in nature or made ourselves in anything like large enough quantities. These are usually lumped under the term "exotic materials". There are a few solutions I've seen that suggest that quantum effects could also be used - but since we don't have a good marriage between quantum mechanics and gravitational effects, that's very speculative.

Which amounts to there being ways in theory. Which makes sense, as wormholes have not been observed, so they only exist in theory anyway

I always imagined them as not having a visual representation.

Well, yes and no. When you look at a wormhole, you aren't looking at a *thing*. The wormhole is a path through space. So, like when you look through a doorway, you'll see whatever is on the other side of the door. If both ends of the wormhole are in basically open space, this won't look like much, no. But, if one is in New York City's Central Park, and the other end is in the Sahara Desert, you're looking trough a door into a radically different environment.

Someone actually did an image rendering, taking the curvature of space involved, for one type of wormhole. It looks like this:


(this is "Wurmloch" by CorvinZahn - Gallery of Space Time Travel (self-made, panorama of the dunes: Philippe E. Hurbain). Licensed under CC BY-SA 2.5 via Wikimedia Commons )

There are other, slightly different solutions for what we'd call a wormhole, that have somewhat different appearances to our eyes. But I think it is this type that was used in "Interstellar".

Time dilation would almost certainly happen, but of course that's relative to someone who doesn't go through or too near the wormhole.

I am not sure this is correct. The actual path through the wormhole is pretty much normal, flat space. The wormhole has an odd appearance, but there is no singularity, and so no ever-increasing curvature of spacetime that creates time dilation as you see around a black hole.

Now, if one end of the wormhole is *moving*, relative to the other end, then funny things can happen. Since it is a deformation of spacetime, it can be moving in space and/or in time...

 

[freyar]

I am not sure this is correct. The actual path through the wormhole is pretty much normal, flat space. The wormhole has an odd appearance, but there is no singularity, and so no ever-increasing curvature of spacetime that creates time dilation as you see around a black hole.

Now, if one end of the wormhole is *moving*, relative to the other end, then funny things can happen. Since it is a deformation of spacetime, it can be moving in space and/or in time...

Gravitational time dilation isn't only found near singularities or extremely high curvature. In fact, it's measurable even in the weak gravity of the earth --- GPS units have to account for it. Generically, meaning except in extremely special circumstances, there should be some degree of time dilation, and usually we expect weird situations to include some fairly substantial

But I'll freely admit that I didn't look up any wormhole metrics before making that statement, so I went and looked just now. One thing I found was a pedagogical paper by Michael Morris and Kip Thorne, who seem to have pushed the serious study of wormholes in the late 20th century. They make a point of analyzing precisely how to reduce time dilation effects --- since that also reduces tidal forces. There are indeed wormhole solutions with no time dilation, but they have "exotic matter" everywhere. We live in a universe without much exotic matter, so a realistic wormhole solution requires matching onto a long-distance solution with normal matter. Then you do get time dilation. If you want to keep time dilation effects small and the exotic matter localized to the wormhole itself, you need a wormhole that's about 600 AU across. Given that the exotic matter needed to create these things is pretty rare, naturally-occurring wormholes would seem likely to have significant time dilation effects. On the other hand, maybe an advanced civilization could construct one without much time dilation.

That's of course depending on whether exotic matter with precisely the right properties to make wormholes exists. It's certainly possible to violate the energy conditions that might look like they forbid exotic matter; indeed, some kinds exotic matter of that type looks to be perfectly fine. But other types of exotic matter seem to cause mathematical inconsistencies, so I can't say about what's needed for wormholes. Morris & Thorne also note that wormholes of the type they study are also necessarily time machines, so that may or may not be a clue that they're not allowed.

It's also worth noting that the Morris-Thorne wormholes and the eternal black hole wormholes (called Einstein-Rosen bridges) don't connect two points on the same part of space. They connect two different parts of space. In other words, I travel from earth to a wormhole, go through the wormhole, then travel to planet X. If I want to get back to earth, I can't go the "long way around," I have to go through the wormhole (or some wormhole) again.

 

[tomBitonti]

To say, Interstellar shows two different phenomena: The initial step of the journey is through a wormhole which orbits Saturn. A journey through that wormhole takes you to the black hole, Gargantua. There were depictions of both the wormhole and of the black hole.

