How would you arrange wormholes throughout the galaxy so that they don't violate the Chronology protection conjecture?

Question

Any form of FTL, including traversable wormholes, allows backwards time travel. (EDIT: I mean going backwards in coordinate time. We get to closed timelike curves later in the post.) My world has traversable wormholes, so I just bite the bullet and say yes, anyone with the ability to use wormholes can travel back in time as much as they like. For example, if you want to appear on the moon 1 second ago, you can set up wormholes to do that.

How do we deal with time travel paradoxes then? Well, there is one rule about how the wormholes work. You can't arrange them into closed timelike curves. The moon example is fine, because even though you can go to the moon 1 second ago, it takes you at least 1.28 seconds to get back to Earth, so you can't actually change your own past using them. In fact, most things we think of as time travel just don't work; time travel is only allowed because physics demand it, but we take away its ability for you to influence your own past.

What if you tried to make a wormhole that took you to the moon 2 seconds in the past? Well, if you tried to set up the wormholes to do that, the wormholes would just blow up. Quite violently in fact. All the wormholes are forced to obey the Chronology protection conjecture in my world. If you try to arrange wormholes close to violating it, enough wormholes will blow up that the violation is never reached (usually more). Quoting from that Wikipedia article:

Initial attempts to apply semiclassical gravity to the traversable wormhole time machine indicated that at exactly the moment that wormhole would first allow for closed timelike curves, quantum vacuum fluctuations build up and drive the energy density to infinity in the region of the wormholes.

Anyways, with those rules, humanity wants to take over the galaxy with these things, but without the wormholes blowing up. What is the most efficient solution to colonizing the galaxy with wormholes that obey Chronology protection?

• There are currently wormholes that can take you from Earth to Alpha Centauri, 4.2 light years in the future. The goal is to build wormholes from Alpha Centauri to every other solar system in the galaxy (the government does not want people building all of these wormholes from Earth for alleged safety reasons).
• Around Alpha Centauri, there is a machine that creates wormholes. At creation time, the mouths are created at almost the same point in spacetime, but after that can be separated and carried wherever. EDIT: The machine specifically can create Ellis wormholes (and Ellis drainholes).
• The spaceships that carry the wormholes are traditional chemical rockets. However, they can go at great speeds because fuel and other resources can be delivered through the same wormhole it is tasked to carry. Also keep in mind that this means the wormholes will be time dilated significantly. In fact, that is a good thing, because it allows you to use the wormhole before its completed!
• An end of one wormhole can traverse through another wormhole.
• The only real restriction on how they are placed is that if they are arranged in such a way that they would form a closed timelike curve, they violently explode instead. However, it is also preferable for efficiency reasons to place them in orbits around things (because then the machine only needs to stabilize the wormhole, not levitate it).
• Wormhole Inc. has access to the galaxy's finest time-dilated quantum super computers and are willing to spend years on mission planning, so you have time to find a solution. Cheaper and faster is better.

EDIT: The question is how Wormhole Inc. can most efficiently distribute wormholes according to these rules, not how to change the rules to better accommodate Wormhole Inc. (although that is itself an interesting question).

Answer 1

The classic Traversable Wormhole FAQ goes into wormhole networks in some detail. Essentially, a wormhole network defines an "Empire time" of mutually spacelike-separated points which have, thanks to the wormholes, a shared simultaneity. Creating such a thing without violating the CPC would require some amount of planning; the FAQ suggests sending probes containing wormholes at high sublight speeds, using them as "seeds" through which you send more probes branching off in different directions to fill the entire space. Creating a plan for this sort of staggered penetration shouldn't be too hard for your quantum supercomputers.

The biggest problem I think you'd have is that, once you started off, pretty much everything would happen all at once. At high speeds, the amount of time dilation on the probe end of the wormhole would be significant, so you'd be able to go further and further in less and less time as the probes accelerate. Accelerating at 10g (and they could accelerate continuously, since you can pump fuel to them through the wormhole), in a year after launch your wormholes would be about 15 ly away; but only a year later, they'd be about 3000 light years away, and it'd only take 15 more months to get to the Andromeda galaxy. If you want to keep up a uniform probe density, you'll have to shoot more and more branch probes through more and more frequently as time goes on; either that, or throttle the acceleration based on the production rate for new wormholes.

Answer 2

The simplest solution is to assume that the 'laws of physics' including those pertaining to the creation of wormholes (WH) prevent anyone from using WH that violate the chronology protection conjecture (CPC). As as a result the CPC is no longer a conjecture but rather a fundamental principal of physics.

You can even 'write' into the background of your story that experiments conducted with (mirco) wormholes shortly after their first 'discovery' proved conclusively that any attempt to violate causality using one caused the WH concerned to 'collapse' the instant any attempt is made to send information through it.

It doesn't have to be a violent explosion either. The instant a particle or photon enters a micro-sized CPC violating WH it 'collapses' in on itself and/radiates out its (tiny) mass as sub-atomic particles.

