Wormholes & Warp Drives: Refuted by AANEC?

[A Middle Aged Man]

TL;DR Summary

overwhelming evidence against such concepts?

I'm not an expert, I'm definitely a scifi fan, But I'm hoping for professional opinions on a particular view of the old wormholes and/or warp drives issue...

A quote from scientist Tim Andersen:



"Achronal Average Null Energy Condition or AANEC may be the ultimate cosmic traffic cop making all FTL travel from warp drives to wormholes impossible. Graham and Olum showed that quantum physics never violates the AANEC. Any time machine, they further showed, has to violate this condition."

He goes on in further detail, but it's not a long read.

Though these kind of scientific topics can be difficult to parse out, is he correct? Does the science behind AANEC, more or less, render those science-fiction notions as, well, really only fit for fiction, no matter how advanced humanity [or any other species in this universe, for that matter] might get in our real future?

 

[Ibix]

Paper at arxiv https://arxiv.org/abs/0705.3193.

 

[PeterDonis]

the science behind AANEC

To be clear: the AANEC has never been observed to be violated, but we have no theoretical proof that it must hold. We only know, theoretically, that things like time machines are impossible if it holds.

The interesting theoretical question will be what various theories of quantum gravity, as they are developed, say about conditions like the AANEC.

 

[A Middle Aged Man]

Informative, interesting, and I want to know more, however...

even the kind of lay explanation given in the medium.com article left me confused [to say nothing of actual, technical papers]. How is it theorized to work? Or maybe it can't be described simply enough for me. My fault of course.

And, are you saying that AANEC is currently just theoretical, as in, the burden of proof would be on the person arguing FOR AANEC, and currently that burden has not been met?

 

[PeterDonis]

How is it theorized to work?

I'm not sure it is theorized to "work" in any particular way, if you are asking about a mechanism.

The condition itself basically just says that average energy densities over any spacelike hypersurface can't be negative. Energy densities at particular points could be negative, but the average over any spacelike hypersurface cannot be. That turns out to be sufficient to rule out time machines.

are you saying that AANEC is currently just theoretical

No; as noted, no one has observed any violations of AANEC. So it's an observational fact, at least within the domain of our current observations.

The theoretical question is about whether we should expect to observe violations of AANEC in the future, as our ability to observe increases. AFAIK, there is not general agreement on that question.

 

[A Middle Aged Man]

Thanks for your help, I appreciate it!

The condition itself basically just says that average energy densities over any spacelike hypersurface can't be negative. Energy densities at particular points could be negative, but the average over any spacelike hypersurface cannot be. That turns out to be sufficient to rule out time machines.

Is it enough to rule out the other stuff i.e. wormholes and warp drives? I thought there were theoretical ways of having those without 'closed timelike curves', or time travel.

 

[PeterDonis]

Is it enough to rule out the other stuff i.e. wormholes and warp drives?

AFAIK yes, it rules those out too.

 

[A Middle Aged Man]

Ok, so to recap what I think I understand and remember from reading about wormholes:

a) wormholes are consistent and allowed with current knowledge of physics, however...
b) it requires some kind of negative mass to actually keep them open and functional, and...
c) AANEC, if its predictions are true, would rule out negative mass existing in such a usable form, so...
d) wormholes, though they can exist, would collapse and close off so fast that not even a single photon could get through, and therefore could not be used to transport anything at all.

Did I get it right?

 

[PeterDonis]

Ok, so to recap what I think I understand and remember from reading about wormholes:

a) wormholes are consistent and allowed with current knowledge of physics, however...
b) it requires some kind of negative mass to actually keep them open and functional, and...
c) AANEC, if its predictions are true, would rule out negative mass existing in such a usable form, so...
d) wormholes, though they can exist, would collapse and close off so fast that not even a single photon could get through, and therefore could not be used to transport anything at all.

Did I get it right?

a) through c) describe the impact of AANEC, yes.

d) describes a "wormhole" solution--the maximally extended Schwarzschild spacetime--that is not physically realistic for other reasons that have nothing to do with AANEC (basically, that it's impossible for such a spacetime to form from a real gravitational collapse). It is true that even if this solution were physically realistic, it still would not allow anything to get through the wormhole, for the reason you give. But that also has nothing to do with the AANEC.

 

[Ibix]

The situation we're in is a bit like the situation with conservation laws pre Noether, isn't it? We had conservation laws for energy, momentum, mass, etc, but no particular reason for them beyond the observation that they worked. Then along came Emmy Noether and showed that conservation laws followed from differentiable symmetries of the Lagrangian - and suddenly we had a solid theoretical justification for conservation laws.

All the energy conditions are analogous to such laws in that they're rules that seem sensible. Although they're not quite so successful - we keep finding circumstances that violate them. This is a yet more slightly relaxed condition that we (or at least the authors of the paper) think will hold. Hopefully one day we'll figure out a solid theoretical justification for it (or its successor...).

 

[A Middle Aged Man]

PeterDonis,

So the wormhole that falls apart so fast that even a single photon isn't fast enough to get through it (therefore making it useless for transporting anything), is THAT also ruled out by the physics knowledge we have so far?

 

[PeterDonis]

the wormhole that falls apart so fast that even a single photon isn't fast enough to get through it (therefore making it useless for transporting anything), is THAT also ruled out by the physics knowledge we have so far?

I already answered this in the d) part of post #9:

not physically realistic for other reasons that have nothing to do with AANEC (basically, that it's impossible for such a spacetime to form from a real gravitational collapse)

 

[A Middle Aged Man]

I didn't know that (then again, I don't know much I admit). If the details are too much I understand, but if its doable to summarize...what are the other reasons that its impossible for such a wormhole to form?

