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As we know, bi-directional faster than light (FTL) travel can cause paradoxical situations. One possible way to resolve this would be a multiverse theory: Whenever a paradox could arise, the universe splits into two (or maybe more) more or less internally consistent universes, and whenever a paradox actually would arise this split becomes observable.

Let's take the Alice and Bob example from the wikipedia page on the tachyon antitelephone:

Alice and Bob are travelling at 0.8c away from each other from a common starting point. After 300 days subjective time, She eats bad shrimp and sends a message to that effect "I ate some bad shrimp" to Bob. The message travels to Bob at 2.4c. Bob receives the message at his subejctive time of 270 days (due to time dilation as seen from Alice's standpoint, math behind the link). He immediatly sends back a warning "Don't eat the shrimp" at 2.4c relative to his frame of reference which reaches her at 243 days "Alice-time". Provided Alice doesnt forget the warning in the following two months, she won't eat the shrimp, won't message Bob, won't receive a warning, will eat shrimp, will message Bob ...

(Edit to add: The preceding paragraph summarizes a thought experiment that was first thought up by Einstein in 1910 and worked on by other physicists. If your answer boils down to "Bidirectional FTL travel cannot create paradoxes, Einstein was wrong on relativity" your answer is bad and you should feel bad)

How could this play out in a Multiverse as sketched above? From Bob's perspective, he will receive a message from a futre that will never happen. Weird but not non-sensical. The same holds true for the Alice who receives the warning.

The possible paradox happens from the Alice-primes perspective: She sends a message to Bob but has not received the return message. When Bob and Alice communicate via non-FTL means she will learn he sent a warning that she did not receive (it simply vanished). The only way I see to resolve this is that return messages or trips that are quick (and close in time) enough to cause a paradox vanish from their senders perspective, and consequently from some receivers. While this requires a serious rethinking of causality (things happen for which the cause is outside this universe), within one timeline there are no causality violations.

Most times this will only happen when someone wants it to: Say ESA launches a space telescope at .99 c to observe the future history of the universe, or commanders on opposing sites of a space battle use relativistic spysats to adopt their battle plans by looking at one outcome (that is rendered impossible immediately).

The biggest downside from a storytelling perspective I see is this: Anyone capable of accelerating many tons of matter to relativistic speed and have it travel back with an FTL drive can duplicate matter: Instead of eating a shrimp Alice sends it to Bob, who sends it back. Now secondary Alice has two shrimp. Unless we limit FTL to information.

My question is: Do the preceding paragraphs make sense or is there a serious flaw in my thinking?

For storytelling purposes this works best with FTL devices where the travelling ship vanishes into a sort of warp bubble and cannot communicate with the rest of the universe until it pops back into sublight space. Maybe it could work with wormhole-like travel.

p.s. Let me explain the spirit of this question: FTL is impossible in two distinct ways. There's (IMO) no mechanism in sight that could feasibly allow any signal to travel FTL - that's one impossibility. The other is that unless relativity is grossly wrong (and we'd know by now?) FTL could lead to paradoxes as described above. The latter is IMO the "deeper" problem: you could add a new observation that allows an FTL signal or maybe the exotic matter required for an Alcubierre-style warp drive is suddenly observed. That would still require relativity, specifically the experimentally well established time dilation aspects, to be grossly wrong.
So the idea of this question is to ignore the first impossibility for now and look soleyly at the second one.
There's a reason I ask this here, not on Physics: An SF Author can apply an infinity of handwaves to tell their story. This question hopefully helps those who for whatever reason don't want to handwave relativity away.

Or to put it yet another way: If one breaks relativity as we know it in an SF story, the story ceases to be about an unlikely future and starts to be about an alternate universe. There's nothing wrong with that, it's just not what I'm going for.

p.p.s. This, by Demigan, ist too good to reamin hidden in the comments:

I never understood why this is a paradox. It is so easy to describe what happens that you do it right here! Bad shrimp->message->return message->doesnt eat shrimp->doesnt send message (somehow creates a problem with her own timeline), recreates the old timeline where she eats bad shrimp. Cause and effect, clear and simple (except for the twist where not sending the message recreates the old timeline. Why would it?).

