FTL travel and causality

[RedImperator]

I'm trying to get my head around how traveling faster than light violates causality, and I just can't do it.

Say you're an observer at star A. An event happens there that you feel the people at Star B, five light years away, ought to know about right away. So you fire up the ansible and tell them. Now they know about the event before they could have if you let them wait until they could have observed it.

According to what I've read (and managed to understand), the recipient at Star B could violate causality by using his ansible to warn you about the event before it happens, allowing you to either prevent the event or escape before it happens, thus you never send the first message to B in the first place, thus creating an unsolvable paradox. I don't get this at all: to my way of understanding, the lightspeed lag is equivilant to the lag between when an event happened in 18th century London and when the news arrived by ship in Philadelphia. The ansible is analogous to a transatlantic telegraph cable. When B learns about the event, he's not learning about an event that's going to happen five years in his future, he's just hearing about an event that happened shortly in the past. I don't get at all how him learning that violates causality, let alone how B could create a paradox.

Any help would be appreciated; I'm trying to build a sci-fi universe with as little handwavium as possible, and I'd like to deal somehow with the causality problem (I'm resigned to insulting relativity with FTL travel). The only solution I've come up with is a partial FTL drive. From the point of view of a ship and its crew, travel between two distant points is instantaneous (and since it uses non-Newtonian methods, no propellant is needed for the interstellar portion of the trip), but from the point of view of an observer at point B, it took exactly as long for them to travel the distance as it would have if they'd moved at exactly c. It's an interesting dramatic limitation, I think, but a bit more than I want to deal with. But I can't find another way out without understanding the relationship between FTL and causality first.

[Hotfoot]

Causality is a messy thing, but here's the basic thing you have to understand about time:

Time is NOT constant.

If your FTL moves in such a way as to create a sort of "Time Constant" that prevents it from moving backwards, then you can preserve causality, because at best things will happen simultaneously. Otherwise, there is a distinct possibility of travelling so fast as to move backward in time.

The most widely accepted method of travelling faster than light is to cheat relativity by using a wormhole. Say you start off with the two ends near one another. Then you send one end off at relativistics speeds, and then have it come back. That end of the wormhole will now lead back not just to a specific place, but a specific time, one that exits during, effectively, the past, thanks to the time dilation. If it only "aged" two years, but you sent it off for twenty, and you left yourself a note that your wife will cheat on you eight years from now (because it happened ten years ago to you), then two years after you send one end of the wormhole off, you get a note from the other telling you that your wife is about to cheat on you. Alternatively you could kill yourself, a variation on the grandfather paradox.

Of course, current physics speculates that once you bring the first wormhole back, both wormholes would explode. That doesn't stop you from doing other naughty things with causality, however...

[RedImperator]

Causality is a messy thing, but here's the basic thing you have to understand about time:

Time is NOT constant.

If your FTL moves in such a way as to create a sort of "Time Constant" that prevents it from moving backwards, then you can preserve causality, because at best things will happen simultaneously. Otherwise, there is a distinct possibility of travelling so fast as to move backward in time.

The most widely accepted method of travelling faster than light is to cheat relativity by using a wormhole. Say you start off with the two ends near one another. Then you send one end off at relativistics speeds, and then have it come back. That end of the wormhole will now lead back not just to a specific place, but a specific time, one that exits during, effectively, the past, thanks to the time dilation. If it only "aged" two years, but you sent it off for twenty, and you left yourself a note that your wife will cheat on you eight years from now (because it happened ten years ago to you), then two years after you send one end of the wormhole off, you get a note from the other telling you that your wife is about to cheat on you. Alternatively you could kill yourself, a variation on the grandfather paradox.

Of course, current physics speculates that once you bring the first wormhole back, both wormholes would explode. That doesn't stop you from doing other naughty things with causality, however...

Ok, so let me see if I understand your example:

1. You have a wormhole with both ends, say, a few feet apart, on January 1st, 2010.

2. You send one end of it on a long trip at near c. It goes out for ten years, and then it comes back for ten years, from your point of view. It returns to its starting point on January 1, 2030. Because of time dilation, though, the end you sent out has only experienced two years.