My understanding is that we have a pretty good idea of lensing effects around a black hole. Here is a discussion of the black hole images from the movie:

http://io9.com/the-truth-behind-interstellars-scientifically-accurate-1686120318

Kip Thorne did evidently collaborate closely with the movie producers:

http://www.space.com/27701-interstellar-movie-science-black-holes.html

There is a nice view of the wormhole here:

http://www.quora.com/Why-did-the-wo...nding-of-light-at-the-periphery-of-the-sphere

I don't think that the wormhole in this depiction is actually "shiny": The apparent reflection at the edges is more an illusion of the way the light reaches us through the wormhole.

I would presume that there would be effects on the outside of the wormhole, too, but, these are not visible because they are too faint. That would be lensing of the background field, but it would seem to be much fainter than what would be visible through the wormhole, and would be washed out of the view to the naked eye.

I would think that the image is correct for a specified topology and curvature, but very possibly inaccurate in that additional effects are not depicted, say, particle creation (the worm hole might be a strong particle emitter), or instabilities (the wormhole, as shown, is perfectly uniform). Then there is the problem of a mass-energy distribution which could create the curvature (egad!)

In any case, I imagine the view is much more realistic than the "funnel in space" type view, for example, from Farscape:

http://www.foundation3d.com/index.php?categoryid=38&p13_sectionid=376&p13_fileid=461

I do wonder what the view would be for a non-spherically symmetric wormhole, e.g. Sliders or Stargate. Could you actually move curvature to the edges and have simple uncurved flat transition at the center?

Here is a thought experiment: Would a spherically symmetric wormhole create a detached space representing the prior "interior"? That is, in 2D, if you glued two sheets together and cut a hole in them, then stretched both sheets to make for a smooth transition around the edges, that would leave you with the two cut discs, which you could also smooth out to make a closed but unbounded space. (I've used this in one my games as a prison for a Mythic Rune Giant )

Edit: There is a nice animation of a black hole moving across an edge on view of a galaxy:

http://en.wikipedia.org/wiki/Gravitational_lens

And if you are up for the maths, here is a discussion of wormhole lensing:

http://www.nipne.ro/rjp/2012_57_3-4/0736_0747.pdf

Thx!

TomB

 

[Umbran]

Gravitational time dilation isn't only found near singularities or extremely high curvature. In fact, it's measurable even in the weak gravity of the earth --- GPS units have to account for it.

With respect, the fractions of a second involved there are not what laymen are thinking of when they hear the term. They're thinking about the Interstellar "if we take this path, we will age little, but many years will pass on Earth," variety.

One thing I found was a pedagogical paper by Michael Morris and Kip Thorne, who seem to have pushed the serious study of wormholes in the late 20th century.

Kip Thorne wrote, "Black Holes and Time Warps: Einstein's Outrageous Legacy" in 1994. It has been a while since I opened my copy, but on the other hand it is now 20 years old. I'd be surprised if Kip hasn't gone well beyond that work by now.

There are indeed wormhole solutions with no time dilation, but they have "exotic matter" everywhere.

The ones that *don't* use exotic matter require a particular modification to General Relativity, Gauss-Bonnet gravity, involving some extra spacial dimensions, to be correct. Such solutions are often associated with brane theory. So, unless we have enough branes, we need exotic matter to do the job. Pun intended.

It's also worth noting that the Morris-Thorne wormholes and the eternal black hole wormholes (called Einstein-Rosen bridges) don't connect two points on the same part of space. They connect two different parts of space. In other words, I travel from earth to a wormhole, go through the wormhole, then travel to planet X. If I want to get back to earth, I can't go the "long way around," I have to go through the wormhole (or some wormhole) again.

You might want to clarify what you mean by the "same part of space".

 

[Umbran]

I do wonder what the view would be for a non-spherically symmetric wormhole, e.g. Sliders or Stargate. Could you actually move curvature to the edges and have simple uncurved flat transition at the center?

Something like a Stargate wormhole presents difficulties - what happens at the edge of that circle?

If you get your stargate by taking a sphere and squashing it flat, such that both "sides" (and the edge, technically), are still wormhole, then you're okay. But if it has a "front" but no "back" so to speak, you have a discontinuity in space - what we'd tend to call a singularity, but in this case as a loop, rather than a point.

I think there are solutions with such, but they tend to have things like cosmic strings at the edge. And you don't get much more exotic than that.

Here is a thought experiment: Would a spherically symmetric wormhole create a detached space representing the prior "interior"?

