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You can't have faster than light travel without violations of causality. And while the equations of General Relatively allow for universes where causality is routinely violated, the probability that we are in such a universe seems vanishingly small. E.g., just because you can violate causality does not mean that you can go back in time and kill your grandfather. If you were to try, something would stop you, as a universe in which you kill your own grandfather is not consistent with General Relativity.

A universe that gives you the means to go back in time and try to kill your grandfather, but then somehow always thwarts you, would be a very strange universe indeed.

Edit: To whoever down-voted me, have you taken any classes on General Relativity? I have.

In any case this is from Wikipedia:

Causality is not required by special or general relativity[citation needed], but is nonetheless generally considered a basic property of the universe that cannot be sensibly dispensed with. Because of this, most physicists[who?] expect that quantum gravity effects will preclude this option.[citation needed] An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle.

The "Novikov self-consistency principle" is the the one that states that you could try to create a time paradox, but that you would never be able to succeed. I.e., the universe would be a very strange place!

We aren't talking about time travel. So many people confuse the idea of FTL with time travel. General Relativity talks about frames of reference.

Suppose you had a base on Mars and sent a radio signal to it from Earth. It would take between 4.3 to 21 minutes to reach Mars, depending on its distance from Earth at the time.

If you simultaneously jumped in your 10x warp drive and set out, you would arrive at Mars in 25.8 seconds to 1min 26 seconds, again depending on distance.

In this scenario, there has been no violation of causality. You aren't arriving before you sent your radio signal. All that is happening is that you're arriving before your radio signal does. From the perspective of a telescope or radio antenna at the Mars base, you would view Earth in its state 4.3 to 21 minutes before, because it simply takes that long for the electromagnetic waves to get to you.

So yes, you can travel faster than the speed of light without violating causality. If you travel in a relativistic way, i.e. speed all the way up to 99.99999% of light speed, you will most certainly run into time slowing down in your local frame, while it continues at a normal frame back at your departure point.

But with a warp drive that works as described in the article, there is no changing of reference frames. Since you're warping space itself, the spacecraft isn't actually undergoing acceleration in the relativistic way of a rocket. For passengers on board, the clocks are going to run at the same rates as back home.

You are not correct. If anything with information travels faster than the speed of light, then there are frames of reference in which that information arrived at the destination before it left the origin.

Furthermore, unless your FTL drive is limited in ways that would make it utterly useless, any FTL drive can be used to make "closed time-like loops", which would allow travelers to meet up with their own past selves.

I want to make a point of clarification about something I wrote above. I wrote:

> any FTL drive can be used to make "closed time-like loops", which would allow travelers to meet up with their own past selves.

That should have read "closed causal curves", or perhaps "closed space-like curves". I made the same typo on another occasion or two in this thread.

"Closed time-like curves" do also exist, at least theoretically, and they also let you visit your our own past history, but they do not involve FTL travel. Instead, they are artifacts of General Relativity, in which causality is violated without traveling faster than the speed of light. They typically involve traveling around certain kinds of very massive objects. Another kind involves traveling in a very very large circle at close to the speed of light.

>>You are not correct. If anything with information travels faster than the speed of light, then there are frames of reference in which that information arrived at the destination before it left the origin.

No. If you send a radio signal to Mars, and then warp to Mars to find yourself there 0.1 seconds later, you are still 0.1 seconds after the moment on which you sent the signal from the point of origin. You are traveling faster than light, in the sense that you are traveling at [Earth-Mars Distance]/[0.1 sec] speed, but you are not actually traveling backwards in time to a point where you have not sent the signal yet.

Nothing you just said contradicts my statement, which was, "there are frames of reference in which that information arrived at the destination before it left the origin."

I suspect that you don't know anything at all about Special Relativity, in which case, there's not much more I can tell you except to go educate yourself.

Special Relativity only applies to cases where there is uniform relative movement in two or more inertial frames of reference. That is not the case with this theory - the relative movement is clearly not uniform and although I've not read the paper I'm certain that the time warp provides a non-inertial frame.

TL;DR - ignore Special Relativity completely, General Relativity is the only thing that applies here.

We're not applying SR to an observer who warps, just to two observers in inertial frames of reference.

Suppose we have guy A and guy B who have clocks. They're on spaceships which are both drifting away from each other (i.e. provide inertial frames) at speed c/root 2; at time t=0 they were in the same place. From SR it should be clear that in A's frame, his clock reads 100 at the same time as B's frame reads 50, while in B's frame, when his clock reads 50 A's clock reads 25. All this should be basic and obvious.

So suppose an event happens on A's ship at time tA=100, and he transmits this instantly (or sends a courier C on a warpship) to B at time tA=102, when B's clock reads tB=51.

From B's perspective, he's just received a message from A at time tB=51 (which is simultaneous with tA=25.5), which A is not going to send until tA=102 i.e. tB=404. Thus, B perceives a violation of causality.

(This becomes very obvious if B can send an insta-message back to A with the same technology; B sends it at time tB=54 which is simultaneous with tA=26, A receives it at tA=26, well before he sent the original message at tA=102)

So This may not be an FTL drive, but the way I always sort of pictured it is that the FTL moves you forward in time to the relative observer (so if you move distance x you move (c/x)^-1 forward in time). So if you send an FTL courier (assuming travel time of 2) from point A with times tA=102 tB=51 it would arrive at point B at times tA=52 tB=104 (A time 53 units in the future from tA), if it got sent back it would arrive at point A at tA=106 tB=53 (A time 53 units in the future from point B). The distance traveled would be c*53 distance (53 units of time for light to travel) in 2 units of time.

This also works for the mars/earth scenario (say they are 14 minutes apart). Traveling to the place that the light you see in 14 minutes will be coming from instantly would only ever be traveling forward in time. Forward time travel doesn't break causality(?)

This is always sort of how I envisioned wormholes work (and is indeed how they work on shows like star gate). You go in one end and come out the other, unless you can communicate through the wormhole it would take light (distance times c) years to tell people on the other end you succeeded.

But perhaps I'm missing something...

So as far as B's concerned, when he sends the FTL courier to A that courier will goes slower than a light-speed message? He could send a message at tB=53,tA=26.5 and it would reach A well before tA=106.

This only works if you assume the FTL drive is fixed to some sort of absolute reference frame (which happens to be the same as A's frame). At which point you've given up on relativity, and I'll bet it's possible to come up with some cute paradoxes

I realize how this violates relativity, but I don't understand your counter example (if it was one?) because I wasn't talking about absolute time frames, I'm talking about going forward in time when going FTL. And at no point in my example could B reply before A sends a courier.

It's not a counterexample as such, but it seems obviously absurd (and violating relativity) that B's FTL message to A arbitrarily goes a lot slower than A's FTL message to B, given that the situation is completely symmetrical (you can even have them both send their messages at tA=100,tB=100, which is simultaneous from the point of view of an observer C who stayed behind on the asteroid where the two spaceships initially met up).

