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Humanly Traversable Wormholes (arxiv.org)
149 points by apsec112 41 days ago | hide | past | favorite | 129 comments

Did a double-take seeing Maldacena's name on this. He's better known for discovering AdS/CFT, which is the foundation of a lot of modern work on quantum gravity.


> An even bigger problem seems to be producing the wormhole in the first place. It would be interesting to understand whether they can be produced in the RS model. Since they require topology change, this seems difficult.

Has there been any serious (or at least semi-serious) thought given to this? I've perused some literature on wormholes, and it seems like even if you can somehow handwave away the GR energy conditions, the causality violations, etc., when talking about wormholes, everyone's always stuck on the issue of getting one to begin with. Do we know anything about whether the topology of spacetime can be changed?

So far as changing the topology of spacetime, NASA is (or was) investigating it as part of Alcubierre/Warp drive research[1]. That being said, a warp bubble is a far simpler goal than a wormhole.

> According to White, these results showed a vanishing but non-zero difference between charged and uncharged states after signal processing, but this difference remains inconclusive due to external interference and limits in the computational processing.

[1]: https://en.wikipedia.org/wiki/White%E2%80%93Juday_warp-field...

Isn't that changing the geometry, not the topology?

The Alcubierre Drive does not change topology (number of shortest paths), only geometry (lengths of the shortest path).

A few results from a quick search on changing the topology of spacetime. There was a bunch more. It seems to be an area of research anyway.




Follow up question: When a black hole is created, is that a change in spacetime topology?

Topology basics would tell me that fundamentally at least as far as a simple overview goes... a “black hole” doesn’t imply a topological change however a “wormhole” does imply a topological change. One “punches through” the otherwise “flat” space time, creating another “opening” in the surface and increasing the complexity of that space time surface.

To use the proper topology related words... The presence of a wormhole would make a region of space time that contained both ends of that wormhole, non-homeomorphic with that same region of space time without the wormhole. A black hole would not affect how homeomorphic the two regions of space time are, therefore it’s not really a change in the “topology” of the space even if the black hole would definitely change the geometry of that space quite drastically.

A highly nontrivial issue connected with the change of topology associated with wormholes is whether passing through a wormhole reverses chirality or not.

Would a wormhole enable escaping our local group, in theory? From what I understand the current assumption is that we will never be able to travel beyond our local group because of the accelerated universe expansion.

If the wormhole is somehow artificially made, no, because, as far as I understand, you have to drag the exit hole through space, and thus you are limited by the speed of light.

As to naturally occurring wormhole, I don't think there is any accepted and likely ocurring phenomenon that creates a wormhole, let alone across galaxies.

So most likely, no.

The only example I can think of is a wormhole created by quantum fluctuations in the early universe, stabilised by a negative energy cosmic string, then cosmic inflation expanded it to macroscopic size and flung the two ends far apart. But of course the various features of that aren't universally accepted and are not likely to occur, so eh.

Thanks to Kurzgesagt videos I am able to follow this discussion.

If you enjoy Kurzgesagt, you'll probably enjoy Isaac Arthur.


If we ever figure out FTL travel then presumably we could escape the local group, no?

Depends. We might only be able to discover a form of FTL that requires a received that you need to bring over first.

We might find an alien race has already done that

hahah, yeah, like we're gonna find out there's a piece of alien technology buried inside charon or something.

Idea for Sci-Fi novel. Man made wormholes are possible, but we don't have any true FTL travel. This means that humanity's expansion is limited to it's "light cone", at the time we get wormhole tech. What we don't realize is that there could be aliens limited by their own light cones, that by co-opting one of our wormholes they can essentially combine the two light cones into one, doubling their rate of expansion. This provides a hard-scifi setting where there can be a vastly technologically superior enemy, but where humanity still has a chance, as the initial wormholes act as natural choke-points and destroying them would stop the invasion.

A similar process is used in "Timelike Infinity" by Stephen Baxter.


His work generally uses this kind of extreme physics as plot devices and he's one of the best hard sf authors for this type of physics exploration.

It's an interesting idea. Though to be pedantic: this wouldn't double the rate of expansion for long, as soon as our light cones intersect once, their overlap will increase more and more in the future.

you should check out "The Expanse"

According to some highly accurate documentaries I've seen, Giza is a more likely place.

Sounds like Mass Effect :-)

It’s pretty clear why we’re all fascinated with faster than light travel (it makes the Universe feel accessible on our comparatively tiny timescales), but it’s also a sheer display of narrative obstinacy on our part that we continue to try to find loopholes in the rules of the Universe to allow something that so patently ain’t meant to be.

Just build ‘em dormant A.I. probes, set ‘em off on their long lonely drifts, and let the magic of self-reproducing Von Neumann automata take hold once they arrive in a star system with suitable resources!

Unfortunately probes just don't capture the human imagination like manned exploration does.

Perhaps a reason to invest in tech like neuralink? If we eventually merge with AI, perhaps each of those probes will ultimately feel like an appendage that is just slower to respond.

Unfortunately probes just don't capture the human imagination like manned exploration does.

Perhaps a reason to invest in tech like neuralink? If we eventually merge with AI, perhaps each of those probes will ultimately feel like an appendage that is just slow to respond.