Wild-arsed guess - you don't cut out a circle to make a stable wormhole. You start with a pinpoint aperture, on the Planck scale of distances, and widen it. So, the process is more like putting a needle through a sheet of clay and slowly deforming into a larger hole.

 

[tomBitonti]

Something like a Stargate wormhole presents difficulties - what happens at the edge of that circle?

If you get your stargate by taking a sphere and squashing it flat, such that both "sides" (and the edge, technically), are still wormhole, then you're okay. But if it has a "front" but no "back" so to speak, you have a discontinuity in space - what we'd tend to call a singularity, but in this case as a loop, rather than a point.

I think there are solutions with such, but they tend to have things like cosmic strings at the edge. And you don't get much more exotic than that.

Wild-arsed guess - you don't cut out a circle to make a stable wormhole. You start with a pinpoint aperture, on the Planck scale of distances, and widen it. So, the process is more like putting a needle through a sheet of clay and slowly deforming into a larger hole.

Yeah. Stargate conveniently avoids a problem by hiding the edges.

What I was wondering, though, is if you squashed a surface of a spherical wormhole flat, there would still be a big transition between the throat and flat spacetime. The curvature up to the flat section of the throat would be uniform in two dimensions (perhaps), but not in a line moving away from the throat.

Thx!

TomB

 

[Umbran]

What I was wondering, though, is if you squashed a surface of a spherical wormhole flat, there would still be a big transition between the throat and flat spacetime.

You shift from wondering (which implies a question) to a statement.

Would there be a big transition? That depends on what you call "big". In general, this thing is supposed to be traversable. You need spacetime to be pretty flat on distance scales roughly on order of the size of the object that goes through - otherwise you either turn the item into spaghetti, or you have a problem of the subject's head being in today, while her feet are already in next week. So, where you expect people to go, spacetime isn't terribly curved, and what curvature there is can't change a whole lot.

I think most of the traversable solutions have spacetime largely flat along the throat of the wormhole and out into "normal" space, and squeeze to very steep curves towards the edges/sides. So, you can travel down the middle, but hitting the "wall" would be bad for you.

 

[tomBitonti]

You shift from wondering (which implies a question) to a statement.

Would there be a big transition? That depends on what you call "big". In general, this thing is supposed to be traversable. You need spacetime to be pretty flat on distance scales roughly on order of the size of the object that goes through - otherwise you either turn the item into spaghetti, or you have a problem of the subject's head being in today, while her feet are already in next week. So, where you expect people to go, spacetime isn't terribly curved, and what curvature there is can't change a whole lot.

I think most of the traversable solutions have spacetime largely flat along the throat of the wormhole and out into "normal" space, and squeeze to very steep curves towards the edges/sides. So, you can travel down the middle, but hitting the "wall" would be bad for you.

Sorry, writing too quickly. I have a better understanding of the topology than the physics, so I'll approach from that direction.

Putting this in two dimensions: You could imagine a clean splice/join, with two sheets joined across a cut. If you made the cut a line, then you would have a discontinuity at the ends of the slice, but a completely flat transition across the cut.

You can make the join a ring, which avoids the end effects, but you end up with a different problem. The join shifts you from a concave segment to a convex segment. (Imagine pushing a curved bar through the cut: It ends up curved the other way.) Crossing the throat would be the same as a bend, and probably a big problem for a small ring. The problem is the shift from heading in to the ring to heading away from the ring. There is no adjustment to the join which avoids this problem (without changing the local metric).

If you use a ring and set the metric to make the join locally flat (not sure if that makes sense), then you have the problem of the transition from asymptotically flat space to the join, with curvature required by the transition. Which means there are apparent forces and tidal stress, so still a problem.

The question, then, is how much does this line of thinking make sense: For a physical wormhole, what case occurs? I'm thinking the third. But then, Stargate or Sliders would have forces (potentially huge ones) near the throat. Is there any way to avoid these?

Thx!

TomB

 

[freyar]

With respect, the fractions of a second involved there are not what laymen are thinking of when they hear the term. They're thinking about the Interstellar "if we take this path, we will age little, but many years will pass on Earth," variety.

Fair enough. Please note, I've not seen the movie, so I'm just going on hearsay there. However, the rest of the point is that Morris & Thorne have argued that, if you want to engineer a wormhole to have negligible time dilation and tidal forces (ie, comfortable for human travel), it has to be big. Like 20x as big as the solar system.