3. Meanwhile, on January 1, 2020, my wife cheats on me.

4. Because wormholes are points in spacetime, not just space, the voyager end is not connected to the end that stayed at home and now exists a few feet away on January 1, 2030. Rather, it's connected to the wormhole end that exists in the same spot on January 1, 2012. If I send a message back that my wife cheated/will cheat on January 1, 2020, myself in 2012 can kick that bitch to the curb before she cheats on me, violating causality.

5. If I jumped through the stationary wormhole end, I'd wind up a few feet away on January 1, 2048, since the stationary end is now 18 years behind its counterpart.

If I have this all right, then this all generally makes sense to me, but I don't get why the mobile end plugs into the stationary end 18 years in the past, instead of the end 20 years in the past, at its start point.

Would it be accurate to think, instead of a single stationary wormhole end, a series of them like still frames from a movie, one for each moment that passes? So if the mobile end experiences two years of time passing, it plugs into the stationary end that's experienced two years worth of moments as well?

[SirNitram]

Any help would be appreciated; I'm trying to build a sci-fi universe with as little handwavium as possible, and I'd like to deal somehow with the causality problem (I'm resigned to insulting relativity with FTL travel). The only solution I've come up with is a partial FTL drive. From the point of view of a ship and its crew, travel between two distant points is instantaneous (and since it uses non-Newtonian methods, no propellant is needed for the interstellar portion of the trip), but from the point of view of an observer at point B, it took exactly as long for them to travel the distance as it would have if they'd moved at exactly c. It's an interesting dramatic limitation, I think, but a bit more than I want to deal with. But I can't find another way out without understanding the relationship between FTL and causality first.

That sounds like it works out correctly: The 'information' of the ship departing arrives at the same time as the ship, and there's no violation. Indeed, this not-so-cheating method is seen in quite a few of the so-called hard sci-fi: Niven's teleporter universe used it for the Phoenix test-craft, first interstellar ship by virtue of teleporting through a 'receiver' carried by a sublight drone ship.

Also, Manifold: Space by Baxter used similar: Portals which used quantum entanglement to transmit things between them at exactly cee, but they experienced no time, because as the above, they were existing as.. Whatever something being teleported is. A potential particle, Niven used to describe it.

There's no violation and also no time passing for those inside. Relativity demands that, as they moved at cee, time stopped..

If you'd like more dramatic fleshing out, there may be a need for a receiver: Either a pre-made, stationary portal like in Manifold, or ships with huge receiver cages plying through space for decades or centuries. Or whatever else interests you.


As for the actual question, I've no idea why it is, but the 'information' of a ship departing a system can't be outrun by the ship itself. Insofar as I grok any of it, the only way out of this is to postulate an information-carrying tachyon, which just shoves the speed limit higher.

[Wyrm]

With many problems in relativity, the problem of FTL travel and causality boils down to "simultaneous events." In relativity, an observer defines his x axis to be the locus of all points such that, for all a, if he sends out a light pulse at the event at time t = - a, he will receive the reflection at t = a. This is because the light pulse spent equal time (from this observer's perspective) getting to the event as coming back.

Now, suppose the signal from your FTL communication device gets to a distant receeding galaxy instantly from your frame of reference. That is to say, if the galaxy is located at (t_0, x_g) in your coordinates, then if you send the FTL signal at (t_0, 0) [ie, here and now], then you can verify that your FTL signal got to the distant galaxy at (t_0, x_g) in your coordinates. Meanwhile, your friends in that distant galaxy has a simiar setup, and is able to verify that if they sent their FTL signal at (t_0, 0) in their coordinates, then they can verify that their FTL signal got to you at (t_0, - x_h) in their coordinates.



Suppose you want to ask your friends in the distant galaxy whether they see helicopters out their window, sending your message at event A. This event is simultaneous with event B, so your friends receive the message at B. They look outside their window and see that there are indeed no helicopters, and send a message back using their own FTL apparatus at event B (or very nearly the same event as B, but these galaxies are distant), which you will receive at an event simultaneous with their event B, or C.