If Moore’s Law keeps on going, it’s only a short matter of time before not only can we upload a single consciousness to a probe, but a fully functioning copy of all our society’s members’ consciousnesses. They will either be able to interact and amuse themselves and evolve during the trip, have their threads suspended and thus essentially put into hibernation until arrival, run at some clock-reduced rate so they perceive the travel as being extremely swift, or some combination of any of these items, and then some.

If Moore’s Law doesn’t keep on going... well, then... perception of (very) swift travel it is... ;)

I disagree. http://localroger.com/k5host/pitv.html

I have re read that dozens of times. It's a striking and powerful vision of a possible future.

So the machines put them on a barren planet in the middle of interstellar space with no source of natural light? Seems like a pretty desolate end for humanity.

I'd rather merge my consciousness with the probes and explore, something like this: http://www.skyhunter.com/marcs/GentleSeduction.html

Home is home. But keep reading for more :)

I was curious how we'd go about detecting wormholes:


> In the new paper, scientists write that if a wormhole does exist at Sagittarius A, nearby stars would be influenced by the gravity of stars at the other end of the passage. As a result, it would be possible to detect the presence of a wormhole by searching for small deviations in the expected orbit of stars near Sagittarius A.

I assume that would be a rather large worm hole, for us to detect the gravitational effects on stars that exist on the other side.

I wonder if there's any approach to detecting micro-wormholes closer to our own star? Perhaps by setting up tens of thousands of micro-satellites around (Starlink), blasting radio waves in all directions, and seeing which ones don't make it to the receiver?

There is some gravitational anomaly in our solar system. There was a paper from earlier this year suggesting that it might be caused by a small black hole, although I guess there is no reason it couldn't also be caused by a wormhole.

Edit: Here is the paper https://arxiv.org/abs/2004.14192. I misremembered it as a gravitational anomaly, but that is not completely inaccurate (it concerns the clustering of Kuiper belt orbits). The author (Ed Witten) proposes something similar to what you described for detecting the object.

> I assume that would be a rather large worm hole, for us to detect the gravitational effects on stars that exist on the other side.

Would the size of the wormhole actually affect the amount of gravity bleeding through? And how do we even define the size of a wormhole?

Perhaps we could measure it by the amount of gravity bleed through.


makes entirely too much sense. Altough, I still would question the validity of it, because in cases where there could be VASTLY different masses on the other end. So, the bleed through would only really give an indication of the gravity well on the other side.

All just from my knowledge which is VERY limited.

Yeah, I thought of that after I replied to your comment and I guess you'd have to use some standard mass located a standard distance.

I'd imagine a unit people would use would be the gravitational force exerted by an object the size/mass of the sun located 1 AU away from the wormhole. Though I imagine there would be some more fundamental unit for measuring this kind of thing.

This also makes me wonder: would accelerating end A of a wormhole have the same effect on the environment around end B of the wormhole as holding end A stationary in a gravity field?

Motivation: Can there be in-universe traversable wormholes which can never be time machines?

Caveat: no I have not studied GR, so if I’m asking the physics equivalent of a CompSci fresher asking how to pass the Turing test, tell me.

>Motivation: Can there be in-universe traversable wormholes which can never be time machines?

There was a paper(?) that noted that specific configurations of wormholes (basically tree shaped, no loops) do not allow time travel. I think it or another paper postulated some mechanism for wormholes collapsing if they violate that property.

If there are any naturally occurring wormholes, would they have different external properties as compared to black holes?

The original Ellis drainhole [1] has an attractive end and a repulsive end. They are both spherically symmetric and asymptotically flat, i.e. their gravitational effects fall off with distance like you'd expect, and it wouldn't be immediately obvious from gravity alone that there's anything unusual about the attractive end.

There is a limit case [2] of the drainhole which doesn't gravitate, in the sense that the "attractive" end has vanishing attraction and the "repulsive" end has vanishing repulsion. The wormhole in "Interstellar" was based on that solution [3].

[1] https://en.wikipedia.org/wiki/Ellis_drainhole

[2] https://en.wikipedia.org/wiki/Ellis_wormhole

[3] https://arxiv.org/abs/1302.7170

At the least light should escape a wormhole, and we should "see" what is on the other side. Otherwise I'm not sure how it'd be possible to detect any difference between a wormhole and a blackhole.

Thats the question. Even if wormholes exist, the Universe is under no obligation to make them observable to us. If they are always on the other side of a black hole event horizon, then there would be no way for us to detect them, even in principle.

It is true no physical law obligates the universe to make them observable to us. But, this is the same universe that gave rise to Star Trek, Firefly, and especially The Expanse making so many of us dream of interstellar travel. So, I’d say ethically it’s pretty damn obligated to make them observable :)

/s (Sort of.. not really)

This is the same universe that gave rise to the Tide Pod challenge.

Perhaps in the far future there will be a Find a wormhole challenge where future human teenagers will dive their spaceships into a blackhole they think is in fact the entrance to a wormhoe and scream YOLO just before entering the event horizon.

Firefly is all STL. It’s ambiguous how they got to the system they now occupy.

Wait, really? I haven't watched the show, but aren't there like six different habitable planets involved?

You can't have that all in a single star system.

They kinda try to patch it up in the movie "Serenity". Supposedly the whole show takes place in a gigantic star system full of giants with dozens of moons amounting to hundreds of worlds. They also have some form of terraforming tech to make inhospitable worlds habitable.