The point I was trying to make was that your example description makes sense if the FTL drive is somehow fixed to A's reference frame, i.e. A's reference frame is some kind of absolute reference frame and therefore the situation is not symmetrical between A and B. But that introduces its own problems.

Sure, B sees things happen in the wrong order, but I will maintain that causality is not actually violated until an effect actually disturbs a cause.

In other words, if B sends that message back to A, you have violated causality. If B just sits there and watches events happen out of order, then the causality is obscured but not broken.

> Sure, B sees things happen in the wrong order, but I will maintain that causality is not actually violated until an effect actually disturbs a cause.

You maintain incorrectly. All inertial frames are equally good in Special Relativity. If there is any inertial frame that observes events elsewhere in the universe where an effect precedes a cause, then causality has been violated.

Furthermore, whenever Special Relativity is violated like that, there is always a way to get the violation to turn up in your own frame of reference, unless you constrain things so severely that what you are proposing isn't going to be useful for much.

All inertial frames are equally valid. All inertial frames see that the effect does not munge the cause, even if it happens out of order.

I know that 'causality' is a bad term for me to use here; I'm open to suggestions. But my point is that cause and effect are still intact. Cause, with effect not inside its light cone in the past, sends information toward effect. Effect, with cause not in its light cone in the future, receives information from cause. I don't care what order those happen in, as long as the thread of causation is intact and one-way.

Yes there are 'ways' to create proper violations, but you can avoid them if you intentionally choose to.

> I know that 'causality' is a bad term for me to use here; I'm open to suggestions.

I think that you are looking for the term "closed causal curve" or "closed causal loop". If you use FTL to achieve this, this is often called a "closed spacelike curve". If you use GR without FTL to achieve this, it is often called a "closed timelike curve".

I'm not convinced that other sorts of violations of causality are any better than closed causal loops, since you can typically use the other violations to create closed causal loops. And even if you do have closed causal loops, you can decide not to go back in time and kill your grandfather, so if the issue is just what you chose to do, then closed causal loops are no worse in this regard.

In any case, whether or not you chose to go back in time and kill your grandfather, you won't succeed, since you did not succeed.

Well the important part here is that you can pretty simply have a self-consistent universe that has mildly-limited FTL (and highly-limited time travel) if nobody makes a loop.

And I'll try to use something like 'causal loop' in the future.

And what happens if you try to make a loop? Do you think it sensible that the universe provide you with the ability to make causal loops and then somehow forbids you from actually making them, even though once you've been given the ability, they are very easy to generate?

Additionally, if the universe is going to keep stepping in your way of what it has given you the ability to do, there's no reason for it to forbid you from making causal loops. All it has to do is forbid you from generating a paradox via such a loop.

I.e., you can have a self-consistent universe that has unlimited FTL and unlimited time travel as long as everyone plays nice. In fact, you can have unlimited time travel even is everybody is trying to kill their grandfather. They just won't ever succeed.

Never did I assert anywhere in this entire thread that a universe where causality is violated--or even one with closed causal loops--is impossible. They do have serious issues, however. And for anyone to propose FTL travel as a serious possibility and then ignore the causality issues as non-serious, either indicates some amount of either ignorance, disingenuousness, or rationalization.

If, on the other hand, a proponent of FTL travel plainly states that they have no problem with a universe that always steps in somehow and prevents you from succeeding in killing your own grandfather, then at least they've made their position clear, and everyone can make up their own mind as to whether that's a likely way for the universe to be.

There are other solutions, too. It might simply be infeasible to accelerate an FTL device to sufficiently relativistic speeds. Or what if there were fields coming off of FTL devices that interfered with the speed when they criss-crossed. That one would stop any sort of loop and it wouldn't require the universe to somehow specifically forbid paradoxes.

FTL devices don't have to "criss-cross" for you to be able to create causal loops. And even if you don't have any causal loops, other violations of causality violate thermodynamics. It's not as if if you've solved the problem of causal loops--which as far as I'm aware, no one has done without postulating a preferred frame of reference, which is basically rejecting Relativity outright--then you're off the hook. All violations of causality are going to make most scientists shake their heads. And, if it is infeasible to accelerate an FTL drive up to speed, then the point is moot for space travel or communication.

By 'criss-cross' I mean that your FTL devices in different reference frames need to repeatedly get close enough for causal contact. Is there another way to make a loop using simple FTL devices?

And I might not have been clear enough on acceleration. I meant you might be able to construct a device capable of FTL transport, but it might be far harder to traditionally accelerate this entire device to high speed. The FTL isn't moot, but if your FTL is only 5c and you can't accelerate your turned-off FTL device faster than .1c you're not going to make any loops with it.

In other words, in this scenario, there isn't a preferred frame of reference per-se, but there's no way for such a large and complex construct as an FTL device to get far enough away from the galaxies' default reference frame.

You might be able to cook up something, but I doubt that it will be any more plausible than positing a preferred reference frame.

Personally, I think that supporters of FTL should stick with subspace and run with it. And, hey, the author of the FTL faq even wrote a whole subspace faq too.

Maybe. I can't directly see an event disturbing a cause after the first message, but that doesn't mean there's not a way to make it do so.

Of course the cheap answer is that it violates SR (and common sense, given the complete symmetry of the situation) for A to be able to send an insta-message to B but B not able to send an insta-message to A.

Well, either one can send a single message. It's the reply from a different frame that causes trouble. In fact you can have unlimited FTL messages sent in a single reference frame. It's only when you combine multiple FTL reference frames that things get wonky.

But if B can't send an FTL-message to A because he's going to receive an FTL-message from A in what to him is the future, that's your causality violation right there.

Right, I should be more precise with the scenario. A cancelled-message is still a transfer of information. To avoid problems you have to set up the scenario such that only one ship would send a message no matter what. But it can be either ship, and you don't have to know which ahead of time.

Special Relativity applies ANY TIME that you transmit information from one point A in an inertial frame to another point B in an inertial frame.

If you can use your warp drive to transmit information from A to B, then Special Relativity applies.

If you cannot use your warp drive to transmit information from A to B (e.g., from Earth to Mars), then what good is it?

(I've mentioned several times in this thread that you might be able to come up with some sort of FTL drive that doesn't violate causality if you put enough constraints on it to make it useless.)

> Special Relativity applies ANY TIME that you transmit information from one point A in an inertial frame to another point B in an inertial frame.

Not true. It also implies uniformity of space-time in all inertial frames and the space between them. Since the theoretical purpose of the warp drive is to create a non-uniformity by definition SR does not apply.

Yeah, pretty much. I'm actually amazed that so many people (nessus included - as he seems to be the most vocal poster on this thread) do not know this.

