I wasn’t aware of the constraint that travel within wormhole must take longer than travel between the mouths. Given that, is there any real practical use for them? In scifi they are usually presented as shortcuts, but this constraint makes that seem less likely to ever be true.
But that's not a problem per se. The speed of light is only a limit locally but globally there is no such thing and in General Relativity there is nothing preventing time travel (closed timelike curves) at a global level, even though the existence of such curves is rather unlikely.
The paper notes:
> Interestingly, they are allowed in the quantum theory, but with one catch, the time it takes to go through the wormhole should be longer than the time it takes to travel between the two mouths on the outside.
Does anyone know why exactly "quantum theory" would impose such requirements? A priori to me it sounds like quite a stretch to take a local theory like quantum mechanics to make claims about the global topology of the universe, given that QM and GR haven't been unified yet. Unless of course by "quantum theory" Maldacena actually means "string theory" or "AdS/CFT" – which wouldn't surprise me at all.
But not "time travel" in the sense that you could go back and kill your grandfather. Only in the sense that different observers could not agree on the order of events.
And this doesn't seem so problematic to me. There always seems to exist some "true" order of events that results in the observations experienced by all observers, even if they don't agree based on their own individual knowledge.
The paper indicates they will "resemble intermediate mass charged black holes". The nearest black hole at the moment, maybe a worm hole candidate, is V723 Monocerotis at 1500 LY away. This would be tens of thousands of years of travel.
I was just about to say that same thing - any time I've seen wormholes in sci-fi (I'm reading Peter F Hamilton right now!), you go through in an instant (for all observers).
It's like sci-fi uses wormholes as a practical alternative to travelling at sub-C, relativistic speeds.
In Contact, <spoilerAlert> the pod drops instantly through from everyone's perspective outside the wormhole, but inside the wormhole 99 hours elapsed (potentially).
In the game Free Space there is travel time through wormholes (subspace jump nodes). In the finale the player intercepts and destroy the enemy flag ship as it is travelling through a wormhole to Earth.
Only scifi example I can think of wormholes with travel time.
An infinite source of power. Place one wormhole at the top of a hill, another at the bottom. Send rolling generators through them, stop them once in awhile to swap dead batteries for charged ones.
I suspect that (if wormholes can actually be made) gravitational potential would be smooth throughout, and that you’d be pulled up as much while falling out of the top as you get pulled down while approaching the bottom.
This holds true for regular travel nearing light speed too: For an external observer the spaceship never goes faster than light, but the passengers clocks slow down and they can experience arbitrarily high faster-than-light speeds.
For some reason I never see this discussed when people talk about FTL travel, maybe I'm wrong?
If anyone else never heard of the "Anti-de Sitter space" [0] here a short description from Wikipedia:
> In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe.
Sadly this is so far outside of my level of understanding that I still don't have a clue.
Think about 2D surfaces. Which ones are the most symmetric? A flat plane is a very nice space: every point is as good as any other (there’s nothing intrinsic to any point to distinguish any point from any other, except arbitrarily), and no direction is particularly special either. A space like that has a lot of symmetries. A sphere also has a lot of symmetries, it also has no directions or points which are distinguished until you declare, “this is my North Pole” arbitrarily. (The earth isn’t a perfect sphere of course and we can use the imperfections as the way we define north and south.) The last type of symmetric space looks like a saddle (like on a horse). It bends one way in one direction and bends the other way in the other direction. An idealized saddle also has no distinguished directions or points.
The analogs of these things in higher dimensions, and where one of the directions is time, are important in general relativity. The analog of the plane is called “flat space” or “Minkowski space”. The analog of the sphere is “de Sitter space”. Finally, the analog of the saddle is “anti-de Sitter space” (usually abbreviated AdS, with a lowercase d). It’s a bit of an odd space in a lot of ways. When you look at what space looks like at any given time, it’s a bit like M.C. Escher’s “Angels and Devils”.
Surprisingly, Anti-de Sitter space is the easiest space to understand quantum aspects of gravity in. That’s because anti-de Sitter space is curved in such a way that the complicated stuff can be neatly separated from the easy stuff. You can start from something you understand well and turn on the complexity piece by piece. Roughly speaking it’s because the gravitational stuff becomes less important as you go farther and farther away from any matter you’re considering, in a way which is even faster than this happens in flat space or de Sitter space. It turns out that we can exactly understand everything in this gravitational theory by mapping the physics one-to-one to a nongravitational model which we understand really well. There’s a lot of evidence that the map works perfectly. This is called the AdS/CFT correspondence. A lot of work goes into testing the correspondence and attempting to prove it, and this is a big research area.
de Sitter space doesn’t have the same desirable properties. Nevertheless there has been great progress in understanding quantum properties of de Sitter in the last year [0]. These results would not have been possible without understanding AdS first.