Frankly I find that whole set up only slightly more plausible than some kind of FTL, especially since they also have gravity manipulation tech already.

More. All geo engineered. Ambiguous how humanity got to the system though.

That said recent talks about habitable zone around a black hole made me wonder if that would work.

IIRC it's spelled out somewhere that the colonization fleet was generation ships.

I honestly did not remember that.

Good point.

Life imitates art, the universe will surely give :)

If they are undetectable, that is, never ever influence anything in the observable universe, the Occam razor instantly shaves them off.

Would we not be able to infer their existence by finding a white hole? I do see how calling that a detection could be a stretch.

Actually, GR describes white holes, along with black holes, but no ideas how a white hole would form in the real universe apparently exist.

If they're not observable then they're all unidirectional from here to somewhere over there (or from there to here but there is nothing over there, not even vacuum fluctuations).

Would the entry and exit points be orbiting another body somewhere?

They could be. Absent other forces acting on them, they would move along geodesics, like everything else. Near an ordinary massive body, geodesics are orbits.

Popular example: the wormhole in "Interstellar" was orbiting Jupiter.

> Using them, one could travel in less than a second between distant points in our galaxy. A second for the observer that goes through the wormhole. It would be tens of thousands of years for somebody looking from the outside.

Unless the energy requirements are lower, it sounds like this isn't much better than just traveling close to c (assuming you had adequate shielding).

However, with a wormhole you can step back through it.

Which, yes, in this case would send you back in time. No problems there; it isn't a causal loop.

The stepping back in time would make it a causal loop if you were able to observe something happening in the past (light traveling from the source) from the exit side, then go back through the wormhole to change this.

To prevent this, the observed wormhole traversal time would need to be slightly faster than the speed of light, because then you also couldn't go back far enough to change something you already observed (assuming the "time" here is symmetrical to the time it takes going in the other direction).

However there are other problems: What happens when I have 2 matching wormhole pairs, each exit being located to the entry point of the other. If I step back through the exits again and again can I go back in time as far as I wish?

Not sure I understand, why is it not a causal loop?

The wormhole sends you back in time, but not far enough back to arrive at your point of origin before you left.

If you could treat the wormhole like a magic door that takes you across space, then two people looking at each other through the door wouldn't see anything unusual. One would be in the distant future, by the galaxy's clock, but not by the wormhole's.

So going through in one direction takes you into the future, and the other takes you into the past, but it's a constant offset. The size of the offset depends on how you moved the other end to where it is.

It's true that with multiple wormholes you could try to create a loop, though. That would probably fail due to virtual particular loops.

> 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[a]

> [a] This also implies that they can not be converted into time machines

This doesn't seem like "classical" wormhole, right?

But it could still be useful. As a source of energy, propulson for example. Sink one end into a star and put the other where you need power.

If the wormhole travels all the way to the core, then it will relocate about half of the star to the other end. If the wormhole can be closed, then it would act as a giant pizza cutter for stars. Potentially very useful to defuse supernovas. Or to utterly annihilate your enemy's stronghold...

What would happen is more complicated to answer if the wormhole stays open. The star would effectively have double the surface area, but apart from that, the consequences for the star's future development elude me right now.

I can’t believe I’ve never thought of that... wow, what a ‘blast’!

Wouldn’t it cause the core to collapse inwards though, as it would basically provide a “safety valve”-type release (though I presume if you were to place it on the edge of the fusing core, it would basically replace a patch of pre-existing surface area at the expense of convection and radiation pressure above taking a nose-dive).

This reminds me of a great hard sci-fi book, Greg Evanses Diaspora.

Any suggestions on what to learn so that I can understand this paper? I would love to be able to fully comprehend this paper.

The following assumes you are comfortable with Linear Algebra, Calculus, and Basic Physics (Newtonian Mechanics and Thermodynamics) at an early undergraduate level.

Start with the Lagrangian and Hamiltonian formations of classical mechanics (Landau & Lifshitz - Mechanics). Then, study Quantum Mechanics (R Shankar - Quantum Mechanics). Statistical Physics while not key here, will be useful for building up an intuition (Landau & Lifshitz - Statistical Physics is good). Classical Field Theory, i.e. Electromagnetism should now be learned (J.D. Jackson).

Then, I'd recommend learning Calculus on Manifolds (Spivak) and Differential Geometry (I can't remember a good textbook on this right now).

If you're at this point you will now have a solid understanding of the maths needed to know GR and QFT. Zee has two good pedagogic books for these "Einstein Gravity in a Nutshell" and "QFT in a Nutshell". Once you know QFT, read a textbook on the standard model.

That'll get you most of the way there. Strictly speaking, you could do possibly learn a lot less to understand this paper, but to be able to pick and choose which parts of the above are actually needed would require a significant amount of work in itself.

For the uninitiated, Jackson's EM book is considered the book on E&M. There really is no other book to learn from, if you want to learn EM correctly.

It is also horrifically difficult even for dedicated PhD students at top 50 physics programs.