All Special Relativity requires is that space be more or less flat between point A and point B. It doesn't matter if the information travels from A to B through a wormhole and then into another universe and then out the butt of Dumbo, if it ends up at B before light would, then causality has been violated.

If, on the other hand, your FTL drive bends up space all around us to be like a giant hyperspace pretzel, (1) we're going to have a lot more problems than just a little violation of causality, and (2) causality still ends up being violated via General Relativity.

Causality is a consequence of the physical laws you are currently using, not a law in themselves. It just paints a logical boundary condition around what is possible using the current set of laws that you are using.

Compare Newtonian causality where there is only one timeframe everywhere to SR causality with its local timeframes to GR which supports warping of space and time. All different and not interchangable.

Wormholes cannot exist in SR, therefore applying SR's brand of causality is equally invalid. Under GR the concept of simultaneity is relaxed: the effect is only limited to the light cone of the cause.

Special Relativity is not invalidated by GR: Special Relativity is a special case of GR that tells us what to expect in inertial frames in a flat space. As long as points A and B are in a flat enough space, then the predictions of Special Relativity about the causal nature of information transmitted between A and B BY ANY MEANS will still be true, even if there are nearby wormholes. If Special Relativity tells us that we can make a closed causal loop via the FTL signals that make it through a wormhole, then GR will not overturn this, no matter how the information made it from A to B.

I agree that if the space Between A and B is distorted enough so that the light that travels in open space between A and B is seriously affected by a curvature that extends from A to B, then it is true that you cannot use SR to make your predictions, as the premises of SR are violated. But then GR will predict that causality can be violated anyway. (It's generally easier to find ways to violate causality in GR that SR anyway, since it doesn't require FTL transmissions of information in GR to create causal loops.)

I refer you to the FTL faq, since it seems that I am not able to talk sense into people on my own:


This is as good a place to start as any:


Wake up. Quantum entanglement is at least 10000 x c, and somehow it doesn't brake causality. And information first leaves the origin and gets to you before you know that it left its origin. But no causality is broken. Everything is still happening in proper order.

A pair of FTL communication devices (jargon: ansible) can be arranged in a configuration which would allow the future to speak to the past, violating causality.

A lot of people responding to this thread do not understand relativity. The OP is correct, the fundamental problem is causality, relativity and FTL do not mix. The common way of saying it is that you can have two of the three: FTL, causality, or relativity. You cannot have all three. Here is a very nice explanation of why:


Also, I've never understood how the Novikov self-consistency principle would work in reality. Causality violations can be a lot simpler than killing your grandfather. Say, for example, you set up a pool table with a pool ball and hit it through a time machine such that it went back in time and hit itself, making it miss the time machine? Would the pool ball be suddenly acted on by some invisible force? Would it explode? Would the universe just end? The whole scenario seems so implausible that addressing this theoretical concern is a lot more relevant than worrying about the energy levels required to manipulate space time.

> Say, for example, you set up a pool table with a pool ball and hit it through a time machine such that it went back in time and hit itself, making it miss the time machine? Would the pool ball be suddenly acted on by some invisible force? Would it explode? Would the universe just end?

No, none of these. Well, something would prevent this from happening, but whatever happened would have a perfectly reasonable explanation at the time.

You have to understand, firstly, that in GR, the universe doesn't start at the beginning of time and slowly evolve until it reaches the end of time. Instead, all of space and time that ever was or ever will be, exist now and forever. And this one big constant eternal space-time is one of many possible solutions to the equations that constrain the universe.

If a potential universe does not satisfy those equations, then it can't exist and therefore it won't exist.

A universe in which your pool ball goes back in time and deflects itself, is not a solution to those equations, and therefore, that will never happen in any GR compliant universe.

So, what might happen instead? Well, you might get bored with the experiment and give up before you get it working. Your girlfriend might come along and tell you that you are neglecting her. Burglars might steal your time machine. Or most likely, you might never invent the time machine to begin with.

It's quite conceivable that in some sense a time machine is theoretically buildable, but the reason our universe is one of the solutions to GR is that no one ever actually builds one in the history of the universe.

Why not, you ask? Because if they did, that universe is much less likely to be a solution to the equations, so we just so happen to find ourselves in one of the more likely universes.

Another way to think about this is that perhaps all possible universes actually exist. In that case, we have to find ourselves in one of the existing universes. We can't find ourselves in a non-existing universe, since non-existing universes don't exist.

The link had a really interesting but unsatisfactory explanation, IMO. The way I am understanding it is as follows: Man A and Man B are traveling (with combined speed of 0.866c) away from each other. Because of time dilation, to A it appears that B's clock is twice slower (1/sqrt(1 - 0.866^2) == 2). Then A shoots from some sort of weird space gun whose bullet is instantaneous. The bullet passes B at 4 seconds (relative to B). B notices that and shoots back, and B's bullet, due to equivalent effect hits A at 6 seconds causing a dead grandfather paradox.

However what I don't understand is this -- to say that the bullet shot by A passes B at 4 seconds presumes that we are talking about A's frame of reference (because it is from A's point of view that B is 4 seconds "behind" -- and likewise A is 4 seconds behind from B's perspective). However, what if, from B's frame of reference, A's bullet actually passes B at 0 seconds?

For anyone reading this, the referenced explanation finally did make sense after I drew a Minkowski diagram of the two duelists. I guess this means that I finally understood special relativity... Brief summary: FTL would indeed violate causality, unless a special frame of reference is proposed (this violates special relativity) or a specific new property of Universe is established such that it would prevent certain events from occurring (aka Novikov conjecture) -- and we don't have evidence for any of the two being true.

I remember reading a paper that dealt with this issue. The setup was that a spherical mass hit another one into a wormhole that sent it back in time. The velocity was such that it would deflect the first mass before the initial collision, creating a casual paradox. If I remember correctly (and it has been years since I read the paper), they found that the second mass was garaunteed to come out of the wormhole with a velocity that would cause the first mass to hit the second in a way that would result in the new velocity, leading to a consitent system; however the final velocities were probabalistic, not deterministic, of the initial conditions.

Again, I have not seen that paper in years, so my memory might have just made half of that up.

Tachyons do not necessarily violate causality if you actually take the time to derive the laws of tachyonic kinematics consistent with special relativity.

Sure, tachyons will be strange (different observes won't agree on direction of travel or charge of a tachyonic particle - if we are even able to localize the particle at all; there will be frames of reference where a tachyon won't have energy but will still have momentum, ...), but not really any stranger that what we deal with in quantum mechanics and field theory, and the laws of physics will still hold in all frames of reference.

This answer doesn't deserve its downvote: The problems with tachyons were largely resolved in the 80s, based on work by Stückelberg and Feynman, Schwartz, Recami and others.