Flat space quantum gravity remains challenging, although again some progress has been made recently too [1].
I think it was an article posted on HN a little while back that got me thinking about the time travel paradoxes that wormholes could enable. There was one thought experiment about a wormhole with one end on your front lawn, and the other in a spaceship that leaves with your partner, accelerating away at 1g to eventually reach the speed of light, and at some point turning around and coming back.
The way I envisioned it is that the wormhole would act like a Zoom call, where you could talk/interact at "normal" speed of time during the entire voyage. Through the wormhole on your front lawn, you'd see your partner arriving back in your front yard and greeting future you despite the fact that their ship was still years away from arriving back on your yard from your frame of reference. Not to mention that you could also step through the wormhole at that point and join the future you and your partner, and then the partner that would arrive on your original lawn would find you missing. Obviously this turns into spaghetti quickly.
Now, this post is the first time I learn that travel within the wormhole must take longer than travel between the mouths of the wormhole. This got me thinking about whether my concept of looking through the wormhole was correct.
Would you actually see your partner moving at "normal" speed, or would their movements appear to you to begin to slow down as they approached the speed of light, with your movements appearing to them to accelerate dramatically? It seems as if their EM radiation towards you would eventually shift to infrared or radio and yours towards them would shift to gamma?
Have I made a total mess of my understanding of all of this? Apologies for the amateurish questions.
Also only "in some previously considered theories for physics beyond the Standard Model," and
> we engage in some “science fiction”. Namely, we will introduce a dark sector with desirable properties for constructing macroscopic traversable wormholes.
Seems unsurprising that if you purposely introduce hypothetical physics with desirable properties for making traversable wormholes, then it turns out the physics supports traversable wormholes.
I can see why it might look like that from the outside, but the set of mathematical results that led up to it actually come from the angle of, “let’s try to prove that traversable wormholes and the negative energy densities required to create them are impossible.” In trying to prove that, you learn a lot of interesting things along the way:
1. Negative energy densities are a universal prediction of all quantum field theories, and therefore are not as outrageous to think about as one might naively believe. [0]
2. The amount of negative energy density permitted by quantum field theory is NOT enough to support traversable wormholes, as long as you make some mild assumptions about the behavior of spacetime. [1]
3. Those mild assumptions seem NOT to be required by string theory, and string theory supports some solutions with traversable wormholes. [2]
4. Those solutions of string theory appear to be self consistent in an unusual and novel way, which is why string theorists like Juan Maldacena find them interesting. [3]
Every step is all super nontrivial and tells us something new about the mathematics of spacetime. Of course they’re models, maybe they all rest on some faulty assumption about nature that will later turn out to be wrong. So the final pillar of the story, the one that’s hard to communicate without spending years of your life studying it, is that every remaining assumptions about quantum gravity that goes into these arguments appear to be impossible to get rid of without having horrible consequences where spacetime can’t become smooth or relativistic at large scales. So these models are at least very plausible even though the ultimate truth will have to come from experiments.
[0] Proof appears many places, I like the one in arxiv:1803.04993 on page 11
Sure. But it still seems interesting to see in what ways you must bend the rules to make it possible. Consider that the goal here is not really to produce working human-traversable wormholes, but rather to learn more about various models of physics and how they behave in extreme conditions.
Trying to Make sense of: “with an AdS3 radius which is of order of the AdS5” Maldacena
Feel free to correct me, and also if you think there’s something terribly wrong with the formula, feel free to share along.
Now, AdS3 is a three-dimensional space with negative curvature, which is used in string theory as a model for the three-dimensional world. The AdS5 radius is the distance from the center of AdS3 to its boundary. Maldacena is saying that the AdS3 radius is of the same order as the AdS5 radius, meaning that they are both large compared to the Planck length.
Is this supported by empirical evidence?
No, this is not supported by empirical evidence.
This is based on the fact that the AdS3 radius is much larger than the Planck length, while the AdS5 radius is only slightly larger than the Planck length. This means that the two spaces are of the same order of magnitude, and so the AdS3 radius is of the same order as the AdS5 radius.
