Humanly traversable wormholes (2020)
arxiv.org
arxiv.org
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 as this is in a closed loop of time, from the outside it goes to infinity instantly.
(It does feel like trying and failing to make one, getting asymptotically close should release infinite free energy as virtual photons almost get into a CTC, but IANAP).
Yeah, that probably only makes sense in armchair physics. Which is all I'm licensed for anyway, so fine with me!
https://en.wikipedia.org/wiki/Novikov_self-consistency_princ...
The wormhole solutions from the paper are semi-classical: they are obtained by taking the expectations value of the energy configuration of a quantum theory and feeding that into the classical Einstein equations. Therefore, no string theory or AdS/CFT is needed for the construction.
But it seems they were indeed merely announcing a result specific to the wormhole they constructed since on p. 6 the authors say:
> In deriving (2.12) we assumed that the distance d between the two black holes is smaller than l, d << l. Even when we do not make that assumption we find that the time through the wormhole is always longer than through the outside, πl > d.
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.
What I should have said is that different observers can already, in the absence of FTL, disagree about the order of events with space-like separation, but it doesn't matter because by definition anything that happens at one such event can't affect anything happening at another.
FTL removes that restriction -- if something can travel faster than light, it can be present at two space-like separated events -- and that's what threatens causality, assuming something like the Novikov consistency conjecture doesn't hold.
========
Original comment:
> Only in the sense that different observers could not agree on the order of events.
But that's already true of events with space-like separation anyway. You don't need FTL travel for that.
With FTL, you run the risk of observers disagreeing about the order of events with time-like separation, so you are getting into grandfather-paradox territory.
Trying to make conclusions about that by using simple analogies to light isn't likely to get you anywhere. You're not dealing with the actual thing you're interested in in the first place.
I don’t know if that’s correct, but the analogy helps me (until I think about it too hard, and then my head hurts).
Imagine you’re riding on top of a moving train carriage, standing exactly in the middle of its roof. Suddenly you see lightning strike the front end of the carriage, and simultaneously you see it strike the rear end. You know the strikes must actually have been simultaneous, because you’re standing exactly halfway between them: if the flashes arrived at the same time, they must have left at the same time.
However, from the perspective of someone standing at the trackside, you are moving towards the source of the front flash and away from the source of the rear flash. So the rear flash has further to go to reach you than the front flash. So the flashes can only reach you simultaneously if the rear strike happens first.
Who’s right? Do the strikes happen simultaneously or not?
Answer: both observers are right. Simultaneity, and the order of spacelike separated events, are relative, not absolute.
It's not like we can't see a nova from three different points with the light coming after three different delays due to gravitational lensing.
If we had three black holes in a circle, with some light coming through the middle and the rest lensing around, the middle would seem like a shortcut compared to the lensed light that went around the three, but I fail to see how that, or the wormhole instance, matters at all other than to confuse the observer if they are unaware of the foreshortened distance.
But if a hostile observer sees the spaceship emerge from the wormhole before it enters, and they have access to FTL weaponry (or another FTL wormhole to fire missiles through), they could conceivably destroy the ship before it enters the wormhole, which would be a paradox.
(I think, anyway: this is my layman’s understanding.)
What I don't understand is this time travel thing. Two events can happen simultaneously here and on Proxima Centaur, and both observers here and there will see that event in another system with 4 year delay. So what? Just like a speed of sound lags behind the speed of light, speed of light will just lag behind the actual events that take place. How is this time travel?
Not necessarily. If the wormhole allows FTL travel, then the spaceship's entry into and exit from the wormhole are by definition spacelike-separated events. Such events have no absolute, universally applicable order. Therefore there is at least one reference frame in which the ship leaves the wormhole before it enters it. Note: it does not just appear to have done so; in the chronology of that reference frame, the ship leaves the wormhole, then sometime later it enters it.
See https://en.wikipedia.org/wiki/Relativity_of_simultaneity
Your weapon might reach the location where the ship had entered the wormhole faster than any telescope there could see light emitted from your star, but the ship will still have moved into the wormhole prior to exiting.
Assuming that to be able to send or receive FTL data implies breakage in causality itself seems pretty preposterous.
Seeing billions of years into the past when looking at distance galaxies doesn't imply that if we had FTL we would be able to affect them billions of years in the past. They have continued to move and emit light in all the billions of years since. It just hasn't reached us yet.
Or read these posts on Ask a Mathematician / Ask a Physicist:
- this one explains the basis of the phenomenon: https://www.askamathematician.com/2010/12/q-according-to-rel...