So if you assume every 'large'/traversal WH starts off life as a 'seed' or micro hole that has to be actively expanded from a quantum scale anomaly up into something useful over time there won't be a violent explosion because you can't grow a CPC violating WH. You can either shield it from a CPC event or 'grow it' but not both at once. This means the only WH you can 'grow' are ones that don't violate CPC.

PS: and no-one would try such an experiment even if they could with a macro sized WH because the dam things are hugely expensive to build - requiring an investment in exotic matter/negative mass/upsidasium/ whatever to expand upwards in scale. It would be like risking blowing up the LHC just to reproduce the same results you would get with $1000 worth of equipment in any run of the mill science lab.

Answer 3

The network topology you want is a tree. Earth is the trunk. Branches split off at Alpha Centauri. Each branch may split into as many branches as it likes, but they cannot connect to other branches.

What this means, practically, is that any world is allowed to send wormholes to any neighbouring solar systems that does not have any wormholes yet. But they are forbidden from sending wormholes to a system that is already connected to the network. Each system may have one uptime gate and as many downtime gates as they like.

For ease of navigation, you can let systems assign network addresses simply by counting their wormholes. Earth's address is 1. Alpha Centauri's address is 1.1. Alpha Centauri's connections: Beta Centauri is 1.1.1, Proxima Centauri is 1.1.2. And so on.

If you were at 1.1.2.6.2.5 and you wanted to get to 1.1.2.3.8.1 then you would immediately know that you have to go through the single uptime gate in each solar system until you get to 1.1.2 at Proxima Centauri, then follow the numbers downtime to 1.1.2.3, 1.1.2.3.8, 1.1.2.3.8.1.

This network will put Alpha Centauri at the centre of more galactic trade routes and communication lines than any other system. After a few centuries it may start to feel like Alpha Centauri is the capital city of the galaxy and Earth is the quiet suburb on the capital city's fringes.

Answer 4

I am not sure there is a problem. No need to blow anything up. See EDIT at the end for a more formal explanation.

Your assumption is that traversing a wormhole does not take as long as making the same trip by light speed. This is NOT a given. A wormhole between here and Alpha Centauri, for instance, could take 4.4 years to traverse, whether through a wormhole or the more scenic route traveling at the speed of light. Since wormholes are pure conjecture, time itself in a wormhole may not be (probably isn't) the same as time in normal space/time. I suppose it could be conjectured that, to the traveler, it may seem instantaneous. Wooops, in a blink of my eye, 4.4 years passed.

But if you WANT to use wormholes, so that you can travle FTL, such that you can only go into the future to protect the Chronology protection conjecture (a neat concept) then design the physics such that, when you travel through a wormhole in the direction you came from (the return loop of the circle), it takes twice as long as the trip would have at light speed. That is, you end up taking a very slow boat throught the wormhole to come back home, on the return leg. Leave the calculations for the time lapse up to your physics, not us poor humans. It's your world, since you are playing around with the laws of relativity anyway, you get to modify the rules in whatever fashion you want. Warp time in a way that suits your story, and make your wormholes into reverse time machines.

EDIT

To clarify the 'reverse time machine' concept.

If, for instance, I leave point A and go through a wormhole that actually takes less time to traverse than going the same distance the 'scenic' route to point B at cee, relative to the observer taking the scenic route at cee, it is true that I will arrive at the destination B before the light 'pulse' containing the information of my departure from A gets to B, so it might appear as if I arrived before I left. However, if I take the return trip (B to A), I will 'pass' that pulse of light in the opposite direction. I will NOT arrive back at the original destination A before the pulse of light is 'sent' from A, I will have passed that pulse of light in its journey. I will have 'caught up with time', and will still arrive back at my origin A after I first left.

If I turned around and looked 'back' to B, yes I would have arrived back at my original point A before the information containing my departure from B arrived at A, but again if I returned back to B, I would pass that pulse of light (information) and still arrive back at B AFTER I left B. In fact, I could pass the pulse of light going from A to B of my first departure, again, going in the same direction, and arrive at B beore both pulses of information arrive at B (first and second departure from A). But at no 'time' would I have an opportunity to change the data in either pulse of light. The 'ripples' of information from A would still be contiguous in time, as they arrived at B. The history would not have changed.

TL:DR That is, if you travel AWAY from the point that information is being transmited (originated) from at FTL, you are going one direction in 'time', ahead of the information travel. But if you travel back TOWARDS the origin of that information, you are traveling FORWARD in time again. You will always arrive at the origin A after the pulse of light was originally sent, relative to an observer at A.

Answer 5

It has been proven that, given that wormholes exist and they connect two regions of space instantly, you can hurt the Chronology already with a single wormhole.