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    $\begingroup$ I am a bit puzzled about something that starts with "in a universe where FTL is possible" and ends with "does it make sense?". It's no different than magic. $\endgroup$ – L.Dutch - Reinstate Monica Mar 26 at 14:10
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    $\begingroup$ The usual solution to FTL paradoxes is to postulate that FTL travel always takes place with respect to a unique privileged reference frame. Note that in the scenario described in the question the paradox arises because the phrase "the message travels at 2.4c" changes meanings; first it refers to Alice's frame of reference, then it switches to Bob's. If by "the message travels at 2.4c" we always understand "2.4c with respect to a fixed frame of reference" then no paradox arises. (This has the downside of breaking the philosophical base of physics by introducing a privileged frame.) $\endgroup$ – AlexP Mar 26 at 14:39
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    $\begingroup$ (And information cannot exist without a material support. We cannot send pure information; we must send something, a support, to carry the information.) $\endgroup$ – AlexP Mar 26 at 14:42
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    $\begingroup$ @AlexP: Plus you can still create paradoxes with a privileged frame, because you can have events occur in multiple different orders when viewed from frames of reference that are not privileged. $\endgroup$ – Joe Bloggs Mar 26 at 15:10
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    $\begingroup$ I never understood why this is a paradox. It is so easy to describe what happens that you do it right here! Bad shrimp->message->return message->doesnt eat shrimp->doesnt send message (somehow creates a problem with her own timeline), recreates the old timeline where she eats bad shrimp. Cause and effect, clear and simple (except for the twist where not sending the message recreates the old timeline. Why would it?). $\endgroup$ – Demigan 2 days ago
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First of all your issue isn't FTL travel, your issue is time travel. In theory if you can teleport from one world to another you have FTL but not time travel, you're linking them but that's ok.

Whenever a paradox could arise, the universe splits into two (or maybe more) more or less internally consistent universes

A good way to think of this is there's an infinity of multi-verses, the universe is always splitting or merging an infinity of times. What happens in one multi-verse can affect another but doesn't have to.

If you have the technology to send messages to your cross time selves, then getting warnings about things that don't or even never happened won't be a big deal.

This means you can get warnings that are totally irrelevant to your current situation. The spaceship that gets the message warning about Alice eating bad checks and there is no Alice on board. So the timeline that sent the message was serious but was too far from the current one to be relevant.

Or it is relevant. However the characters can't be sure the messages were sent with good intentions (Alice's sister is trying to do something sneaky, or even Alice#2 is trying to steal Alice's boyfriend because her own died).

If it takes a starship to invoke this problem then presumably it will only happen with serious things... but scale these issues up to a society and we'll find out that governments can lie, pull sneaky deals, and so forth.

That matter duplicating thing you're talking about isn't a downside, it's the creation of a villain.

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    $\begingroup$ A particularly fun 'theory' in cosmology is that if you use the right set of infinities then there is, in the universe, an infinite number of copies of the universe all playing out at infinitesimally small time differences from each other. There is also an infinite number of copies of very similar universes. Seen from that standpoint it's not time travel at all, it's just sending a very, very, very long distance message. $\endgroup$ – Joe Bloggs Mar 26 at 16:46
  • $\begingroup$ Teleportation doesn't imply time travel? If I teleport to some planet, when I get there is part of the equation. I have to respect a certain reference frame if I do not wish to time travel. $\endgroup$ – BMF For Monica Mar 27 at 17:30
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I’m on a mobile device so my answer is brief here. A multiverse allows for FTL of a sort. The catch is, you (the FTL traveller) can never return to the previous universe. Nor can anyone or anything else. Not even a photon.
The problem of calling it FTL is that there’s no common framework, so it’s not “Fast”, and it’s therefore not really FTL, even though it may appear to be. It’s merely switching or hopping from one universe (where planet foo-foo is far away from your boat) to another universe (where something that looks like planet foo-foo is close to your boat).