The community just lost interest in them because our current models of particle physics prevents bare tachyons:

QFT does predict real tachyonic particles. However, they are solutions of unstable vacua, which transit to a tachyon-free phase via symmetry breaking.

Stringtheory predicted tachyons as well, but got rid of them again when superstringtheory came around.

Tachyons are not gone completely, though: Virtual particles can be off-shell and thus tachyonic and feature in the description of self-energy.

Tachyons can also be useful to explain EPR-type quantum 'paradoxa' without having to give up reality.

But you can't use them to transmit information at FTL speeds without violating causality.

[Background note: I'm a physics professor with a background in string theory and relativity.]

You're raising a sensible point, and most of the objections raised here are invalid. But it nevertheless turns out (surprisingly, to me!) that your argument doesn't work. This topic came up a lot during the short-lived superluminal neutrino excitement last year, and one good discussion of it by Sean Carroll can be found at:


That post includes a link to a paper by Bob Geroch that goes into the topic in detail. The very short summary is that there is no mathematical necessity for "causality" to be defined just by relativity: the union of the relativistic definition and some other well-defined causal theory can work just as well, even if that theory involved faster-than-light travel.

So thank you for raising a very good point about this topic, even if it wasn't quite accurate. And to those who've objected here: unless your objection explicitly quoted Geroch, odds are very good that they're wrong.

The issue is addressed explicitly in Alcubierre's paper where he mentions (at least twice) that there are no closed causal loops in his metric. So there's no violation of causality, and the standard intuitions from special relativity don't apply. Pretty remarkable! The lack of closed causal loops apparently follows immediately from standard results about the sort of metric construction he uses. There's no need to invoke Geroch.

I'm not surprised that Alcubierre addressed this point, though I'm glad to hear that for certain. (I've done little more than glance at his original paper... I never have enough time for all the cool stuff.) But my understanding is that his metric is "eternal", in the sense that the warp bubble exists into the infinite past and future. That's obviously not practical for any actual application of the idea (as you'd need in a "warp drive" as discussed in this original article).

Instead, people want to find a way of creating a similar warp bubble where one did not exist before (presumably analogous to the way that stellar collapse creates a black hole that eventually approaches the Schwarzschild solution). So my question is, if someone does eventually find a GR solution that "creates" a warp bubble, would it be possible to patch multiple such solutions together in a way that allowed closed causal curves? (I'm imagining sending a warp "pulse" from Earth to a distant star, then having the recipient boost into a different rest frame, and then send a new warp "pulse" back to Earth, for instance.)

The answer may still be a clear "no", mind you. But it's not obvious to me what arguments you'd use to show that (particularly since we don't know what form a "warp bubble creation" metric would take, assuming it's possible at all).

I would certainly defer to your much superior knowledge of physics. Mine is only that of an MIT student who was thoroughly indoctrinated with Special Relativity as part of MIT's general science education, and who sat in on an undergrad course on GR taught by cosmologist Max Tegmark.

If I understand Bob Geroch properly (much of his paper is Sanskrit to me, but I think I understand the parts that are in English), he acknowledges that FTL particles would seem to allow you to set up "closed causal curves" (i.e., violate causality in a way that would allow you to try to generate a time paradox), but he asserts that you would never actually be able to achieve this goal due to something like the "Novikov self-consistency principle", although he doesn't mention this principle by name.

This is similar to the position that many physicist think about the existence of closed time-like loops in GR. Sure, in some sense they are possible, since GR shows you how to set them up, but something like the Novikov principle would either prevent you from setting one up or from doing anything nefarious with one.

So, if I understand things correctly, Geroch's claim doesn't really different too much from assertions that I made elsewhere in this thread, that sure you might be able to build an FTL drive, but if the universe lets you do this, it's not going to let you make good use of one, like, for instance, creating an FTL space-liner fleet, because if it did, you'd generate a time paradox soon enough. Or if the universe were so kind as to let us do that, we'd end up finding ourselves in a very strange world where Novikov's principle was mucking with our daily affairs in a very creepy manner.

I've admittedly not worked through Geroch's paper thoroughly myself, so I won't make strong claims here. But based on my understanding, I'd say that his assertion is a bit stronger than what you're suggesting here. He's not just giving a sort of meta-argument that "the space-time manifold of the universe must be consistent, so some mysterious effect will always stop you from killing grandpa".

Rather, his point is that your second theory (the one that you're adding to standard relativistic physics) has already been assumed to be causal when taken on its own (it must have a well-defined initial value formulation: that's one of his postulates). What he demonstrates is that putting the two causal theories together will still preserve causality. So when he says that you won't be able to use standard SR tricks to create closed causal curves, he really honestly means that any possible arrangement of the matter/energy content that could do that would be forbidden by the fundamental laws of the theories you're using. (Not just that it "wouldn't happen to work out".)

To phrase it yet another way, Geroch would say that you could not build a time machine in such a theory, not just that you couldn't use it to change the past in a meaningful way.

That being said, I'm not certain whether there's any way to avoid causality violation if the hypothetical FTL travel results entirely from within relativity itself. (Geroch's argument, as I understand it, is based entirely on combining two different theoretical structures.)

In General Relativity, Faster-Than-Light travel is only prohibited locally. Its possible for space-time itself to expand and shrink faster than light. This is why distant-enough galaxies are receding from us at faster than the speed of light.

Mathematically, the structure of the proposed warp-drive is such that the spaceship is moving at << c locally, so no causality is violated. See the author's answer here:


Nowhere does he state that causality is never violated.

I'm not the down-voter, but I think you were likely down-voted because this article/discussion is not about time travel. And your first statement is that "you can't have faster-than-light travel..." is precisely what this paper discusses -- that with certain loopholes in physics (and consistent with General Relativity), faster-than-light travel is at least theoretically possible.

Faster-than-light travel allows you to travel backwards in time. This is an essential part of Special and General Relativity. Those who don't understand this and who are not ready to address its consequences, should refrain from speculating on what is and isn't possible.

> [Those] who are not ready to address its consequences, should refrain from speculating on what is and isn't possible

Really? Do you hear yourself? I hope you're taking down badge numbers because I'm not sure that all these guys are qualified to address the consequences of faster-than-light travel.

Badge numbers? Are you talking about the badge numbers of the authors of the original article? If so, I'm sure they are quite aware that their proposed drive violates causality. Some scientists are willing to bite that bullet. It's some people on HN who don't seem to understand the chose-two-out-of-three principle when it comes to Relativity, FTL, and causality, and want to willfully ignore it.

I have very little experience with post newtonian physics, so could you explain why FTL implies time travel.

Also, doesn't quantom entanglement imply that data travels faster than light?

I keep hearing about faster than light communication with quantum entanglement. It seems to be a very persistent misconception. The same "communication" as with quantum entanglement can be done in the classical universe. You can easily create two entangled envelopes. People's minds are blown just because we put the word "quantum" in there.