Check out this episode of Sean Carroll's Mindscape podcast where he explains a lot better than I could ever do:

https://www.preposterousuniverse.com/podcast/2020/11/23/124-solo-how-time-travel-could-and-should-work/

Here is a quote from the transcript. I really advise to take two hours during commute and listen to this podcast.

snip

Now, in fact, they later worked it down to just a single wormhole, and this is a little bit elaborate, but it’s worth explaining ’cause it’s just so cool. So, imagine one wormhole. Imagine we make a wormhole, don’t ask me how we make it, but we have these two spherical regions of space, the mouths of the wormhole, and you go in one, you instantly come out the other one, okay? And imagine that somehow, we can manipulate the mouths of the wormhole. We can basically put a tractor beam on and move one end of the wormhole around independently from the other one. So, this is the point, that there remains zero distance if you travel through the wormhole. You don’t actually traverse any distance going from one sphere to the other one, but from the point of view of someone outside, the two mouths of the wormhole could be very close, or they could be very far away. And so what Thorne and his friends say is, imagine that we move them, but we start them right next to each other so they’re very close, and we move one of them far away, and then we move it back. Okay?

1:22:25 SC: And they know the other one just stays constant, the other one stays put. This little thing that we just did, one mouth of the wormhole stays put, the other one moves out, let’s say close to the speed of light and then comes back, that should remind you of the twin paradox. If you put a clock on one wormhole and on the other one, the clock on the wormhole that stayed the same might know it reads an hour has passed. Well, let’s say this. Yeah, let’s say two hours have passed on the wormhole that stayed the same, on the mouth of the wormhole that stayed put, whereas the other one that went out and came back, its clock only reads one hour. Okay? So initially the two clocks, again, from the point of view of someone outside who’s watching all of these shenanigans, there’s two clocks, they both say noon, and then two hours passed from the point of view of the wormhole that stayed stationary, so its clock now says 2:00 PM, but the wormhole that went out and came back, its clock just as 1:00 PM. So they’re now out of sync by an hour.

1:23:28 SC: And you say, “Alright, that’s fine. Good special relativity, twin paradox. I get it.” But here’s the twist: When you look through the wormhole, you see what’s on the other side. You don’t see flashing lights, it’s not a subway, you see whatever is on the other side. It’s like a window, it’s like, you know, a telescope or something. You’re seeing through a view portal in space-time. And let’s imagine that our clocks are so arranged that you can see the clock on the other side, you can see the other wormhole’s clock, the other mouth of the wormhole’s clock, by looking through either sphere. So, when you’re moving, when the one wormhole is moving, it’s going out and coming back, what would I see if all along, I was looking through that wormhole at the stationary clock? Well, from the point of view of looking through the wormhole, nothing’s moving. There is still zero distance between the two mouths of the worm hole from the point of view of through the wormhole as opposed to outside. Outside the wormhole, the wormhole mouths are moving apart and then back together, but from looking through the wormhole, there’s always no change in distance whatsoever.

1:24:40 SC: And so you don’t see the other clock moving; you see it stationary. And therefore what you see is that clock ticking at one second per second, just like your clock. And that sounds paradoxical, because you say that, “Well, if I’m outside and I look at both clocks, one does a little twin paradox motion and goes forward one hour in time; one just days stationary and goes forward two hours, so now they’re out of sync,” but if, I instead of looking them from the outside, look through the wormhole, to borrow a phrase, they’re in sync. They both read the same time. So, once the wormhole that went out on a journey comes back, it says 1:00 PM, its friend that stayed behind says 2:00 PM, but when we look through the wormhole from the one that went out and came back to the other direction, we still see it saying 1:00 PM, ’cause it still has to say the same thing as the clock that was moving out and came back.

1:25:37 SC: And what that means is, I hope you followed this, I hope you bought everything I just said, what it means is if you go through the wormhole yourself from starting in the mouth that went out on its journey and came back and its clock says 1:00 PM, you come out the other wormhole not just in a different location in space, but also at a different moment in time compared to the point of view of the external observer. Since you are looking at the clock on the other side of the wormhole and it says 1:00 PM, you come out at 1:00 PM from the point of view of that wormhole mouth. So you have moved into the past from the point of view of the external observer. What the external observer sees is at 2:00 PM, you entered the wormhole, and at 1:00 PM, you exited. You exited before you left. And then you could hang around and there could be another copy of you that said hi to the copy of itself that went through the wormhole. An honest-to-goodness closed time-like curve that you made in a local region of space; you didn’t just put it into the universe from the start.

snip

Again, this is the link. Go there, take a look.

https://www.preposterousuniverse.com/podcast/2020/11/23/124-solo-how-time-travel-could-and-should-work/

Answer 6

Wormholes Pairs Take a Lot of Time to Set up

Suppose you want to create a wormhole pair between here and Andromeda. The only way is to take two nearby regions of space (which are already entangled with each other by virtue of being next to each other ) and push them apart until one reaches Andromeda and the other reaches here.

The bridge takes 2.5 million years to build.

Of course after the bridge is built we can pop back and forth between galaxies very quickly. But the long setup period prevents information being transmitted faster than the speed of light. This protects the chronology.