Story time:

As an undergrad I had a TA that was in the astrophysics program. He told us a story of a final he had to take in his EM class, using Jackson, of course. The final was to present his solution, if any, to the PI. Pass or Fail. He went home and started work on the problem about three weeks before the due date. When his wife would go to work, he would be sitting at the kitchen table, when his wife came home, he was still at the table. For weeks straight. As the deadline got closer, he started sleeping less and working on the problem more. In the last few days, he stopped sleeping entirely. Eventually, he gave up on the problem and took the bus to campus to report on his failure and receive the Fail. Once his deprived mind relaxed on the bus, he had a Eureka moment and was able to solve the problem. Unfortunately, his sleep deprivation caused him to hallucinate. While presenting his hastily put together findings, he was trying to dodge imaginary bats, deal with imaginary blaring car horns, keep from falling asleep while standing, and present very nuanced and complex EM equations. After the presentation the PI said: "Pretty Okay", and passed him.

This is considered a slightly atypical end to a semester with Jackson.

How bad Jackson is depends highly on which problems are attempted and in which context. The content is fine and perfectly understandable. We used it during my third year of undergrad. Homework mostly consisted of the easy-to-medium problems, and self-study could focus on the medium-hard.

Between that and the highly-abstract statistical physics course (it started with an introduction to differential forms), I learned more in my third year of college than in any other.

That said, I now work in IT.

This is a really great list. I'm currently about midway through a very similar list that I arrived at through trial and error. It would've saved me a lot of time to have seen this a couple of years ago :).

I've got a couple additional suggestions/pieces of advice: First, if Calculus on Manifolds is too advanced Munkres's Analysis on Manifolds is very good and covers mostly the same material. Second if you are shaky on trigonometry it's worth taking a couple of days to relearn it since trig identities and manipulations are used all the time. It makes you feel a bit stupid to review stuff you probably learned in middle school but if you're like me and hadn't used this stuff in years the review will save you lots of time down the road. Third, get used to working problems. It's easy to fool yourself into thinking you understand something because you can follow the worked examples, but you can't actually apply it. I try to do at least a few exercises from each chapter. Shankar's QM book is awesome because the exercises are interspersed with the text, so doing them as you get to them really helps you understand the material. I wish more textbooks had this format.

Munkres is also a great book! It slipped my mind when making the list.

Looking back, maybe I should also have added a group theory textbook.

> This is a really great list. I'm currently about midway through a very similar list that I arrived at through trial and error. It would've saved me a lot of time to have seen this a couple of years ago :).

Thanks, but I wouldn't have had the list a couple of years ago! I finished my undergrad in maths/physics about a year ago, so that's a rough compilation of the books I found most useful. Some were recommended by lecturers, others I found on my own.

I have read part of Zee's Group Theory in a Nutshell for Physicists and it seems pretty good. (Zee is a great writer). It's my only exposure to group theory though so I'm not sure how it compares to other books.

There might be better or more modern references for Differential Geometry but I enjoyed Barrett O'Neills' book.


Also Misner-Thorne-Wheeler and Wald's book on General Relativity.

Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry.

One note on expectations - each of the domains you mentioned is typically an upper level undergraduate course (except for the first three). These courses usually progress at a rate of maybe 10 - 15 pages per week (~200 pages of a textbook covered in 16 weeks). It's genuinely hard to absorb this material in that amount of time, and unless you're exceptionally capable you should assume it will take you even longer under self-study.

If you proceed with doing this, make sure you work through at least a few of the exercises at the end of each chapter of each book, and try to compare your solutions against solutions you find online.

This is not to discourage anyone - studying all of this will probably be very rewarding! It's just a lot of work. It takes a massive amount of effort to get to the point where you can understand all the prerequisites needed to follow a research paper in modern math or physics.

> Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry.

Maybe. I'm just going by how all of these were taught during my undergrad. IIRC it doesn't cover metric spaces at all, but in fairness an introductory GR course will cover that; CoM will set up the mathematical context for you.

Counter productive way to travel as it takes longer to use this worm hole to get to point B using conventional travel. But it seems like a good way to travel to the future. Just skip to point 4 in the doc.

It sounds like things falling into wormholes accelerate terribly -- a natural particle collider? Should we be able to see the detritus?

Bro, what's negative energy?

I thought this was simple. You can't go faster than light.

If you go through a wormhole (Or just send information) you go faster than light (Ignoring Hollywood's incorrect movie Event Horizon where you just bend paper), so you go back in time.

So it's not possible.

Because you can kill you father (or something mathematical with information) which is a paradox.

End of story.

I don't understand why "faster than light" automatically implies "go back in time". If it takes me 10 seconds to travel 10 lightyears, then that means I should still be traveling forward in time (specifically by 10 seconds), no?

Like, it might apply on a "moving through local space faster than light" sense because physics is weird like that, but the whole idea behind wormholes is to shrink the actual distance traveled (from the traveler's point of view).

Because of relativity, you can have locations A and B in spacetime and a frame of reference such that A happens before B and a different frame such that B happens before A.

So, if you're at A, you can travel faster than the speed of light and arrive before B happens. Then, after B happens, you can travel back to before A happens.

I don't fully understand;

> if you're at A, you can travel faster than the speed of light and arrive before B happens

But if we assume A and B happen "at the same time" and your frame of reference is closer to A than B right? As the light showing B happening is still traveling to the observer while A has already arrived.

If that's the case,

> Then, after B happens, you can travel back to before A happens.

Doesn't make sense, If the following happens:

> Traveler starts at A, jumps the wormhole to point B and immediately jumps back to A, arriving 10 seconds after leaving A.