Kip Thorne wrote, "Black Holes and Time Warps: Einstein's Outrageous Legacy" in 1994. It has been a while since I opened my copy, but on the other hand it is now 20 years old. I'd be surprised if Kip hasn't gone well beyond that work by now.

I just did a literature search on the best research database for this kind of thing, looking for research papers by Kip Thorne about wormholes. I don't find any evidence for such work between 1993 and 2015 (the 2015 papers were about visualization for Interstellar). A number of other authors have worked on wormholes, of course, and I'm skimming through some of that literature for curiosity's sake.

The ones that *don't* use exotic matter require a particular modification to General Relativity, Gauss-Bonnet gravity, involving some extra spacial dimensions, to be correct. Such solutions are often associated with brane theory. So, unless we have enough branes, we need exotic matter to do the job. Pun intended.

I think I must not have explained properly. Morris & Thorne weren't looking at wormholes without exotic matter. They just didn't want exotic matter filling up the entire universe, so they wanted spacetimes that have a wormhole created by exotic matter surrounded by space with normal matter (including people, space stations, etc), like where we live. To do that, they found a "comfortably traversable" wormhole needed to be very large. Smaller than that would have large tidal forces and at least noticeable time dilation. Keep in mind that Morris & Thorne were specifically trying to make wormhole spacetimes with small amounts of time dilation and were willing to postulate any characteristic of matter necessary.

Side point: Gauss-Bonnet gravity need not be associated with brane-world models. The point is that the Gauss-Bonnet term doesn't change the Einstein equations in 4D; they only do that in 5D and above. That's interesting for brane-worlds as well as other extra dimensional models. Also as a side note, I've written a paper using 5D GB gravity myself.

You might want to clarify what you mean by the "same part of space".

In technical terms, the wormhole solutions written down connect two distinct asymptotic regions. In plain English, the two ends of the wormhole are connected to two distinct universes, or maybe more precisely two regions of space that don't connect to each other except through the wormhole. In principle, I don't think there's a reason you couldn't make a wormhole connecting two parts of the same universe, but I haven't yet seen a metric that does that. It's not what people typically study when the look at wormholes.

You shift from wondering (which implies a question) to a statement.

Would there be a big transition? That depends on what you call "big". In general, this thing is supposed to be traversable. You need spacetime to be pretty flat on distance scales roughly on order of the size of the object that goes through - otherwise you either turn the item into spaghetti, or you have a problem of the subject's head being in today, while her feet are already in next week. So, where you expect people to go, spacetime isn't terribly curved, and what curvature there is can't change a whole lot.

I think most of the traversable solutions have spacetime largely flat along the throat of the wormhole and out into "normal" space, and squeeze to very steep curves towards the edges/sides. So, you can travel down the middle, but hitting the "wall" would be bad for you.

And how to make them flat enough to traverse was the point of the Morris-Thorne paper. Key point --- you have to make them big to avoid either tidal forces, time dilation, or both.

 

[Umbran]

Fair enough. Please note, I've not seen the movie, so I'm just going on hearsay there. However, the rest of the point is that Morris & Thorne have argued that, if you want to engineer a wormhole to have negligible time dilation and tidal forces (ie, comfortable for human travel), it has to be big. Like 20x as big as the solar system.

I am completely unsurprised and unfazed by that. We are talking about taking apart spacetime for our own use, after all. "Big", in purely human physical terms, is not really an issue by comparison.

Side point: Gauss-Bonnet gravity need not be associated with brane-world models.

I know. I noted it merely because it is a model that some folks may have heard of that was relevant.

The point is that the Gauss-Bonnet term doesn't change the Einstein equations in 4D; they only do that in 5D and above. That's interesting for brane-worlds as well as other extra dimensional models. Also as a side note, I've written a paper using 5D GB gravity myself.

Yes. To my knowledge, no 5+D model has made a practically testable prediction. Thus theories that use them are pretty speculative. Thus, let us not *expect* wormholes that don't use exotic matter.

In technical terms, the wormhole solutions written down connect two distinct asymptotic regions. In plain English, the two ends of the wormhole are connected to two distinct universes, or maybe more precisely two regions of space that don't connect to each other except through the wormhole.

Since you've done more of the reading recently than I now: is that "not connected" in an absolute topological sense? Or is it "not connected" in the causal, "won't be in each other's light cone even though there's continuous spacetime between points" sense?