The key is that there’s no return journey. You can go to somewhere that looks like home - maybe down to a fine level of detail - but it’s a different universe.

Of course, even when you come back from the office (in pre-covid commuting), your home is not the home you left - our own experience of an unchanging world is a necessary fiction - but to talk about universe hopping, there’s a continuum break.

There are other issues with multiverse hopping : one of purpose / choice. Since you can choose a universe where planet foo-foo is filled with bananas, or where it is filled with apples - why bother? Just hop to a universe that suits you ( until it doesn’t, of course ) - but then that is Alladin’s genie/ get a wish stuff.... and as everyone says, you may as well switch FTL with MAGIC.....

You will have to find some sort of energy conservation ( and a shedload of other problems) to enable universe hopping - but I leave that to you as an exercise!

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    $\begingroup$ There's been a couple of interesting stories with similar rules. One where you could only communicate with "close" universes, and they found a problem: they couldn't communicate, because when they asked questions, so did everybody else. They solved that by sending "answers" (I remember they sent the movie Casablanca, and got one back with Ronald Regan in the lead role. "They got a classic, we got a joke."). $\endgroup$ – NomadMaker yesterday
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Yes!

There are some physicists who have proposed exactly this: closed timelike curves (a more technical name for a specific kind of time travel that might be allowed by general relativity) create alternative universes which exist in quantum superposition.

From Wikipedia:

In 1991, David Deutsch came up with a proposal for the time evolution equations, with special note as to how it resolves the grandfather paradox and nondeterminism. However, his resolution to the grandfather paradox is considered unsatisfactory to some people, because it states the time traveller reenters another parallel universe, and that the actual quantum state is a quantum superposition of states where the time traveller does and does not exist.

And the idea that the FTL drive vanishes into a sort of warp bubble not only makes the storytelling easier, but also is more consistent with these speculative ideas from physics (although for verisimilitude you might want to call it a transient wormhole rather than a warp bubble).

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Here are some common theories that allow two-way FTL that can solve your antitelephone problem. It is important to note though that nearly every field of theoretical physics has actually ruled out the possibility of time travel, and maintains that IF superluminal travel is possible, that you will not actually be able to go back in time. If you can not go back in time by exceeding the speed of light, then there is no antitelephone effect, and therefore, no paradox to worry about.

Using Tachyon Particle Theory

According to the Tachyon Particle Theory, speeds of >1C are possible when a particle moving at 1C hits a negative slope in spacetime; so, single-directional FTL is entirely possible according to the rules of relativity. That said, two-directional FTL is not. If you send a tachyon at 2C out to a relay and bounce it back, then the return signal would max out at 0.5C (as perceived from the original reference frame) because it must fight against the spacetime gradient which you used to your advantage on the way there. This means that the return signal of an antitelephone cannot actually arrive back at the sender before he sends it making the antitelephone impossible, and therefore, causality violation is also impossible.

Professor Erasmo Recami's paper titled The Tolman “Antitelephone” Paradox: Its Solution by Tachyon Mechanics offers a much more detailed explanation of this.

To achieve 2-way FTL, the multiverse model introduced by Plate Theory might work for you. My understanding is that it allows for a multiverse of universes that may or may not have the same alignment of spacetime. If you assume your universes do not have the same alignment, then you could fall down the curvature of spacetime in this universe, then you punch through to another universe (or maybe to the back of our own universe?) where you are at a high point, and then ride that down to where you can punch back into our own reality. Now you have two-way FTL.

This is all very theoretical, but I believe this may still resolve to not arriving before you left because in the other universe, your relative relationship with space time in our universe is upside down; so, while you are going slower in time in the upside down, you are going faster in time relative to our universe. This way you can in theory break the light barrier in two directions, but still not come back in the past; so, causality is safe.

enter image description here

One caveat here is that it this system of FTL makes arbitrary warp drives (as in Star Trek) impossible by any means I can think of off of the top of my head. Your ships will need to travel along natural "warp-lanes" where the universe already has strong gradients, or they will need to use some kind of crazy future tech that allows them to manipulate the curvature of space on an interplanetary scale.