Notice that event C lies in the past of event A, the initial message. Therefore, the event A caused the event C. If you resolved that you would send your message only if you did not receive the answer before you call, then you'd have a happy little mini-grandfather paradox!

As for avoiding such problems in hardish sci-fi, the principle is this: Relativity, Causality, FTL travel -- choose two. The only way to avoid causality problems when using FTL travel is to break relativity in some way when using FTL. The most straightforward way to do this would be to have some OTHER definition of simultaneity than what relativity uses.

[Kuroneko]

Consider the following spacetime diagram:

Stationary observer at A measured events according to the unprimed axes--all events on lines parallel to the x axis are simultaneous according to this observer. Thus, A and B are simultaneous in this reference frame. The primed observer, here pictured as traveling at a significant fraction of the speed of light (the dotted line is a light ray), judges events simultaneous if they are on a line parallel to the x' axis. Accordingly, events B and C are simultaneous according to the primed observer. But C is clearly in the past of A--if the ansible allows instantaneous communication between A and B, then in some reference frames, B receives the signal before it is sent. If there is a relay at C with another ansible, then the original sender at A can receive his or her own signal before it is sent.

[Rye]

This is something I don't get as well; if time is different depending on where you are and how fast you're going, why is all of that limited by lightspeed? I mean, wouldn't the universe just be self correcting? Like, if you wanted to send a message to any other hypothetical point contemporaneous to yourself, wouldn't there be a hypothetical "accessible" velocity/direction/location relative to you that would define the point you want to reach?

Say I'm at the sun as it goes nova, whereas 8 light minutes away, on the Earth, is John. Now, why couldn't I use a machine that converts what I say into an electric signal, which converts that into light, and then converts light into some sort of faster than light particle, to reach earth in 4 minutes, and John gets a 4 minutes heads up on the planet dying? 4 minutes before the nova hits, John still exists, as does the lag between the two events, the sending and the recieving, it was just reduced because it used a faster means. Me, being near the sun when it goes nova, I know where the earth will be in 4 minutes time, relative to me, so, why can I not bombard that area with ftl particles, and the message not get through?

I kinda feel like I'm stupid and missing something obvious, here.

[Hotfoot]

Ok, so let me see if I understand your example:

1. You have a wormhole with both ends, say, a few feet apart, on January 1st, 2010.

2. You send one end of it on a long trip at near c. It goes out for ten years, and then it comes back for ten years, from your point of view. It returns to its starting point on January 1, 2030. Because of time dilation, though, the end you sent out has only experienced two years.

3. Meanwhile, on January 1, 2020, my wife cheats on me.

4. Because wormholes are points in spacetime, not just space, the voyager end is not connected to the end that stayed at home and now exists a few feet away on January 1, 2030. Rather, it's connected to the wormhole end that exists in the same spot on January 1, 2012. If I send a message back that my wife cheated/will cheat on January 1, 2020, myself in 2012 can kick that bitch to the curb before she cheats on me, violating causality.

5. If I jumped through the stationary wormhole end, I'd wind up a few feet away on January 1, 2048, since the stationary end is now 18 years behind its counterpart.

This is correct, except that you would be coming out of the mobile end. Stationary -> Mobile and Mobile -> Stationary.

Of course, this begs the question of what the hell happens to the 20 year old stationary end. Truth is, I have no idea. I would imagine, however, that it leads to some point in the mobile ends future, which can cause another paradox if you jump through and then someone destroys the current version of the mobile end.

If I have this all right, then this all generally makes sense to me, but I don't get why the mobile end plugs into the stationary end 18 years in the past, instead of the end 20 years in the past, at its start point.

Because the 20 year tripe took it 2 years, thanks to time dilation. If the trip were at the speed of light, it would essentially be instantaneous, but then comes the little problem of needing more energy than exists in the universe.

Would it be accurate to think, instead of a single stationary wormhole end, a series of them like still frames from a movie, one for each moment that passes? So if the mobile end experiences two years of time passing, it plugs into the stationary end that's experienced two years worth of moments as well?