Take two indistinguishable envelopes. Put a green card in one and a red card in the other. Shuffle the envelopes so that you do not know which card is in which envelope. Have a friend take one of the envelopes many kilometers away. Your envelopes are now entangled.

If you now open your envelope, and it contains the red card, you instantly know your friend's envelope contains the green card. Did information travel faster than light? No, it did not, since in order to communicate by this method you still need to tell your friend what it means to have the green card.

You still need to send slower than light information that Red is 1 and Green is 0 which you can only do once you've measured your own envelope, after which you've destroyed the entanglement of your envelopes.

Quantum entanglement is a phenomenon where you can tell something about the other part of the entangled pair by measuring one part. Just like with the entangled envelopes, you cannot communicate anything by this since you don't know in advance what you're going to measure.

But isn't the essential difference (and what makes the QM effect seem like spooky action-at-a-distance) that it's been proven that it isn't like the envelope example? Namely, there's no definite "redness" or "greenness" to the entangled particle before you examine it (unlike the envelope, which contains a red or green card the whole time). Whether you have a "red" or a "green" quantum part isn't decided until you look, at which point the wave function collapses in both parts simultaneously, no matter how far apart they are.


If the Many Worlds interpretation of QM is true, then there is no wave collapse.

No, quantum entanglement does not allow Information to travel faster than light. Classic channel is needed to know what if any unitary transformations are needed. Otherwise requiring roll of massively many sided dice. Check out No Communication Theorem.

I can't provide a coherent explanation of Relativity in one little HN box, but what I can say is that Special Relativity is pretty easy to learn and understand if you're willing to put in a bit of effort and deal with some high-school level algebra.

General Relativity is much much more difficult, but once you understand Special Relativity, a lay-person's understanding of GR gets the job done for most purposes.

Re quantum entanglement, no it doesn't imply that data travels faster than light. The versions of QM where the probability waves collapse might, but in the Many Worlds interpretation, which is probably the most popular interpretation now among physicists and philosophers of science, the probability waves never collapse, and so there is nothing to transmit.

In the Copenhagen interpretation, one might argue that the probability wave collapsing transmits information all along that wave instantaneously, but if so, this happens under the covers of the universe. There's no way for anyone to use this feature of QM to transmit usable information from one place to another at faster than the speed of light.

Under SR, for two events (an event is a point in 4D space, i.e. a space and a time) with spacelike separation (i.e. outside each other's light-cones), neither comes objectively before or after the other. Different observers travelling at different speeds have different "surfaces of simultaneity", which say which events happen simultaneously. It's a theorem (or intuitively obvious) that for any two events with spacelike separation, there is a frame (i.e. a velocity at which you could be travelling) for which those two events are simultaneous.

So consider the events A=point 1, time 0; B=point 2, time 0; C= point 1, time 1 hour. As long as points 1 and 2 are more than 1 light-hour apart, it is legitimate to say that A is simultaneous with B, or that C is simultaneous with B. And so if you have a device that lets you travel from point 2 to point 1 in less than an hour (i.e. faster than light), you leave at B and arrive after A but before C. Then from the perspective of some observers (and the point of relativity is that all observers are equally legitimate), you arrived before you left.

The collapse of quantum entanglement can be confusing, which is part of why I prefer to follow many-worlds (i.e. no collapse postulate). You can construct quantum wavefunctions such that they're consistent with SR; for two entangled but spatially separated particles, you simply have a wavefunction that's a superposition of two states. When you as an observer observe one of those particles, you entangle yourself and your own state becomes part of the superposition. Of course "from the inside" it feels like you measured the particle and got one result or the other, but the actual wavefunction is just an ordinary superposition. From this perspective it's obvious no data was transmitted - you just became entangled with this distant particle without communicating with it, which is kind of odd, but no danger of violating causality.

But is it really important that it looks like you arrived after you left? Can't we just know that the light from one thing took longer to reach us than the other so what we are seeing is just an artifact of FTL.

Can that prevent causality? Or does it prevent relativity?

All observers are equally valid under SR; it would be very arbitrary to say that some of them are seeing "artifacts". Physics is based on observation, and the natural way to interpret our observations is to say that what we saw really happened. (Obviously this isn't true if some observable effect is distorting our perception, but that's not what's happening here - the observer who sees the person arrive before they left is a perfectly normal observer using perfectly normal equipment). Now if you want to say physics works differently for observers in different frames, that's fine, but it goes against relativity and all known physics.

Now assuming we accept that FTL-traveller really did arrive before they left, if that's all they do it's a matter of language as to whether they have violated causality by so doing. But it would take some very perverse physics (again, basically discarding relativity) to say they couldn't simply jump back, again going backwards in time, and arrive back at their starting point before they left it, at which you definitely have causality violation.

I don't know the specifics about quantum entanglement, but any means of making information travel faster than light that can work reliably in two different inertial frames (thus communicating four different points, two not moving relative to each other in space in each) can be used to break causality or relativity. This is achieved by constructing a loop in which if the second pair of devices is used to disable the first you have a time paradox.

This is the clearest place explaining it I'm aware of, but I bookmarked this a while ago and maybe now some video or animation explains it better: http://www.theculture.org/rich/sharpblue/archives/000089.htm...

Is FTL the same as warping space? what happens in a (reduced dimensions for intuitiveness) scenario where a universe is like a line segment, and gets bent into crossing itself, allowing jumps from one point to another? Then there is a long way and a short way to send a message, kind of like travelling through vacuum is faster than traveling through water.

FTL is not the same thing as warping space in the same way that speeding is not the same thing as driving a Maserati. But if you can warp space at your will to give you the power to effectively get from point A to point B faster than a beam of light would, then you will also be able to construct "closed time-like loops", which will allow you to travel backwards in time.

I think the "faster than light" part wording seems a bit off since from what I gather the point is not to go fast to get to a location but to get there through warped space-time.

I imagine a 100 km long and 1km high brick wall, you're in the middle but want to get to the other side of the wall.

Option #1 is to travel as fast as you can 50km to one end and then 50km back to the spot on the other side.

Option #2 tunnel through the wall.

Option #1 is fast but the option #2 is faster although you didn't exceed the speed of option #1.

That's not the scenario described in the OP. The FTL drive described in the OP is a traditional "warp drive", that allows you to travel faster than light by moving the space around you faster than light, while you continue to travel slower than light within your rapidly moving space bubble.

You're still effectively traveling faster than light, however, and you'd still be able to use this to travel backwards in time.

I don't think you are understanding the concept here. http://en.wikipedia.org/wiki/Alcubierre_drive#Physics

I understand it perfectly fine for the purposes of this discussion.

Edit: I can't believe people down-vote irrefutable facts, so let me state this ONE MORE TIME:

It is an irrefutable fact of Special Relativity that if you can transmit any information from point A to point B faster than light would travel from point A to point B in a vacuum, then there are inertial frames of reference in which the information arrived at point B BEFORE it left point A.