Using Wormhole Theory

Wormholes are allowed according to the laws of relativity, but they do not create causality issues because they are not actually FTL travel. They are just shortcuts that allow you to take a quicker path. Wormhole theory is based on the idea that a universe can be folded in such a way that what appears to be a straight line, but is actually not, and that you can move between two point by taking an "actual" straight line which would be the wormhole. Because your speed never exceeds 1C, your time dilation stays positive; so, you can travel distances greater than light moving through normal space while actually going slower.

enter image description here

Like the tachyon issue, wormholes must rely on a preexisting condition in spacetime since you cannot move the mouth of a wormhole faster than light.

Wormholes do not need a multiverse to exist, but they do rely to a degree on plate theory; so, a reality where wormholes exist generally allow for the existence of some sort of multiverse.

Using Quantum Entanglement

This is an interesting one in regard to spacetime because it pretty much violates everything spacetime says should probably be possible, but it's completely and repeatedly proven in laboratory experiments. Einstein himself eventually accepted that it really does happen, even though it seems to contradict his theories.

The way Quantum Entanglement works is that when you generate a pair of particles, they will continue to share mirrored images of the same quantum state indefinitely, even when separated by massive distances. This seemingly allows for instant long ranged communication of information since one should be able to manipulate the quantum state in one particle and observe the outcome instantly in the other.

The most common attempt to justify this while preserving the laws of relativity I've seen is the node (or "boiling space time") model which says that as you approach the quantum scale, spacetime stops looking smooth like a cartesian plane, but instead becomes a complex web of connecting nodes of various lengths and vectors that average out to what we perceive at the macroscopic scale. It this model, space time is not a coordinate system at all; so, to say a distance in perceived space is 1-inch is to actually say that there are an average of 1.572E+33 nodes between two points but that there may be a single node that actually spans the whole distance.

What this means in terms of the speed of light is that the speed of light is not so much ~299,792 cartesian kilometers per second, but ~1.855E+43 nodes per second. Like wormhole theory, this allows one to take shortcuts through spacetime if you know how to find the optimal path. In this model, any particle pair is permanently adjacent, but its other nodes change as they move through space. This means that if you put an emitter at a mid-point between two distant locations, you can have people at either end stimulate the passing particles for instantaneous communications.

This, like the wormhole method, does not violate causality because the communication is not actually exceeding 1C. Here, your two distant points are also adjacent; so, as long as you do not exceed a motion of more than ~1.855E+43 nodes per second, your time dilation stays positive regardless of how far you've seemingly gone; so, there is no antitelephone effect.

This method does not require or suggest the existence of a multiverse at all, but if you want to have a multi-verse, it does not really disprove its existence either.

Using a Unified Field Theory

Now this last method is controversial as hell, I know the OP does not want to hear it because he does not like its implications on what it means for the theory of relativity, but the point of this list is to give solutions, not to tell him which one he needs to use for his story. Most physicists agree that a Unified Field Theory exists, but they can not agree on what it should look like because we can not separate perception from observation when measuring reality; so, they continue to use relativity because it models well in most practical cases.

The general premise of all unified field theories is that relativity can be described in terms of newtonian physics, or vise versa.

The most common approach is to try to resolve relativity in terms of newtonian physics. This usually relies on explaining that time does not dilate, but that doppler effects and rate of atomic activities change as forces are applied to moving objects. Thus, relativity is a perception of reality and not a literal interpretation. Like relativity, Unified Field Theory typically has to resort to non-cartesian space to explain quantum entanglement.