Not really. A wormhole is literally a shortcut in spacetime. Assuming one exists, it exists as all things would in the universe.

The stationary end would see, effectively, very slow motion for the entire trip of the mobile end. Two years stretched over twenty. This is essentially an extension of the twin paradox, only it creates a series of problems rather than solving one.

As for Tachyons, well, one headache at a time, as Tachyons get quite messy indeed.

Have you ever heard of the "Time Cone" example to describe causality?

[Kuroneko]

This is something I don't get as well; if time is different depending on where you are and how fast you're going, why is all of that limited by lightspeed?

The direction of your inference is incorrect. Lightspeed is not a limit because time is relative, but time is relative because lightspeed is a limit.

I mean, wouldn't the universe just be self correcting? Like, if you wanted to send a message to any other hypothetical point contemporaneous to yourself, wouldn't there be a hypothetical "accessible" velocity/direction/location relative to you that would define the point you want to reach?

If the event is simultaenous to you (a given event on your own worldline), then the required velocity to reach it is infinite. In this sense, the required velocity is defined, but that does not mean it is accessible.

Say I'm at the sun as it goes nova, whereas 8 light minutes away, on the Earth, is John. Now, why couldn't I use a machine that converts what I say into an electric signal, which converts that into light, and then converts light into some sort of faster than light particle, to reach earth in 4 minutes, and John gets a 4 minutes heads up on the planet dying? ...

The causality problem is independent of the mechanism used to achieve a superluminal signal.

If there is a relay at C with another ansible, then the original sender at A can receive his or her own signal before it is sent.

Actually, this is possible even if there is no third ansible. A strictly luminal signal would allow this as well.

[RedImperator]

Consider the following spacetime diagram:
http://i4.photobucket.com/albums/y121/v ... 145fb2.png
Stationary observer at A measured events according to the unprimed axes--all events on lines parallel to the x axis are simultaneous according to this observer. Thus, A and B are simultaneous in this reference frame. The primed observer, here pictured as traveling at a significant fraction of the speed of light (the dotted line is a light ray), judges events simultaneous if they are on a line parallel to the x' axis. Accordingly, events B and C are simultaneous according to the primed observer. But C is clearly in the past of A--if the ansible allows instantaneous communication between A and B, then in some reference frames, B receives the signal before it is sent. If there is a relay at C with another ansible, then the original sender at A can receive his or her own signal before it is sent.

So, if I understand this correctly:

1. Any event with a negative value for t or t' takes place in the past. Any event with a positive value takes place in the future. A value of zero is the present. Any two events which have the same t or t' value are concurrent.

2. For a stationary observer, who measures spacetime by the non-prime axes, A and B have t values of zero while C has a negative t value.

3. For an observer moving at near lightspeed, who measures spacetime by the prime axes, the t' value of A is zero while the t' values of B and C are an identical negative number.

So if the non-prime observer at A sends a message about an event at C by ansible to a reciever at B, he's sending a message from (0,0) to (x,0). However, from the point of view of the prime observer, the message is moving from (0',0') to (x',-t'). From the prime observer's point of view, the message has gone backwards in time. To make matters worse, point C is at coordinates (-x',-t'), where -t' is the same value as B's -t'. So B can send a message by ansible to C, which from the non-prime observer's viewpoint means B has sent a message back in time. If the event at C changes as a result of this message, then causality has been violated and a paradox occurs.

If I understand all this properly, I think I have a passable enough grasp of this to at least get an idea of what I want to do next. The graph is helpful; it seems the trick to avoiding causality violation is to somehow make it impossible for information to move from t=0 to t<0 from any observer's frame of reference.

[Kuroneko]

So, if I understand this correctly:
1. Any event with a negative value for t or t' takes place in the past. Any event with a positive value takes place in the future. A value of zero is the present. Any two events which have the same t or t' value are concurrent.