- this one explains the implications for FTL travel (and why it can result in time-travel): https://www.askamathematician.com/2011/09/q-hyperspace-warp-...
[1]: http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-ti...
Lt Cdr Worf is testing the USS Defiant's impulse engines after a refit. He is currently coasting along in a straight line at a constant 0.6c, and passes Deep Space Nine. We'll call time on board the defiant t and time on board DS9 t', and say that the Defiant flies by DS9 at t = t' = 0.
At t = 10 minutes, Worf decides to reward his efforts with a cup of bahgol, only to discover the replicator is on the blink. After about another 10 minutes of pressing various buttons, he gives up and logs a ticket with the DS9 help desk over the subspace network.
Because the Defiant is travelling in a straight line at a constant speed of reference, it is in an inertial frame reference, and it is just as valid to see DS9 as moving away from the Defiant at 0.6c as the other way round, and this in fact is what we must do to work out what time on DS9 corresponds to "now" on the Defiant. At 0.6c, the Lorentz factor is 1.25: so for every 1.25 minutes that passes on the Defiant, a single minute passes on DS9 -- or put another way, for every minute that passes on the Defiant, only 0.8 minutes pass on DS9. So when Worf submits his ticket at t = 20 minutes, on DS9 it's t' = 16 minutes.
Subspace comms are instantaneous, or so close to it as makes no difference, so O'Brien picks up the ticket very soon after t' = 16 minutes. He replies straight away -- "Have you tried turning it off and on again?" -- and sends the response back over the subspace network.
This is where relativity of simultaneity comes in. DS9 is also in an inertial frame of reference, and in that frame it is the Defiant that is moving away at 0.6c, that has a Lorentz factor of 1.25, and where only 0.8 minutes pass for every minute on DS9. So for O'Brien, t' = 16 minutes is simultaneous with t = 12.8 minutes (not t = 20 minutes): allowing for time for O'Brien to read the ticket and write his response, Worf will receive it somewhere around t = 15 minutes -- while he's still tinkering with the replicator. Somewhat surprised, he tries the solution, it works, and he goes off to enjoy his cuppa, never sending the ticket he's just received a response to.
This is why FTL risks messing with causality.
Next off, I feel that this backwards inertial frame of reference is not right. But I'm too lazy to get into actual math so let's put this matter to rest until we get means of FTL travel or information transfer.
Substitute a virtual particle for ‘you’ and it seems that any potential path back in time runs into this paradox.
For some reason I never see this discussed when people talk about FTL travel, maybe I'm wrong?
This is how the twin paradox gets solved. The twin that leaves earth sees the trip as if it was shorter in both directions, so from their perspective it makes sense that they aged less than the twin that remained on earth.
Also, if you had infinite energy and you could travel at the speed of light you wouldn't feel any movement or time passing during your trip, it would feel like instantly teleporting from one place to another. Photons wouldn't feel their existence if they could. From their perspective they are produced in one place and instantly absorbed in another place.
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.
How does time travel get presented in that game? Searching got me unrelated results.
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.
No matter what you do, you will get less work from the system than the energy you put in, and eventually entropy will eat everything. It doesn't matter if it works on paper, we don't live on paper.
So you would have to start your wormhole with both mouths at the same place, and then move one mouth to the new location, with gravity "flowing" between them all the while.
So I'm agreeing with you, and adding how this gravitational slope is created: It's created at the start of the wormhole and changes as you move the mouths of the wormhole, rather than popping into existence at a later time with the two wormhole mouths separated.
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.
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
So there is flat space, de Sitter space, and Anti-de Sitter space, do we know which one most closely resembles the world we observe?
The quantity that measures this is called the cosmological constant. It’s zero in flat space, positive in de Sitter and negative in anti-de Sitter. It turns out from measurements that our cosmological constant is positive but outrageously small, tiny compared to anything else we know about in physics. This is puzzling because we would love to relate it to something we understand already but it’s hard to arrive at a result so small working with quantities that are considerably larger. So there’s an interesting open question about why it is what it is.
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.
Phys.Rev.D 103 (2021) 6, 066007
Published: Mar 9, 2021
DOI:10.1103/PhysRevD.103.066007
> 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.
Then the paper should not have the clickbaity title "Humanly 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.
According to one of the best English translations The Clear Quran, Maarij is translated as "pathways of heavenly ascent" [2]. In the 4th verse of the chapter it's mentioned "through which the angels and the holy spirit will ascend to Him on a Day fifty thousand years in length". That means based on our (human) reckoning it will be fifty thousand years but for angels (or those travel through this pathway or door) it will only takes one day of journey.