An example of explaining the antitelephone problem with a Unified Field Theory might look like this:

The perception of an FTL ship would present itself much like sound does when exceeding the sound barrier. At >1C, you would see it in reverse because the light reaches you slower than the source, but the thing is still moving forward in time. It could also explain atomic processes as slowing down as a thing accelerates because a portion of the rotational energy in an atom is converted to kinetic energy slowing down how fast it can do the things we measure as time. Relativity in a case like this is an illusion or side-effect of how we perceive and measure reality, and not actually a measure of reality itself.

Unified field theory explains the light speed barrier as a soft cap whereas relativity explains it as a hard cap. In Newtonian physics, a thing can not move something faster than it is already going; so, in a universe when light/gravity is the fastest you can exert a force after releasing all potential energy, there is nothing faster than light or gravity to accelerate something with.

According to Newtonian models of Unified Field Theory, to exceed 1C, you need to impart matter with energy that can not possibly be absorbed from interacting with the physical world. But, if you could impart this impossible energy on matter, then you can use it to not just add unaccountable velocity to your atomic nuclei, but you could also use it to add unaccountable velocity of your electrons allowing you to continue experiencing time in the right direction as you travel faster than light, but the antitelephone effect does not work here because the perception phenomenon does not actually allow for negative time dilation. A negative value in this case would represent electrons moving at 1C and atomic nuclei moving at >1C. If such a thing were possible, it would just mean your electrons could no longer keep up with your nuclei so your matter gets ripped apart as you are turned into plasma... at which point causality is the least of your worries.

Using this method, you could use a multiverse as an excuse to find something faster than light (the fastest thing in our universe), to give your ship or messages an FTL push without making time go backwards.

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    $\begingroup$ If you believe in relativity, and if you believe that it's possible to move wormhole mouths around without destroying them, you get all the time-travel paradoxes. $\endgroup$ – Peter Shor yesterday
  • $\begingroup$ @PeterShor, yes and no... the most liberal interpretations of moving wormholes cap wormhole mouth movement at C and compensate for the "sheer" by applying a resistance gradient in proportion to the movement. So, if your wormholes are moving together, the wormhole speeds you up, if they are going apart, it slows you down... or they can't move at all like you say, just depending on what theorist you are listening to. $\endgroup$ – Nosajimiki - Reinstate Monica 5 hours ago
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My question is: Do the preceding paragraphs make sense or is there a serious flaw in my thinking?

Yes. There is a flaw in your thinking. You are assuming that traveling FTL means that you are also traveling back in time. In reality, FTL is impossible. You can't travel faster than light. But if you could, given that time dilates and reaches 0 at the point of the speed of light, it starts going backwards once you exceed it, and thus your paradox is born.

But science fiction doesn't need to care about that. Like I said, FTL is impossible anyways, so the best way to resolve your problem is to say that your FTL doesn't go back in time. This way no one can go back to the past and no one can send messages to the past. And doing it this way, FTL without time travel, is a sci-fi staple. It's fine if you decide that, in your setting, FTL is not time travel.

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  • $\begingroup$ I donwvoted this answer because I felt it missed the spirit of the question. Then I thought "how is halfthawed supposed to know what I mean" and added a p.s. to the question. Now I can't undo my downvote :( $\endgroup$ – mart Mar 26 at 16:12
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    $\begingroup$ This isn't at all the reason why FTL implies time travel is possible. Going faster than light doesn't magically make you go back in time like superman going backwards around a planet. The combination of FTL and relativistic non-simultaneity lets you set up situations where an effect happens before a cause, which is much harder to get around. $\endgroup$ – Joe Bloggs Mar 26 at 16:43
  • $\begingroup$ @JoeBloggs, that's only true from certain reference frames. If FTL != backwards time travel, and there is a preferred reference frame, then while you might observe an effect preceding a cause, the cause still happened first, you just haven't observed it yet. $\endgroup$ – Matthew Mar 26 at 20:52
  • $\begingroup$ @Matthew: This answer doesn’t assume a preferred reference frame. $\endgroup$ – Joe Bloggs Mar 26 at 21:04

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