People can bitch and moan about whatever they want to, and come up with all sorts of creative ways to try to work around this FACT, but YOU CANNOT.

c, it's not just a good idea--IT'S THE LAW!

I'm sorry, but I just can't find any sort of citation stating that the Alcubierre drive violates any of these principles. I also can't find any mention of paradoxes incurred by the drive and there is only one mention of where the meta-materials themselves would have to violate the light speed limit. Here is how I understand it (and correct me if I'm wrong), but it is not travelling in a vacuum, it is crunching that vacuum in front and expanding it in the back. This doesn't violate any laws because we know our universe is actually already doing this (expanding at a greater than light speed). If what you say is true then the galaxies that are currently moving away from us at those "super-luminal" (not actual super-luminal because we all know that's impossible) speeds shouldn't exist, but we know these do exist and we know why they appear to be doing so. Because of the expansion of the universe. http://curious.astro.cornell.edu/question.php?number=575 So since this is already done naturally is it not feasible to do so artificially?

But aside from all that it seems a little short-sighted to howl about how people can't do something. Time and time again nay-sayers have been proven wrong.

Did you read the part above where I wrote this:

    It is an irrefutable fact of Special Relativity that if you can transmit any
    information from point A to point B faster than light would travel from point
    A to point B in a vacuum, then there are inertial frames of reference in which
    the information arrived at point B BEFORE it left point A.
Is there a reason why I can write this irrefutable fact a dozen times and people continue to ignore it like it was never stated?

Look, I understand that people want perpetual motion machines. And I understand that people want the Earth to be the center of the universe. And I understand the fact that people want one plus one to equal three. But these things aren't going to happen.

With FTL, you have to pick two out of these three: FTL, Relativity, causality.

It is not a fact of science that you have to pick two out of the three. It is a fact of LOGIC.

Unless you've found a way to transcend the laws of logic, then we have to live within this constraint. So, if you want to have FTL, you either have to give up causality or Special Relativity. Is it conceivable that Special Relativity is wrong? Sure it's conceivable. Is it likely? NOT ON YOUR LIFE. And if you're willing to give up on Special Relativity, when why are we designing space ships based on General Relativity??? When Special Relativity goes out the window, so does GR!

So, are we going to give up on causality instead? Well, who am I to say yes or no. But if we decide that it's okay to give up on causality, then we have to bite the bullet and decide that we're okay with us being in a universe that is really, really strange. E.g., one that will thwart you somehow one way or another in any attempt you might make to transmit certain kinds of information, etc. One that might be perfectly okay with letting you visit your past self, and yet will suddenly give you a case of laryngitis if you try to tell your past self which stocks to buy. Who knows how weird it could get!

Re your space ship being in a vacuum or not: (1) It's still in a vacuum, and (2) it doesn't matter. What matters is if you can use it to transmit information from say Earth to Mars at a speed faster than a laser beam or radio signal would make it from Earth to Mars.

Re galaxies moving away from us at FTL speeds: (1) Yes, galaxies that are very far from us do move away from us at FTL speeds. Can you use this fact to transmit information between two points (e.g. two planets) at FTL speeds? No you cannot! Special Relativity says nothing at all about space itself moving at FTL speeds. It only puts constraints on information traveling from one point to another point at FTL speeds.

Go read the irrefutable fact at the top of this post again. Read it over and over again until you understand it. I can't keep repeating it over and over again for it only to fall on willfully deaf ears.

OOoohhhh. I totally get it now. You are an unpublished internet stranger and the Alcubierre drive has been scrutinized by some of the top minds in physics. But your criticisms are more important for some reason I don't know. Mkay, going to bed now.

Edit: By the way. I did read the thing about point A and B and understand it completely. The thing is, it doesn't matter. This is why I'm absolutely sure now that you haven't got a clue as to what the drive actually does. Here let me explain it to you like you are 5. If you send a packet of information from point A to point B, and it goes faster than light, then yes that will screw with causality. But if instead you bring point A closer to point B, it will appear as though it is "traveling" (notice the quotes) faster than light. It is however not traveling. it isn't moving. No movement through space. Freefall. zero movement. Stillness. Think about that for a moment. Absolutely positively no movement. Complete stillness. There is a lack of motion with this drive relative to the speed of light. Mind you this isn't a wormhole because even wormholes can screw with causality. This is a space creator/destoyer. Destroys in the front, creates in the back. No movement is involved. I know it's really hard to wrap your head around but just think about it for a couple of days. think about bringing point A closer to point B instead of going through all the trouble of sending the information. Remember, doesn't move.

Where do any of these top minds of physics say that this drive does not violate causality??? They DON'T! If they asserted such a nonsensical thing, they would be the laughing stock of the scientific world and would no longer be considered any kind of mind, other than a quack. The only reason that you don't see much talk about this violation of causality is that it's just a fact that all physicists know. One physicist doesn't have to tell another physicist that an FTL drive violates causality; it just goes without saying. It would be like one physicist telling another physicist that 1 + 1 = 2. It doesn't need to be said!

It doesn't matter ONE TINY BIT to Special Relativity how it appears to YOU that you got information from point A to point B. What matters is how it appears to an OUTSIDE OBSERVER. If Earth and Mars are still 8 light minutes apart from some point of view, and you managed to transmit information from Earth to Mars in only 4 minutes, then there are frames of reference in which your message arrived at Mars BEFORE it left Earth.

This is just freshman-level Special Relativity. I guarantee you, that no one has found a work-around for that, especially since it is a matter of LOGIC. It follows LOGICALLY from the assertions of Special Relativity. If you wish to deny this conclusion, then you would have to deny Special Relativity.

If on the other hand, you have used your drive to permanently shred up space and time, rapidly crashing Mars into Earth and destroying all life on both planets, leaving the mess like that, and then stating you have successfully transmitted a message at FTL speeds, then more power to ya!

Alcumbierre himself states that it does not violate causality. from: http://www.npl.washington.edu/av/altvw81.html > The possibilities for FTL travel or communication implicit in the Alcubierre drive raise the possibility of causality violations and "timelike loops", i.e., back-in-time communication and time travel. Alcubierre points out that his metric CONTAINS NO SUCH CLOSED CAUSAL LOOPS, and so is free of their paradoxes. However, he speculates that it would probably be possible to construct a metric similar to the one he presented which would contain such loops.

    So either he's a laughing stock and nobody is talking about that or (more likely) you are wrong.

He has only stated that there are no closed causal loops for one particular use-case of his drive. He never stated either that causality was not violated from the point of view of a distant observer in a different frame of reference. Nor did he state that such a drive would not allow closed causal loops to be generated. In fact, he implied the opposite.

I'm sure the authors of the paper know that the warpdrive violates causality.