Not quite. The first part is fine enought, although to be precise, one should say that any event with a negative t-coordinate takes place in the past according to the unprimed (stationary observer), while any event with a negative t'-coordinate is in the past according to the primed (moving) observer. The qualification of for whom is very important. Which brings us to the more problematic error: "the present" is vastly different for the two observers. For the unprimed observer, all events on the x-axis constitute the present, and in general, all events on a line parallel to the x-axis are simultaneous with one other. For the primed observer, on the other hand, "the present" consists of all events on the x' axis.

2. For a stationary observer, who measures spacetime by the non-prime axes, A and B have t values of zero while C has a negative t value.

Right. Hence, A and B, having the same t-value, are simultaneous, while C is not simultaneous with either of them.

3. For an observer moving at near lightspeed, who measures spacetime by the prime axes, the t' value of A is zero while the t' values of B and C are an identical negative number.

Right. Hence, according to the primed observer, B and C are simultaneous to each other, while A is simultaneous to neither of them.

So if the non-prime observer at A sends a message about an event at C by ansible to a reciever at B, he's sending a message from (0,0) to (x,0). However, from the point of view of the prime observer, the message is moving from (0',0') to (x',-t'). From the prime observer's point of view, the message has gone backwards in time.

Exactly.

To make matters worse, point C is at coordinates (-x',-t'), where -t' is the same value as B's -t'. So B can send a message by ansible to C, which from the non-prime observer's viewpoint means B has sent a message back in time. If the event at C changes as a result of this message, then causality has been violated and a paradox occurs.

Right. And C could communicate the message back to the unprimed observer even with a subluminal signal.

If I understand all this properly, I think I have a passable enough grasp of this to at least get an idea of what I want to do next. The graph is helpful; it seems the trick to avoiding causality violation is to somehow make it impossible for information to move from t=0 to t<0 from any observer's frame of reference.

You will always have some observers for which the cause will follow the effect, but if the usage of an ansible automatically disallows further ansible communication (within some time period), perhaps the more dramatic paradoxes like that above could be avoided (I'm not yet certain of this, however).

By the way, in case you are wondering why the (t',x') axes of the moving observer come closer to the t = x (speed of light) line, instead of appearing orthogonal like the (t,x) axes are, there was a thread just now that touches on this issue. The Lorentz boost Λ(α) = [cosh α, -sinh α; -sinh α, cosh α] = [γ, -vγ; -vγ, γ] is a rotation derived there, where α is the angle of rotation (cosh α = γ = 1/sqrt[1-v²]). If some event has coordinates [t;x] according to the stationary observer, then the moving observer has coordinates [t';x'] = Λ(α)[t;x]. Given this, T = [γ; vγ] maps to [1;0], the unit t-vector, while X = [vγ; γ] maps to [0;1], the unit x-vector. The angle that T makes with the x-axis is atan(coth α) = atan(1/v), and atan(tanh α) = atan(v) for X. These both tend to 45° as α→∞ (v→1). Despite appearances, t' and x' are orthogonal to each other (Minkowski dot product is t0t1-x0x1-y0y1... instead of Euclidean t0t1+x0x1+y0y1...).

[Gil Hamilton]

I've got a question. From reading this thread, I've had a thought.

Say I have an FTL RADAR. If I send out a RADAR ping, would the return from the ping actually arrive before I sent it out?

[Hotfoot]

I've got a question. From reading this thread, I've had a thought.

Say I have an FTL RADAR. If I send out a RADAR ping, would the return from the ping actually arrive before I sent it out?

It is possible for that to happen, yes.

[Wyrm]

This is something I don't get as well; if time is different depending on where you are and how fast you're going, why is all of that limited by lightspeed?

The direction of your inference is incorrect. Lightspeed is not a limit because time is relative, but time is relative because lightspeed is a limit.

Or, more fundamentally (and to the point), time is relative because lightspeed is a constant. In order to make the same beam of light travel stubbornly at c in every reference frame, time and space have to be relative to your inertial reference frame.

[Kuroneko]

]Or, more fundamentally (and to the point), time is relative because lightspeed is a constant. In order to make the same beam of light travel stubbornly at c in every reference frame, time and space have to be relative to your inertial reference frame.