The observer would see:

> Traveler starts at A, arrives back at A + 10 seconds and a while later, they are seen exiting and entering the wormhole at B while also being visible at A (Assuming they didn't do anything after exiting there)

These kinds of discussion only make sense to me with images rather than words, but:

> But if we assume A and B happen "at the same time"

Is something you can’t do in relativity. If you see A happen before B, at the same time as B, or after B, depends on your motion relative to A and B.


Wait whaaaat? This is the first I've heard of this. I've a vague understanding of causality. I thought the arrow of Time moved in one direction only? How can A come before B come before A from, from one observer?

Novikov explains it approximately this way.

Suppose you have a wormhole between points A and B. So from A to B - and from B to A - you can go by two different roads, one is pretty long (say, 1 light month), and another is very short (negligible distance).

Next, suppose B end swiftly rotates around point A, so fast that time in B goes slower than time in A. This means clock in B is going slower than in A, and over 20 years in A only 10 years will pass by clock in B. That can be confirmed by observation - telescopes in A will see slower clock in B, telescopes in B will see faster clock in A (it's B going around A, not vice versa).

That is, if we're talking about telescopes, looking through "regular" space. Since A and B are also connected by the wormhole, looking through wormhole will show us that clocks are synchronized. Over the wormhole, A and B are not moving, so clocks don't deviate from one another.

We can stop B flying around A now. Now suppose B clock has accumulated 10 years of difference from A clock - again, looking via "regular" space. We're leaving point A, flying to point B over the "regular" space and spending 5 years - way slower than speed of light, so our clock is practically synchronous to A clock. At the start of flight, A clock show 20 years, and B clock is 10 years, and by the end of flight A clock is 25 years and B clock is 15 years. After arriving at B, we jump into wormhole and get back to A, when A clock shows the same as B clock - that is, 15 years. According to A clock, we left at 20 years and came back at 15 years. Time travel.

This is the scenario the author Stephen Baxter used in the book Timelike Infinity.

Wormhole technology on a ship sent in a relativistic journey circling the solar system, used to bootstrap humanity and influence it in the past.

There is a catch, this sort of time travel like many others only allows one to go back as far as the creation of the wormhole. Sort of like in Primer, it isn't a general form of time travel. You can take the wormhole forward, or from the other end backwards, but not prior to the time it was created.

Nice explanation, this made more sense to me than most of the explanations I have heard about this before. But, wouldn't this just constrain the possible features of a wormhole? The issue is fixed if traveling/observing through the wormhole has the same time dilation:

Both through telescope as through the wormhole, the clocks can be observed to go slower. After 20 years at A, both the telescope as observation through the wormhole show 10 years have passed at B.

If we don't stop B from spinning: The regular space traveler takes 5 years, as observed from A, to reach B, so reaches B at A:25 years, B:12,5 years. If they leave immediately after arrival, they'll end up again at A at A:30y, B:15y. Otoh, the wormhole travel leaves at A:20y ends up at B at 10y and gets back to A immediately: A still at 20y and B at 10y. Mixed travel:regular travel starts at A:20, B:10y, reaches B at A:25y, B:12,5 and jumps back through the wormhole at the same time as seen from A and B.

Exactly ! Why don't we suppose traveling/observing through the wormhole has the same time dilation ?

I've heard of FTL=time-travel a couple of years ago for the first time and I would love to be able to argue with someone knowledgeable about it to understand. I hoped this HN thread would have answers. However all the answers here seem to have holes in same.

I'm starting to wonder if FTL=time-travel isn't like Schrödinger's cat: a hypothetical thought experiment terribly misunderstood by the masses.

If travel through the wormhole takes exactly as long as travel via space, what kind of wormhole is it?

> Since A and B are also connected by the wormhole, looking through wormhole will show us that clocks are synchronized.

Can you please elaborate on that a bit more? That's the part I don't understand. Why would you observe synchronized clocks when looking through the wormhole?

Space in the wormhole is regular space. So we have regular properties of space and time - and if A and B are separated by a short distance, and they don't have accelerated motion against each other, the clocks have no reason to deviate.

> Why would you observe synchronized clocks when looking through the wormhole?

I think it's the same question as why we observe diverging clocks when looking via the "regular" space. Einstein provided answers to that - in "regular" space (that is, outside the wormhole - the space in wormhole is also space, with properties of space, including relativistic ones) we have accelerated motion, which is absolute and slows down clock in B, but not in A. In "wormhole space" we don't have that, so there is no reason to have, or observe, that difference. I think, other than entrance to the wormhole, you can't really say which of paths is "regular space" - the long one or through the wormhole, as you may argue that in fact A and B are close by, but they also have a wormhole with really long path - and the rest of the Universe - inside.

So let's make this assumption explicit: A and B are far apart in distance, and the time between them (in seconds) is smaller than the distance (in light seconds).

This allows different observers to reasonably disagree about which came first. Basic relativity.

Alice sees A happen before B. Bob sees B happen before A.

Everyone will agree that once they saw one event, it was too late to reach the other event before it happened, even at the speed of light.

But faster than light? Then you could get there before it happens.

> How can A come before B come before A from, from one observer?

An observer wouldn't see that.

What they might see is someone exiting a wormhole before they entered it.