It doesn't matter that you're warping space to move points A and B closer from your perspective. If an outside observer can see you at point A at time t, and at point B at distance d away at time <t+d, you have violated causality, and an observer moving at a suitable velocity will see you arrive at B before you left A. That is a basic, irrefutable fact of special relativity.

> Is there a reason why I can write this irrefutable fact a dozen times and people continue to ignore it like it was never stated?

Because the tone of your replies are condescending.

So, I haven't looked closely at it, but he does mention that your clock remains (almost) the same as an earth clock. That implies that there is no frame of reference that shows him traveling faster than the speed of light. I'm not sure that this can be used to violate causality.

>I'm not sure that this can be used to violate causality.

If you can transmit any information from point A to point B faster than light would travel from point A to point B in a vacuum, then there are inertial frames of reference in which the information arrived at point B before it left point A.

It's really just as simple and plain as that. You need consider nothing further once you know the above facts.

Based on this effect though, it doesn't travel from point A to point B faster than the speed of light. Point A and point B are literally much closer together. Perhaps the space time distortion makes impossible to think of it in terms of static frames of reference.

If you've somehow made A and B closer together, then you've made a wormhole, not a warp drive. Wormholes also come with "closed time-like loops", which allow for time travel.

I don't know. This isn't something covered by special relativity. You certainly don't need a wormhole though.


Yes, there are parts of the universe traveling away from us at faster than the speed of light. In fact, it's quite likely that the universe is infinitely big and an infinitely large part of it is traveling away from us at faster than the speed of light.

This fact, however, does not allow information to be transmitted between two points in space at faster than the speed of light. That's the important constraint here. Causality is only violated when you transmit INFORMATION between TWO POINTS at faster than the speed of light.

Causality, though, is a postulate in the system. If you start with the assumption that faster-than-light is impossible and build a system around that, the system you build around that assumption will always prove that it's impossible -- until something else proves otherwise.

Causality it NOT a postulate of the system. General Relativity fully allows for universes in which causality does not hold. Such universes would either turn out to be either very strange, or actual use of FTL drives would have to be extremely rare.

Pick two: relativity, causality, FTL travel.

I'm glad you brought this up. I got into this same argument on a Star Trek fan site and my opinions on the feasibility of FTL travel were not popular with that crowd. I would like to know what Alcubierre himself thinks about the causality issue. You simply can't wish it away.

It's not that the universe might "literally" prevent you from performing an action. It's just that our universe doesn't allow it in the first place. The coherence of the universe is a biproduct of its inherent order.

I guess what I mean, without sounding too pseudo-scientific, is I believe the way it works is that, if, say, you go back in time and kill your grandfather, then what is actually happening is you are killing the person you thought was your grandfather, but they were not, in fact, your grandfather to begin with.

In fact, all you would know going back is that your grandfather was murdered by someone. Let's say you believe it was you, and you have a change of heart. Decide it's not in you to kill someone, even to prove a scientific point. That doesn't mean he doesn't get killed. Nothing's changed. It's simply that someone else killed him.

The answer to the question of Schroedinger's cat isn't that the cat is dead or alive, it's that it is.

Since QED and relativity aren't consistent, and QED says that can photons travel at speeds less than and greater than c, isn't it possible that relativity is just probabilistically true but not "enforced" to be true?

Since I don't know anything about QED, I'm not equipped to answer this question. What I can say, however, is that much of what we consider to be "causality" is just a matter of probability. There's nothing in the fundamental laws of physics that says that a flower pot that fell off the window sill and broke into a million pieces an hour ago, can't now suddenly put itself back together and then fly back onto the sill, just as if nothing had ever gone awry. The fact that flower pots don't typically tend to do so, is that this turn of events is extremely unlikely.

In fact, as far as fundamental physics goes, the forward arrow of time and the backward arrow of time are indistinguishable. I.e., if you were to look at a movie of subatomic particles interacting, you wouldn't be able to tell, if you didn't already know, if the film were being played forwards or being played backwards. (As a slight caveat to this--a caveat that does not detract from what I am saying, but should be mentioned for the sake of completeness--there is one tiny aspect of fundamental particle physics that breaks this time symmetry, but it is a rather subtle one. The physicists who discovered this won a Nobel prize, and as I understand it, why this symmetry should be broken--no matter how subtle the effect--is still a deep mystery.)

What we consider to be the forward arrow of time comes completely from thermodynamics, not from fundamental law. E.g., if the Big Bang occurred at the end of time, rather than the beginning of time, we wouldn't be able to tell the difference, because from our point of view, that would end up being the beginning of time anyway.

Do you think the big bang has universes on both sides of it?

QED is consistent with Special Relativity. The standard introduction to QED starts with the successful attempt of Dirac to create a "covariant" version of the Quantum Mechanics that is consistent with Special Relativity (in that process he explained the particle spin and predicted the positrons).

Then it's necessary to make the theory more complicated to explain some experiments, but the final QED theory is consistent with Special Relativity (or "covariant" in the jargon). The extensions that involve the weak and strong forces are also covariant and they form the Standard Model (with the slightly hypothetical Higgs boson).

Any reasonable extension of the Standard Model is "covariant". And it would be very difficult to make the physic community consider seriously a no "covariant" theory (nothing is impossible).

Nobody knows the quantum version of General Relativity, so perhaps there is a very tiny loophole, but I would not be very hopeful about it.

I feel like a lot of people here misunderstand the speed of light as a cosmic speed limit. The speed of light as a speed limit is a local constraint. On a larger scale there is no such speed limit. Just because you travel faster than light on a non-local scale does not mean you break causality.

For example, light "travels" more slowly through water than vacuum. Well, actually, photons travel at c always -- it's just that light gets bounced around by water molecules, getting absorbed and reabsorbed many many times before arriving at the destination. It's like driving to a destination as opposed to running to it. If the roads are curvy enough, the runner will win because he is not constrained by roads. Could it be that the Alcubierre drive gets past the roads of empty space in a way light cannot?

For a better example, consider the expansion of the universe. Link: http://curious.astro.cornell.edu/question.php?number=575. I quote:

The fact that galaxies we see now are moving away from us faster than the speed of light has some bleak consequences, however. Astronomers now have strong evidence that we live in an "accelerating universe," which means that the speed of each individual galaxy with respect to us will increase as time goes on. If we assume that this acceleration continues indefinitely, then galaxies which are currently moving away from us faster than the speed of light will always be moving away from us faster than the speed of light and will eventually reach a point where the space between us and them is stretching so rapidly that any light they emit after that point will never be able to reach us.

In other words, vacuum fills in between us and far away galaxies faster than light can traverse it. Again, locally, the derivative of position with respect to time is c, but the universe is able to "cheat" by messing around with the definition of position. If the Alcubierre drive messes with the fabric of the universe in a similar way, I don't see any reason why it cannot succeed.