The Gibbons-Hawkings metric is a metric on the space of all Riemannian manifolds. It is defined where S is the action of the manifold and R is the Ricci scalar curvature. If we consider S to be an action under the Gibbons-Hawkings metric, where R is the Ricci scalar curvature of the manifold, In that case, S would be the action of the AdS3 manifold, which is where R is normed curvature of the AdS3 manifold.
There is not enough empirical evidence to determine whether or not the AdS3 radius and AdS5 radius are of the same order of magnitude. However, based on the results of the calculation, it seems that the AdS3 radius is of the same order of magnitude as the AdS5 radius.
Readit News
The paper notes:
> Interestingly, they are allowed in the quantum theory, but with one catch, the time it takes to go through the wormhole should be longer than the time it takes to travel between the two mouths on the outside.
Does anyone know why exactly "quantum theory" would impose such requirements? A priori to me it sounds like quite a stretch to take a local theory like quantum mechanics to make claims about the global topology of the universe, given that QM and GR haven't been unified yet. Unless of course by "quantum theory" Maldacena actually means "string theory" or "AdS/CFT" – which wouldn't surprise me at all.
But not "time travel" in the sense that you could go back and kill your grandfather. Only in the sense that different observers could not agree on the order of events.
And this doesn't seem so problematic to me. There always seems to exist some "true" order of events that results in the observations experienced by all observers, even if they don't agree based on their own individual knowledge.
Deleted Comment
The paper indicates they will "resemble intermediate mass charged black holes". The nearest black hole at the moment, maybe a worm hole candidate, is V723 Monocerotis at 1500 LY away. This would be tens of thousands of years of travel.
So perhaps we can learn from afar but not visit.
It's like sci-fi uses wormholes as a practical alternative to travelling at sub-C, relativistic speeds.
Only scifi example I can think of wormholes with travel time.
An infinite source of power. Place one wormhole at the top of a hill, another at the bottom. Send rolling generators through them, stop them once in awhile to swap dead batteries for charged ones.
Deleted Comment
For some reason I never see this discussed when people talk about FTL travel, maybe I'm wrong?
If anyone else never heard of the "Anti-de Sitter space" [0] here a short description from Wikipedia:
> In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe.
Sadly this is so far outside of my level of understanding that I still don't have a clue.
Would love an ELI5.
[0]: https://en.wikipedia.org/wiki/Anti-de_Sitter_space?wprov=sfl...
The analogs of these things in higher dimensions, and where one of the directions is time, are important in general relativity. The analog of the plane is called “flat space” or “Minkowski space”. The analog of the sphere is “de Sitter space”. Finally, the analog of the saddle is “anti-de Sitter space” (usually abbreviated AdS, with a lowercase d). It’s a bit of an odd space in a lot of ways. When you look at what space looks like at any given time, it’s a bit like M.C. Escher’s “Angels and Devils”.
Surprisingly, Anti-de Sitter space is the easiest space to understand quantum aspects of gravity in. That’s because anti-de Sitter space is curved in such a way that the complicated stuff can be neatly separated from the easy stuff. You can start from something you understand well and turn on the complexity piece by piece. Roughly speaking it’s because the gravitational stuff becomes less important as you go farther and farther away from any matter you’re considering, in a way which is even faster than this happens in flat space or de Sitter space. It turns out that we can exactly understand everything in this gravitational theory by mapping the physics one-to-one to a nongravitational model which we understand really well. There’s a lot of evidence that the map works perfectly. This is called the AdS/CFT correspondence. A lot of work goes into testing the correspondence and attempting to prove it, and this is a big research area.
de Sitter space doesn’t have the same desirable properties. Nevertheless there has been great progress in understanding quantum properties of de Sitter in the last year [0]. These results would not have been possible without understanding AdS first.
Flat space quantum gravity remains challenging, although again some progress has been made recently too [1].
[0] arxiv:2110.14670
[1] arxiv:1905.09809 and many others
The way I envisioned it is that the wormhole would act like a Zoom call, where you could talk/interact at "normal" speed of time during the entire voyage. Through the wormhole on your front lawn, you'd see your partner arriving back in your front yard and greeting future you despite the fact that their ship was still years away from arriving back on your yard from your frame of reference. Not to mention that you could also step through the wormhole at that point and join the future you and your partner, and then the partner that would arrive on your original lawn would find you missing. Obviously this turns into spaghetti quickly.