Let's say Alice observes A, then wormholes over to cause B. And Bob sees B, then wormholes over to cause A.

Anyone watching from the outside will see a logical-seeming series of events: Alice and Bob exit wormholes and each cause an event. A "different" Alice and Bob watch the events and enter wormholes.

Some observers will see Alice exit before entering. Some will see Bob exit before entering. Some will see both. That's obviously weird. But they'll see nothing weird about A and B. A and B are perfectly normal.

But what makes this a paradox/time traveling?

We are talking about observers seeing wrong order (leaving the wormhole at point B before entering at point A), but that's because they are observing everything at a delay or something like that, but I don't see any time travel happening in this example or any order of flying through wormholes that I can come up with.

Alice sees A then causes B. Bob sees B then causes A.

That means that when you analyze the whole system, A causes A. There is a time loop. You could easily make this into a paradox, too. What if Bob goes and prevents A instead? What if events A and B are actually the birth of Alice and Bob, and after they leave the wormhole they land on the other planet and become each other's parents?

> This allows different observers to reasonably disagree about which came first. Basic relativity.

that happens all the time. Lets set aside the Earth being curved for a moment - I'll use real cities but these could be asteroids floating in intergalactic space at the same distance.

I'm in London, I see an event happen in London, Moscow, New York and LA all at the same time, at 12:00:00.500 UTC according to me.

  London-Moscow 9ms
  London-NY 66ms
  London-LA 103ms
Lets imagine they are in a straight line too and all in the same reference pane.

The events actually occurred in the follow order, at the following milliseconds past 12:00:00 UTC, according to our NTP synced clocks.

  LA: 397ms
  NY: 434ms
  Moscow: 491ms
  London: 500ms

From LA's point of view they would see

  LA: 397ms
  NY: 471ms
  London: 603ms
  Moscow: 603ms
From Moscow's POV Moscow: 491ms London: 509ms NY: 509ms LA: 509ms

From NY's POV LA: 434ms NY: 434ms London: 566ms Moscow: 566ms

So LA thinks LA was first, NY was second, London and Moscow co-timed third.

NY thinks LA and NY were co-timed first, then London and Moscow co-timed third.

Moscow thinks Moscow was first, everywhere else was second.

London thinks everywhere was first

So we disagree. So what.

Now sure, if your wormholes are in different reference frames you can get confusions, but why would a wormhole with two ends fixed in the same reference frame and neither end accelerating allow passing information backwards in time?

I know relativity says there is no universal clock everyone agrees on, but isn't that only applicable for points in different reference planes (and even then you can surely adjust if you know your relative velocity to the universal point)?

Back to cosmic scales. Point A, B, C, D, all 10 light years apart, same reference frame

Point A event happens at t+0

B sees at t+10, C and t+20, D at t+30.

D also has a wormhole to A, so sees the event in the wormhole at t+0, and causes a separate event (light up a sign saying "A event just happend")

C would see that D is flagging the event at t+10, but have to wait until t+20 to see it. Why is that bad?

How would D get a signal back to A before t+0. I guess a spaceship in a different reference frame (say v=0.99c) at D could see (old fashioned looking out the window) the "event just happened" message, then use a separate wormhole to send a message to a spaceship at A travelling in the same reference frame as spaceship D. Spaceship A could then light up a message, which planet A could see, but would planet A see that before t+0 on their local clock?

One wormhole with stable end points never causes time travel. You get a privileged reference frame type of FTL travel, which is completely safe. The issues arise when both spaceships have the ability to go faster than light in their own reference frame.

OK, so set up 4 starbases (called A, B, C, D), each 100 light hours from each other in a stable reference frame. They have a wormhole from A to D.

Wormhole from 1 light minute south of A, to 1 light minute south of B, travelling at 0.99c northwards according to the starbase reference frames, both ends in the same reference frame as each other, but in a different one to the starbases.

Everyone looks at A for the time, it says "time = 1200h" at A, B sees "time=1100h", C sees "time=1000h", D sees "time=900h", but they know the distance so can work out that it is currently 1200h, so all set their clocks, which run at the same time as they are in reference frames.

Event occurs at 1200h at starbase B. Event is seen at starbase A and C at 1300h.

How can you use the wormhole to pass information back in time. Assume both ends of each wormhole are in the same reference frame, but aren't changing reference frame (no acceleration)

First off I have to admit I'm having a bit of trouble nailing down the exact math, but I'll do my best.

If we arrange the starbases on the north-south line, I believe that the roaming wormhole would allow a ship to observe the event at starbase B, then jump through and pop out next to starbase A at roughly 1115h. (If that number is wrong, then adjust the wormhole velocity I guess.)

In this scenario, you can't violate causality. You're 100 light hours from B, and the A<->D wormhole is too far away to help.

But if you changed it so that B, C, and D are only 10 light hours from each other, you could then take the wormhole to D. Now it's roughly 1116h, and you're only 20 light hours from B. You can send a signal about the event at 1200h, and it will arrive at 1136h. You sent information back in time.

OK, so 10 light-hours apart

120h on the wall at starbase A

starbase B looks at starbase A, sees it's 110h, but the distance is 10h, so sets their clock to 120h

starbase C sees starbase B's clock as 110h but knows it's 10 light hours away and A as 100h and 20lh away, so sets their clock to 100+20h or 120h

starbase D also sets their clock at 120h

event occurs at 200h wall clock in starbase B

event is seen at 210h wall clock in starbase A, 210h in C, 220h in D

OK, your spaceship could tell starbase D the event has occured when it pops out at t=201h, but so what. How does starbase D get a message back to starbase B back before to get them to prevent the event from occuring?

