For the unwary, this is a paper which used gravitational lensing to find wormholes, since wormholes and negative mass in general produce lenses which look different from regular positive mass lensing.It didn't find any clear^{note } examples in the Sloan Digital Sky Survey Quasar Lens Search. This one is more recent and also puts an upper limit on their frequency.

Since I don't know what a geodesic is, I have the same problem as fighteer. What I'm getting from your comments, Septimus, is that since the topography of a wormhole can be expected to be highly curved, and not flat, traversing one won't be like walking down the hallway from my kitchen. It is beyond my abilities to imagine what it would be like.

However, that doesn't serve to resolve the dispute between Fighteer and myself since his objections to FTL do not derive from conditions during transit, but from the relative positions of various observers while someone makes the trip.

Unless you are claiming that the highly curved topology *within* the wormhole somehow resolves that?

Next two articles: well, there went our timeless intergalactic civilization.

Edited by DeMarquis on Apr 29th 2021 at 10:53:08 AM

Right. I concede that the mathematics of GR potentially allows FTL topologies, but I don't concede that these allow you to avoid violating special relativity in all possible frames of reference, which is required for the universe to retain causal consistency.

A geodesic is basically a path that an object (photon, information, etc.) can take in a coordinate system.

Anyhow, I think the key point here is that what an outside observer sees when something travels through a wormhole isn't necessarily identical to what the same observer sees when something travels like a tachyon because the wormhole distorts the spacetime and a tachyon doesn't. And the distortion of the spacetime has effects noticeable by the outside observer, as demonstrated by the existence of gravitational lenses and that's why I keep bringing them up.

Now you can deliberately construct a wormhole in such a manner that the outside observer sees time travel happening - this one does show one - but you need to specially design the wormhole; it's not an inherent property like with SRT FTL.

"Authorization Required"

Applied to astrophysics, a geodesic typically describes the path that an *inertial* object takes in four-dimensional spacetime. This means that it is not applying any net acceleration: it's moving with the flow of space and time as defined by gravity.

The article is talking about a wormhole whose mouths are moving with respect to each other. Such a wormhole can be used as a time machine.

Yeah, that's a good definition of geodesic.

Upon rereading some of the literature I think I *may* have understood how this works.

A wormhole is a teleportation device, i.e if the "mouths" are at the same time point and the time delay is equal to 0. Thus under Lorentz transformation [going by the Wikipedia definition] deltat is equal to 0 and w equal to infinite. Mathematically that means that deltat' has always the same sign (negative) for each choice of v less or equal to c - v being the relative velocities between observers. Thus all observers agree on the sequence of events and Tolman's paradox does not arise unless there is a time delay between the wormhole mouths or there are multiple ones.

Naturally assuming that Lorentz transformation still applies in this context ... but if it doesn't then there is no reason that Tolman's paradox would either.

You linked to the Wikipedia article for "antitelephone", which discusses the Lorentz transformation in a superluminal context but isn't the defining page for it, and I'm not sure which term is **w** in your summary.

The issue with the wormhole as I see it isn't the effect on the local observer passing through the wormhole but the effect on someone else observing said passage.

Let us say **t** is the time of transit, **d** is the distance between the endpoint, and **v** is the effective velocity of the traveler to an onlooker. Let us assume that the endpoints of the wormhole are at rest with respect to one another. If travel through the wormhole is instantaneous, then **t = 0** and **v = infinity** for any **d > 0**.

When we perform a Lorentz transformation into any distant observer's reference frame where said observer is closer to the endpoint than the start, causality is reversed, hence backwards time travel. They see the traveler arrive before they left. In fact, **t** doesn't have to be zero so long as **v > c**. If our hypothetical traveler then traverses the wormhole in the opposite direction, using the math in the antitelephone article that you linked, it is trivial to show that certain reference frames exist in which they *return* before they left.

If the ends of the wormhole are moving with respect to each other, then those time travel scenarios include local observers as well.

Your assertion that a wormhole defies these mathematics seems based on distortions in general relativity created by the wormhole itself that somehow cause the external environment not to perceive causality violations. I don't see how this is possible but I am absolutely not going to attempt the GR math.

Edited by Fighteer on May 1st 2021 at 6:33:35 AM

w (This icon) is the speed of the traveller going through the wormhole, which is infinite since a wormhole is instantaneous teleportation except when there is a time delay. v (This icon) is the speed an observer has, which is finite and less than c unless they are *also* travelling through a wormhole (the two wormholes scenario).

The v in your post is w in mine. Unfortunately Wikipedia's math icons can't be copypasted here.

I've been looking for a while how Lorentz transformation works like in GRT but ended up empty handed. Mine's a proof by induction, here: If it looks like in SRT Tolman's paradox doesn't occur for the reasons above. If it doesn't look like in SRT we have no reasons to assume that Tolman's paradox would apply in the first place.

I don't see why it's necessary to assume instantaneous transit through the wormhole (**t = 0** for the traveler) as long as **v > c** for an external observer. Unlike the tachyon scenario, the traveler never experiences moving faster than light *through spacetime*, which is the only reason we are considering this to be possible.