Now, this post is the first time I learn that travel within the wormhole must take longer than travel between the mouths of the wormhole. This got me thinking about whether my concept of looking through the wormhole was correct.
Would you actually see your partner moving at "normal" speed, or would their movements appear to you to begin to slow down as they approached the speed of light, with your movements appearing to them to accelerate dramatically? It seems as if their EM radiation towards you would eventually shift to infrared or radio and yours towards them would shift to gamma?
Have I made a total mess of my understanding of all of this? Apologies for the amateurish questions.
> we engage in some “science fiction”. Namely, we will introduce a dark sector with desirable properties for constructing macroscopic traversable wormholes.
Seems unsurprising that if you purposely introduce hypothetical physics with desirable properties for making traversable wormholes, then it turns out the physics supports traversable wormholes.
1. Negative energy densities are a universal prediction of all quantum field theories, and therefore are not as outrageous to think about as one might naively believe. [0]
2. The amount of negative energy density permitted by quantum field theory is NOT enough to support traversable wormholes, as long as you make some mild assumptions about the behavior of spacetime. [1]
3. Those mild assumptions seem NOT to be required by string theory, and string theory supports some solutions with traversable wormholes. [2]
4. Those solutions of string theory appear to be self consistent in an unusual and novel way, which is why string theorists like Juan Maldacena find them interesting. [3]
Every step is all super nontrivial and tells us something new about the mathematics of spacetime. Of course they’re models, maybe they all rest on some faulty assumption about nature that will later turn out to be wrong. So the final pillar of the story, the one that’s hard to communicate without spending years of your life studying it, is that every remaining assumptions about quantum gravity that goes into these arguments appear to be impossible to get rid of without having horrible consequences where spacetime can’t become smooth or relativistic at large scales. So these models are at least very plausible even though the ultimate truth will have to come from experiments.
[0] Proof appears many places, I like the one in arxiv:1803.04993 on page 11
[1] arxiv:1010.5513
[2] arxiv:1608.05687
[3] the paper linked by OP :)
Feel free to correct me, and also if you think there’s something terribly wrong with the formula, feel free to share along.
Now, AdS3 is a three-dimensional space with negative curvature, which is used in string theory as a model for the three-dimensional world. The AdS5 radius is the distance from the center of AdS3 to its boundary. Maldacena is saying that the AdS3 radius is of the same order as the AdS5 radius, meaning that they are both large compared to the Planck length.
Is this supported by empirical evidence?
No, this is not supported by empirical evidence.
This is based on the fact that the AdS3 radius is much larger than the Planck length, while the AdS5 radius is only slightly larger than the Planck length. This means that the two spaces are of the same order of magnitude, and so the AdS3 radius is of the same order as the AdS5 radius.
The Gibbons-Hawkings metric is a metric on the space of all Riemannian manifolds. It is defined where S is the action of the manifold and R is the Ricci scalar curvature. If we consider S to be an action under the Gibbons-Hawkings metric, where R is the Ricci scalar curvature of the manifold, In that case, S would be the action of the AdS3 manifold, which is where R is normed curvature of the AdS3 manifold.
This is the Ricci scalar curvature:
R = \frac{1}{2} \mathrm{tr}\left( R_{\mu
\mu} \right) = \frac{1}{2} \mathrm{tr}\left( \frac{\partial{{\partial x^{\mu} \omega_{
{\mu} - \frac{\partial{\partial {x^{\mu} \omega_{\mu} + \omega_{\mu} \omega_{
u} - \omega_{
u} \omega_{\mu} \right)
where R_{\mu
u} is the Ricci tensor and \omega_{\mu} is the connection 1-form.
This is the Ricci scalar curvature:
R = \frac{1}{2} \mathrm{tr}\left( R_{\mu
u} \right) = \frac{1}{2} \mathrm{tr}\left( \frac{\partial}{\partial x^{\mu}} \omega_{
u} - \frac{\partial}{\partial x^
u} \omega_{\mu} + \omega_{\mu} \omega_{
u} - \omega_{
u} \omega_{\mu} \right)
There is not enough empirical evidence to determine whether or not the AdS3 radius and AdS5 radius are of the same order of magnitude. However, based on the results of the calculation, it seems that the AdS3 radius is of the same order of magnitude as the AdS5 radius.