Where did you get 201h? And you completely changed the layout?? I didn't want you to change the distance between A and B.

But I can make something work with the new numbers. Here:

At 120h according to the starbases, everyone sets their clocks, just like you said.

Event occurs at 200h in starbase B.

A near-light-speed wormhole is passing by B and D in its own reference frame. As far as it can tell, the starbases have their clocks synced really badly. In this wormhole's reference frame, it's simultaneously "200h" at starbase B and "182h" at starbase D.

A messenger ship launches from B right after the event, goes through the wormhole, and lands on starbase D at 183h.

So far, we're paradox-free. We can tell D the results of the event before the light reaches them, but that's not new. People do that all the time with the normal wormhole. And since we're 20 light-hours away from B, any signal we send from here would arrive too late to affect anything.

But then the ship takes the normal wormhole, the one that's always connecting A and D. That wormhole always agrees with the clocks onboard the starbases. The ship enters at 183h, and exits at 183h, now at starbase A.

Then the ship sends a signal toward B. The signal arrives at B at 193h. This is the same location as the event, 7 hours before it happens.

It can't, if that observer always moves slower than the speed of light in all reference frames.

If events A and B are close to each other in space time (light from one can have arrived at the other by then), then the ordering is fixed. If they are far from each other (light won't get from one to another by then), then time gets weirder.

The notion of what is simultaneous to what gets weird. If you and I are moving relative to each other, we're going to disagree on which distant events happen at the same time. If that happens, then whether something's happening now might change depending on reference frame. The ordering can be t(A) = t(B) or t(A) != t(B). Since no frame is privileged, we can also change the other way around, so t(A) != t(B) can be t(A) < t(B) or t(A) > t(B) depending on reference frame.

It's only flexible like that for things that could be simultaneous in some frame, which at least in special relativity means light from one can't have gotten to another yet. I never took general relativity, so who knows how it works in that setting.


Relativity of simultaneity was definitely a wild concept for me in physics class. The idea that a near-c train is longer than a tunnel to its passengers and hence is never fully inside the tunnel to them but is, after relativistic compression, shorter than the tunnel and hence at one moment entirely inside it to a resting observer blew my mind.

I suppose it requires a stretch of the understanding of what it would mean to go "back in time". If you were to literally travel backwards in time, but not retain knowledge of the future, that would be useless. What is desired is to be in a state where you are at time T with knowledge from time T+1. So, by traveling through the wormhole, you would arrive there with knowledge that could not have reached it from the direct path until some time later. You might even travel through the wormhole, observe your own past, and return back again.

But yes, generally speaking, there is no known means to travel back in time before the moment of creation of the time machine itself.

A path is a collection of points in space and time. Certain collections of points in space and time can be said to be all simultaneous to each other. If your path exceeds the speed of light, then to somebody, your path is a collection of simultaneous positions (at least in special relativity. I don't know GR)

My notion of simultaneity can be different from that somebody's. If they think event A and B are at the same time, I might think they're different. Waving hands, no frame is privileged, so I could think they're different as (A < B) if I'm moving this way, or (A > B) if I'm moving that way (relative to this person).

That means that the events this person thinks are simultaneous (you leaving and you arriving) can appear in either order to others depending on reference frame. It can look like you arrived when you left (same time), you arrived after you left, or you arrived before you left.

I don't understand why "faster than light" automatically implies "go back in time". If it takes me 10 seconds to travel 10 lightyears, then that means I should still be traveling forward in time (specifically by 10 seconds), no?

Say you had a faster than light transmitter that can send signals with (from your perspective) twice the speed of light (2c). If the receiver has no relative motion, everything seems to work fine. But if the receiver moves away from you fast enough (I think 0.5c should do it, but don't quote me on that one), then, from the receiver's perspective, the transmission will happen instantaneously. If the receiver moved even faster than that, the signal would seem to arrive before it had been sent(!), and if they had their own faster-than-light transmitter, they could relay the message back into the emitter's past.

> But if the receiver moves away from you fast enough (I think 0.5c should do it, but don't quote me on that one), then, from the receiver's perspective, the transmission will happen instantaneously.

Why? I mean, I get that time is progressing more slowly for the receiver because it's traveling at relativistic speeds, but instantaneous arrival of anything doesn't seem to follow from that, and therefore...

> If the receiver moved even faster than that, the signal would seem to arrive before it had been sent(!)

...neither does this.

Further, the whole point of wormholes (in the context of superluminal travel/communication) is that neither the signal nor the receiver is actually moving at relativistic speeds, but rather that the signal is instead taking a shorter path between two points in spacetime specifically to avoid having to move at such speeds from a local perspective.

You're right and the person you're replying to is wrong. PBS spacetime videos on Youtube explain it well

Best show on YouTube. Such a PBSST addict

Yes you will still be travelling forward in time just that your relative time will be slower at speeds approaching the speed of light. So fundamentally you won't be going back in time but much forward in time than you observe. Checkout minute physics YouTube channel course of relativity https://youtu.be/1rLWVZVWfdY

You might be interested in my blog post about it: http://forwardscattering.org/post/36 (Special relativity, faster-than-light communication, and absolute time and space)

Your blogpost might benefit from explaining further the following line: "Special relativity says that the rocket has a different coordinate frame than the space stations. In particular the x axis, which corresponds to all the points in space at the same rocket-time, is not the same as the x-axis for the space stations."