If the ends of the wormhole are not stationary with respect to each other and the wormhole permits two-way transit, it can be demonstrated that the traveler could return before they left using the same math as in the antitelephone article. Or, equivalently, person A goes through the wormhole and as soon as they arrive person B goes in the opposite direction. B could arrive at the other end before A leaves.

In fact, both A and B would arrive before the other leaves, a double paradox.

Edited to add: No matter what method of FTL is used, there is always going to be a distant observer for whom **v > c**, and thus a paradox is inevitable.

Edited by Fighteer on May 1st 2021 at 8:56:35 AM

The discussions I've seen do not share those assumptions, and include the effect of time dilation on the transit time within the wormhole, which I believe preserves causality. I'll quote myself from a few months back:

"a wormhole, if it could be created, would involve both ends right next to each other in local flat space. Traveling through them isn't FTL, and doesn't cause any temporal paradoxes. To be useful, however, one mouth of the WH then has to be transported to a remote location, presumably light years away. It can only get there using STL. As the WH mouth moves away from it's point of origin, time dilation has an interesting effect on anyone observing through the mouth out toward the traveling end. Let's say it takes 100 years to move the mouth to a distant stellar destination, but onboard the ship towing it, passengers only experience one year passing by. Observers looking through the mouth left back at the origin need only wait a year in order to observe the traveling end arrive at the destination. Thus, the wormhole connects two locations together 99 years before it arrives at the destination using STL.

However, this arrangement does not allow information to travel back in (local) time. An observer at the origin point can see into the traveling ship's future by looking through the WH. But if he then tries to tell the crew of the towship what he sees, it works out that his message will only catch up after the ship arrives at the destination (it starts out one year behind, you see). Someone at the destination can look back through the WH and see 99 years into the past, but sending information back that way wont "change history" locally because the effects of the message must travel through flat space-time from the origin to the destination, taking 100 years to reach them. So it all works out, even though one could simply step through the WH and arrive 99 years in the future or the past.

Provided the flat space distance between the two ends of the WH are greater than the time saved by traveling through the WH, no paradox occurs."

and, a little later on the same page:

"Now, as for distant observers. If someone uses the WH to travel from the origin to the destination what they will see is the traveler entering the WH at one end, and exiting the WH at the other end, one year later (this is the effect of the time dilation when the WH mouth was towed at STL). Note that no matter where the observer is located, causality cannot be violated. If the observer is one light year from the destination, they can be no closer than 99 light years from the point of origin. At no point do they see the traveler leaving the origin before they arrive at the destination."

I'm not enough of a mathematician to convert all this to a light cone diagram. Fighteer did his best a few posts later, and I took the time to draw it out according to his instructions. I did not find that any information arrived back at the destination before it left. Of course, he didn't attempt any Lorenz Transformations, and neither will I.

My general point is this: I don't think it matters if, from a particular frame of reference a given superluminal path appears to go backward in time, provided that no information can proceed backward to the origin. This is prevented because the wormhole (or an Alcubierre Drive) insulates the traveler while in transit. Nothing can affect them between the origin and the destination.

One of you can please tell me if I have made a mistake somewhere.

Edited by DeMarquis on May 1st 2021 at 11:27:12 AM

I can't do the whole math problem, but my issue is that you are looking at it from the point of view that it is possible to construct scenarios in which causality is not violated. I'm not contesting that. What I'm saying is that if there is *any* reference frame in which causality could be violated, no matter how extreme, then the scenario violates special relativity.

One of the core principles of SR is that there is no preferred reference frame.

Well, one mistaken assumption. A wormhole is not two teleportation machines, it's *one* throat held open by negative matter. You are not creating the "openings" one-by-one and next to each other; you create one throat with two openings and we have no idea where the "other" end ends up. It could be close, but it could also end up in the South Pole Wall or 7 billion years ago.

Special relativity does not require causality. Other physical theories and logic do. SRT merely says that when there are speeds c<w<∞ involved you can end up with situations where different observers with different speeds v [using my definition from Wikipedia] disagree on the sequence of events.

Regarding Lorentz transformation in curved spacetime, the only thing I can find is this arxiv article which implies that you need to apply a curvature correction to the gamma factor. And it's an arxiv with no citations so I am not sure how "official" it is.

This article discusses some more ways to turn a wormhole into a time machine

Edited by SeptimusHeap on May 2nd 2021 at 5:10:06 PM

@Fighteer: "What I'm saying is that if there is any reference frame in which causality could be violated, no matter how extreme, then the scenario violates special relativity."

From what I've read, it doesn't violate SR. SR, when applied to FTL, violates causality along at least one frame of reference. There are ways around that.

@Septimus: "you create one throat with two openings and we have no idea where the "other" end ends up."

Why are you assuming this? Of course you know where the other end is going to be, that would all be calculated ahead of time. They don't tunnel through rock until after they know where the other end will be (that is, in fact, the entire point).