Here's a related link: http://curious.astro.cornell.edu/question.php?number=56. I quote:

Technically speaking, the speed of light limit only applies when you are in an "inertial frame" -- that is, sitting where you are, without any forces acting on you, and measuring the speed of an object that moves past a ruler and clock that you are holding in your hand. Across the large distances in the universe, however, we have a very different set of circumstances. No one is in an inertial frame, because everyone is being accelerated with respect to everyone else, due to the universe's gravitational field and the fact that the universe is expanding. In effect, the universe's expansion isn't really due to galaxies moving "through space" away from each other, but rather due to the stretching of space itself, which isn't governed by the same limits that we are.

I'm not sure whether the Alcubierre drive contradicts causality, but if it does, I highly doubt that it is because of the arguments presented on this forum.

I'm not sure whether the Alcubierre drive contradicts causality, but if it does, I highly doubt that it is because of the arguments presented on this forum.

The Alcubierre drive most certainly does violate causality, and this follows from just the most basic amount of Special Relativity that you might learn if only you'd spend your time learning real things, rather than spreading disinformation.

I'm going to ignore your condescension. I'm also going to assume you didn't read the rest of my post, because you presented no arguments to counter my points.

I'd like to point out that the wikipedia article on the Alcubierre drive writes at length to show how this warping process does not violate causality: http://en.wikipedia.org/wiki/Alcubierre_drive. I know you feel strongly about people not understanding special relativity and I actually agree with you on that point, but you're not addressing any of the valid counterpoints that people are making. You're simply closing your ears and exclaiming "special relativity" which only applies locally (if you want an appeal to authority, I talked about this with a former physicist who worked with Stephen Hawking).

1) The universe is expanding faster than the speed of light. In other words, galaxies are moving away from us faster than c (evidenced by the growing redshift of light emitted by galaxies when they were NOT traveling away from us faster than c). That does not violate causality (as I mentioned in my post) because the topology of space itself is changing. Locally, everything still obeys special relativity.

2) Virtual particles, EPR Paradox (I know it's not actually a paradox). (http://math.ucr.edu/home/baez/physics/Quantum/virtual_partic...) My point with these phenomena is that locality and the speed of light are not very intuitive concepts. You can still have "spooky action at a distance" without violating causality.

You're simply closing your ears and exclaiming "special relativity" which only applies locally (if you want an appeal to authority, I talked about this with a former physicist who worked with Stephen Hawking).

If you come up with a mathematical "proof" and I can use its conclusion to prove that 1 + 1 = 3, then I have shown your proof to be incorrect via contradiction, no matter how hard you continue to argue for it.

Special Relativity does not only apply locally. It applies to any system where information can be transmitted between two points that are in inertial frames.

The universe expanding at faster than the speed of light is neither here nor there, since you cannot use the expanding universe to transmit information between two points in at FTL speeds. On the other hand, you CAN use an FTL drive to transmit information between two points in inertial frames at FTL speeds.

QM spooky action at a distance does not let you transmit information between two points at FTL speeds.

This is all you need to do to show that any FTL scheme violates Special Relativity: Information transmitted between two points in inertial frames at FTL speeds. If you can do that, you've either disproven causality, or you've disproven Special Relativity.

I agree with your assessment, but you're still missing my point. Following your analogy, what I'm saying is not that 1+1=3, but that we're not really using the plus operator here.

I think we both agree that wormholes do not violate causality. By creating a wormhole, you are connecting two points in space with a shortcut. As a result, traveling through a wormhole is not even FTL -- there are two paths to the destination and the shorter path is so much shorter that you can beat light that goes on the longer path. You would still lose to light if light also took the shortcut.

That's essentially what I'm arguing -- that the Alcubierre drive somehow warps space so that if you're traveling in one, you're not actually going faster than light, but through a makeshift wormhole. It isn't FTL.

Highly unlikely to be realistic, but the premise still obeys causality.

Wormholes most certainly do allow you to violate causality!

How about I just point you at the FTL FAQ?


Can I talk to you offline? How can I message you on this forum?

I feel like I'm missing something. The FAQ defines FTL as "getting to a location faster than light" but what if light is taking a suboptimal path? Assuming wormholes exist, depending on your frame of reference, it would take light different times to get to the destination.

The FAQ says to consider the case of someone shooting a bullet through a wormhole and killing someone faster than light could have transmitted that information through the long way. I don't see how it's a problem. The light would have also traveled through the wormhole and it would have been possible to know that information. I guess my point is, with the wormhole, the "correct" distance between A and B is no longer the long way.

The way it sounds to me, it's as if I shot a bullet straight at someone at 0.99999c and it killed him, but now you're saying that violates causality because of this star that is between you and the victim and it would have taken light longer to traverse around the star than my bullet.

Special Relativity only applies if the space between A and B is relativity flat. As long as space is flat in the vicinity, then the predictions of Special Relativity hold true. It doesn't matter if you made some weird topological wormhole that provides a shorter path. If Special Relativity has shown you how to, for instance, make a closed causal curve in the flat part of the space, using the events that occur in the flat part of the space, then SR will be correct in that prediction. The fact that there are non-flat parts of space elsewhere that were used to facilitate the aforementioned events in the flat part, is irrelevant to SR.

If, on the other hand, you are talking about cosmological wormholes that might let you travel some place that is far, far away--e.g., outside our Hubble sphere--then Special Relativity might not apply. For instance if the reason we can have a wormhole is because space ever-so-slowly curves back onto itself, and there ends up being a short little bridge between two pieces of the universe that turn out to be very close to each other in the space that encloses our 3D space, but far away when measured as an ant crawls within our space, then Special Relativity won't be of use because the space between A and B is not flat. But in that case, GR lets you violate causality with such wormholes, even if you can no longer analyze the issue with SR:


You can write to me at doug at alum.mit.edu, but I can't provide much deep insight to GR, as my knowledge of it isn't much more than that of a knowledgeable layperson. I only really understand SR and when it can be applied.

Your reasoning is flawed. The argument against the Alcubierre drive cannot stem from special relativity as it would only apply if there were a violation of local causality.

The problem is that using an Alcubierre drive, one could construct closed timelike curves, which are impossible in a 3+1-dimensional, asymptotically flat and singularity-free spacetime where the weak energy condition holds.

Also keep in mind that FTL is less problematic than many physicists think, even in special relativity - see eg 'Tachyon Kinematics and Causality: A Systematic Thorough Analysis of the Tachyon Causal Paradoxes' by Recami.

My reasoning is not flawed. And the paper you pointed me on re tachyons, specifically states that we cannot use tachyons to transmit information via them.

I never stated that nothing can travel faster than light. Only that WE cannot travel faster than light, nor can we transmit information faster than light, without violating causality.

On the other hand, maybe we can violate causality.

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