I'm on the lookout for an explanation of why FTL=time-travel that I'll finally understand. However in your blogpost my limited knowledge of Special relativity fails to make sense of the whole argument.

You start from Earth and go two light years in one year using an FTL drive of some kind.

A day before departing you look and you see your spacecraft in spacedock and, peering through a telescope, your two-year-old spacecraft in orbit around your destination. You’ve been watching it for a year already.

From your viewpoint prior to launch, there’s two of you, and the distant one is old.

EDIT: I’m wrong, and stand corrected. Relativity is so very slippery!

I don't think this is right. You leave at t=0 and arrive at your destination at t=1 year. It then takes two years for the image of your arrival to travel back to Earth, where it can be perceived at t=3 years.

However, when you arrive at your destination, you can look back at Earth and see an image of yourself 1 year prior to your departure.

Yup, I think you’re right, and that I’m wrong.

BTW, the other weird thing about this scenario is that if you look backwards along your trajectory, you will see a movie of your journey playing in reverse!

Also, in regard to your edit: this doesn’t really have anything to do with relativity. Newton would’ve come to the same conclusion.

My reference to relativity was to indicate that I thought it would lead to different conclusions than the Newtonian case.

As for the two images, it’s well covered on PBS Spacetime’s overview of the Alcubierre Drive from several years back that if a bystander were to observe a FTL craft traverse their field of view laterally, they’d indeed see two images, each heading in opposite directions, as you indeed allude to.

> 10 seconds to travel 10 lightyears

You can look at the equations, but you will literally go back in time if you do this. This is simple I believe. Go there, go back, you've gone back in time, up to the SoL time slows then after it reverses. But you can't go 10 seconds to travel 10 light years, speed of light is absolute so no time travel for you.

People believe wormholes are a loop hole because they puncture space or something something Event Horizon.

This I also believe is untrue. Go through a wormhole, either it takes the equivalent of the speed of light to get there for the true distance, or it's not possible to send information through.

> This is simple I believe

If it was simple then I wouldn't be asking.

> Go there, go back, you've gone back in time

How? If it takes me 10 seconds to travel 10 lightyears, then I should've gone forward in time by 10 seocnds, no matter if I'm measuring by my own frame of reference or an observer's (i.e. if it's my stopwatch v. an observer's stopwatch that's counting the seconds).

> But you can't go 10 seconds to travel 10 light years, speed of light is absolute

And it's never been adequately explained to me why that is.

> I thought this was simple. You can't go faster than light.

People also thought that time is universal and common for all places.

According to history of physics, theories usually have limits to their applicability. For relativity theory, currently known limits are in the presence of large gravity centers; but it doesn't mean that those are the only limits. Even putting aside elegant, in my view, proposals to circumvent speed limit, like Alcubierre drive, we don't know if this speed limit is "absolute". It's part of very well working theory, yes, but we don't know what we can learn yet.

Imagine this as a counterexample. A wormhole could connect two distant points as being the same time in some specific frame. Go through either end at t=0, come out the other at t=0. Go through at t=1, come out at t=1. If that's the only FTL travel there is, then there are only two options to get back to your original position. The short way through the wormhole, but we've established that causality is maintained in that direction. Or the long way, but it'll take long enough that in any frame you get back after you leave. Either way, you can't get back before you left and can't affect things before you left.

You get into trouble if there are two wormholes like this that connect points in different reference frames. You could go through the first wormhole at (t=0, x=A) to (t=0, x=B), then the next wormhole at (t'=1, x=B) to (t'=1, x=A), where I'm using t' as the time in this second wormhole's frame. Even if (t=0, x=B) is before (t'=1, x=B) in all frames, there could be some t' frames where (t'=1, x=A) is before (t=0, x=A), letting you return before you left. But at least there's some scenario (only one wormhole exists) that doesn't have tricky causal implications.

And there are other setups where even going back in time isn't paradoxical. Take this viewpoint: You just can't kill your father when you go back. "It didn't happen" is the same as "It won't happen," so it's a non issue. If you go back and try to kill him, then instead of you succeeding, whatever happened will happen (which we already know wasn't your father dying). Mathematically, it's a loop. You can't continue forwards around a loop to get somewhere that isn't behind you. As a tautology, the only loop-containing solutions to the physical equations would be the ones containing self-consistent loops.

Well, wormhole is not about how to travel faster than light, but about creating a shortcut between 2 points in a certain dimensional space by using a higher dimensional space. The most used explanation is using a piece of paper, the shortest route to travel between 2 points in a piece of paper is a straight line. But, we can shorten it by folding that paper and create a hole that connect the 2 points through the 3th dimension.

Distances between objects can increase faster than speed of light (due to expansion of space, for example) the problem here is that with wormholes you might have causality violation (also not sure if the universe’s topology supports holes).

What's to say we live in a world without paradoxes?

I think that might be stretching what it means to be fast. Wormholes seem to be about warping space. Rate of motion doesn't enter into it.

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