 

[PeterDonis]

what are the other reasons that its impossible for such a wormhole to form?

Meaning, why is it impossible for such a spacetime to form from a real gravitational collapse? Briefly, because in a real gravitational collapse, the region of spacetime that, in the idealized mathematical solution, is occupied by the wormhole (and also by a "white hole"), is occupied by the collapsing matter instead. The idealized mathematical solution is a vacuum solution--no matter or energy anywhere. Putting any matter or energy in, which has to be done to model a real gravitational collapse, removes the wormhole region from the spacetime entirely; it's only there in the idealized vacuum solution.

 

[Ibix]

I didn't know that (then again, I don't know much I admit). If the details are too much I understand, but if its doable to summarize...what are the other reasons that its impossible for such a wormhole to form?

Peter (edit: who types faster than I do, I see) is talking about part of a solution to Einstein's field equations called the maximally extended Schwarzschild spacetime. That solution describes a universe that contains an uncharged, non-rotating black hole that has existed and will always exist forever, and nothing else at all. That's not a bad model for many purposes, but the idea of a black hole that just exists for no reason forces the maths to produce a kind of mirror image: a white hole with its own singularity in the past and a second region of spacetime outside the black and white holes as well as the "normal" exterior region. The two exterior regions are joined by a wormhole that you can't traverse because there's no way to get to it - saying that it collapses before you can reach it isn't quite right, but there isn't a better way of saying it, I think.

Anyway - this model is wrong if there is or ever was anything else in the universe apart from the black hole (not counting all the other structure that gets spun out by the maths). In particular, a realistic model doesn't need to spin out all this stuff to make "black hole just exists" make sense because it has a collapsing star as the pre-history of the hole - so no white hole, wormhole, or other exterior region. However, the maths of a realistic model is much messier (you're going to need a bigger computer, whereas Schwarzschild derived his solution with pen and paper while fighting in the trenches of World War I) and you can't actually reach any of the impossible stuff from a realistic start point, so it's frequently a useful model.

 

[A Middle Aged Man]

I'm an amateur, but I think I'm making progress: the gravitational collapse needed to form the 'link', the wormhole between two points, even if incredibly briefly, is impossible?

 

[Ibix]

I'm an amateur, but I think I'm making progress: the gravitational collapse needed to form the 'link', the wormhole between two points, even if incredibly briefly, is impossible?

There is no gravitational collapse in maximally extended Schwarzschild spacetime. The black hole just exists and always has. A spacetime with gravitational collapse doesn't have any of these structures. Instead, it has just a star that turns into a black hole.

The white hole, wormhole, and other exterior region are a consequence of asking for something unrealistic - an eternal black hole in an otherwise empty universe.

 

[A Middle Aged Man]

does the gravitational collapse in question go like this: in wormhole formation, some kind of gravitational collapse is what is necessary to form one. Isn't that what it means when two very dense points [like black holes] 'join' by 'collapsing' and forming a tube i.e. wormhole between each other? I thought that's how it was theorized to work. But if there cannot be any such 'gravitational collapse' then those two dense points just remain, with really high gravity, but never 'collapse' into a wormhole [not even a very brief one]. [edit] And even then, overcoming that, in the absence of negative matter, the whole thing collapses again, too fast for anything to go through it.

 

[Nugatory]

does the gravitational collapse in question go like this: in wormhole formation, some kind of gravitational collapse is what is necessary to form one.

No. There is no wormhole formation.

There is a wormhole in one particular solution to the Einstein Field Equations, namely the “maximally extended Schwarzschild” spacetime that describes a hypothetical universe that contains nothing except a single eternal and unchanging black hole that has always existed and always will exist - and the wormhole that appears in that solution is a result of the black hole having always existed. Clearly this hypothetical universe has little relevance to the universe we live in, in which black holes are formed by gravitational collapse and there’s a lot more there than just the one black hole.

(That does raise the question, why do we bother studying it at all? One reason is that it’s interesting in its own right, but the more important reason is that a subset of that spacetime, the part that we get by not “maximally extending” the solution and that doesn’t contain a wormhole, turns out to be a really excellent approximation for a black hole formed by collapse after we wait for it to stabilize after the collapse).

Isn't that what it means when two very dense points [like black holes] 'join' by 'collapsing' and forming a tube i.e. wormhole between each other?

That’s not what happens when two black holes join. We just end up with one bigger black hole.

 

[A Middle Aged Man]

So, originally, there were never any serious proposals for wormholes in our actual universe? Just wormholes for a hypothetical universe that existed only on paper?

 

[Nugatory]

So, originally, there were never any serious proposals for wormholes in our actual universe? Just wormholes for a hypothetical universe that existed only on paper?

There are other wormhole solutions than the single-point one that appears in the extended Schwarzschild solution - googling for “wormhole metric” will find the most widely discussed one. These are valid solutions of the EFE, they’re interesting, and exploring them has a fair amount of pedagogical value. But I’m not aware of any that are taken seriously in the sense that we think it might be possible to physically realize the stress-energy tensor that would generate that spacetime.

The paper you cited to start this thread might reasonably be paraphrased as “everyone has been pretty sure it won’t happen outside of science fiction, here’s some justification for that skepticism”

 

[A Middle Aged Man]

I'm going to read some more about this sort of topic from some other sources, but its been a stimulating discourse so far. Thanks for the detailed replies from all and I'm looking foward to learning more, both on my own and with more questions!