"Special relativity does not require causality. Other physical theories and logic do. SRT merely says that when there are speeds c<w<∞ involved you can end up with situations where different observers with different speeds v [using my definition from Wikipedia] disagree on the sequence of events."

Yeah, that.

It feels like we're having a semantic argument. Special Relativity establishes the calculations that let you transform any inertial frame of reference into any other inertial frame of reference as well as the relationship between matter and energy, space and time. From a purely mathematical point of view, imaginary mass and time travel are outcomes of the equations, given no preferential reality.

When I say that FTL is impossible because it violates causality, you are correct that SR doesn't state that. It merely establishes that FTL violates causality. Whether causality violation is impossible (and thus FTL impossible) is not perfectly established in relativity. However, it is established independently by the laws of quantum mechanics: specifically the law of conservation of quantum information.

It may be that a potential unification of QM and GR will tell us for certain whether FTL and/or time travel are possible, and writing stories with that in mind is perfectly reasonable.

I will of course offer the rather trite observation that if these things are in fact possible in our universe, we have detected no evidence of them thus far. As someone noted recently (I forget which thread it was in), astrophysicists are looking for signs of wormholes near high-energy phenomena like black holes. If they find any, we may get some more relevant data.

Edited by Fighteer on May 3rd 2021 at 2:57:02 PM

Sometimes I think we need an "is FTL possible?" in OTC so that not every discussion on FTL is derailed by the relativity theory discussion. I know that saying this makes me a candidate for Hypocrite of the Year award, but whatever.

De Marquis, nobody has any use for a wormhole with close mouths other than as a test subject. Assuming that they would be stable in the first place - as far as I know the quantum field theories that posit the existence of Clock Roaches imply that the maximum lifespan of a wormhole is mouth distance/speed of light. I don't know of a physical reason why one wouldn't be able to make a wormhole with one throat here and the other ends up in some random spot of the universe.

If you want a change of topic, I have a question. You know those Mag-lev trains, with magnetic tracks? Is it safe to touch the track while it's "on"? Could you stand on one without any detriment to yourself?

It's an interesting idea, but I don't think putting it in OTC would serve any real purpose. It would get a flurry of posting and then probably die out. It would probably work better in this subforum (World Building).

I don't know if there is one unique design for magnetic levitation trains, so I'm not sure if it's possible to precisely answer your question. It would come down to whether the track is always on — that is, the rails are continually creating a magnetic field from electrical induction — or if it's selectively powered only when a vehicle is passing over. In the latter case, touching it while it's not live would be harmless.

There is no need for the surface of the rail to be electrically conductive in such a system — merely touching one would not connect a circuit and give you a shock. However, in operation the track would have a very strong magnetic field, potentially damaging any electronic devices you carry on your person. You might also get a hair-standing-on-end sensation and similar things.

It's likely that certain parts could be conductive regardless of design, and those would be very clearly identified with hazard markings (in a safe system, anyway). Also, any track that poses such a risk would have fencing and/or other measures to prevent casual intrusion.

Edited by Fighteer on May 3rd 2021 at 3:51:22 PM

Thank you. When I tried asking Google that, I kept getting results like "Do magnets cause cancer?"

**Relationship Status:**Don't hug me; I'm scared

Only to nineties-era computers.

Edited by amitakartok on May 3rd 2021 at 11:03:40 AM

You can levitate a frog using magnets strong enough to repel the water in the frogs body.

This fun little tangent is relevent, because no, it doesnt hurt the frog.

Though it makes them a little disoriented.

That's true. Magnetic fields powerful enough to disrupt organic physiology only exist on Earth in special laboratory environments, but in nature they can be found near such objects as neutron stars. Every now and then someone asks how close we could get to one of those monsters, and while the gravity and radiation are indeed serious problems, the biggest one is the magnetic field.

It varies, but if a neutron star were where our Sun is in the solar system, its magnetic field might be strong enough to erase a magnetic hard disk from as far away as the orbit of Pluto. As we get closer, the field becomes strong enough to magnetize even normally non-magnetic substances. Chemical reactions are disrupted and molecules can get ripped apart.

So in the ever-fascinating question of what about a neutron star would kill us first, it's not the gravity. We'd be disintegrated into molecular paste by the magnetic field long before we got close enough to be spaghettified.

Edited by Fighteer on May 3rd 2021 at 5:49:15 AM

"De Marquis, nobody has any use for a wormhole with close mouths other than as a test subject."

No one has any use for a wormhole that ends in the inky vast emptiness between the stars (or the galaxies) either, because that's almost certainly where a random location would end up.

Relationship Status:Dancing with Captain Jack HarknessThat paper... OMG. Not being a physicist or indeed any kind of academic scientist, I can't critique it or offer any opinions on what it says.

I'm willing to accept that there may be ways for wormholes to get around FTL problems in special relativity, but then we still haven't established that creating stable, traversable wormholes is even possible.

Hypotheticallypossible, maybe, but there are lots of ways to manipulate GR equations to produce things that we have no hope of ever testing.