Not quite strong enough. This speed has to be a limit for all interactions. Just because the speed of light is constant does not mean that all interactions are. Instead of ds²=dt²-dx², which is null for the speed of light (dx/dt=±1 gives ds² = 0), one could have ds^4 = α²dt^4 - [1+α²]dtdx + dx^4, which is null for both dx/dt=±1 and dx/dt=±α. In other words, it is possible to arbitrarily insert null trajectories other than those of light--proper time would dilate to zero not only for light but for other null trajectories.

[Ariphaos]

I'm trying to get my head around how traveling faster than light violates causality, and I just can't do it.

Bad math

Normally, when you see people apply lorentz equations and graphs like the above to show a causality breakdown, it's bad math. I've never seen an example of good math that shows that FTL travel violates causality without at the same time showing that STL travel violates causality.

The problem is that the basic lorentz equation that 'proves' this actually requires the origin (as in, location 0) of both objects to be at the same location in spacetime. If you don't (as nearly every last graph and proof I have seen does), you end having every particle in the known universe violating causality with reference to anything moving an appreciable factor of the speed of light.

After this, you still can violate causality if you play with the math a little, but you can just as easily not violate it, just have weird things happen.

Take two ships cross eachother's path, moving away from eachother at .84 of c (time dilation factor of 2). After 15 seconds, ship A sends an instantanious message to ship B, which sends an instantanious reply.

Method 1: Says that ship A will receive the instantanious reply at 15 seconds, immediately after it sent the original message. This would imply the existance of a static frame of reference that somehow emulates relativity.

Method 2: States that ship B will receive A's transmission at 7.5 seconds, and ship A will receive the reply at 3.75 seconds, thus violating causality.

Method 3: States that ship B will receive A's transmission at 30 seconds, and ship A will receive the reply at 60 seconds. This seems more valid than method 2 as the same principles are used as those in the Twin Paradox.

----

That said, if a particle is moving faster than light, it is going to have to be moving in reverse time, or otherwise not experiencing time in a manner that we understand. It won't necessarily violate causality, though.

[Kuroneko]

Bad math... Normally, when you see people apply lorentz equations and graphs like the above to show a causality breakdown, it's bad math. I've never seen an example of good math that shows that FTL travel violates causality without at the same time showing that STL travel violates causality.

Impressive claim, but it doesn't seem to hold up to scrutiny.

The problem is that the basic lorentz equation that 'proves' this actually requires the origin (as in, location 0) of both objects to be at the same location in spacetime. If you don't (as nearly every last graph and proof I have seen does), you end having every particle in the known universe violating causality with reference to anything moving an appreciable factor of the speed of light.

Of course they must be at the same spacetime location; that's what the Lorentz transformation requries by definition. If they weren't, one would use the Poincaré transformation rather than the Lorentz one. Why is this a problem? There is certainly no conceptual difficulty, as the distance between two observers can be made arbitrarily small, particularly relative to the communication distance, making the Lorentz transformation valid to arbitrarily high precision.

After this, you still can violate causality if you play with the math a little, but you can just as easily not violate it, just have weird things happen. Take two ships cross eachother's path, moving away from eachother at .84 of c (time dilation factor of 2). After 15 seconds, ship A sends an instantanious message to ship B, which sends an instantanious reply.

Instantaneous in which reference frame?

Method 1: Says that ship A will receive the instantanious reply at 15 seconds, immediately after it sent the original message. This would imply the existance of a static frame of reference that somehow emulates relativity.

What does it mean to "emulate" relativity? Which frame are you referring to? One of the ships, some frame inbetween...?

Method 2: States that ship B will receive A's transmission at 7.5 seconds, and ship A will receive the reply at 3.75 seconds, thus violating causality.
Method 3: States that ship B will receive A's transmission at 30 seconds, and ship A will receive the reply at 60 seconds. This seems more valid than method 2 as the same principles are used as those in the Twin Paradox.

You are simply conflating frames of reference, the notion of simultaneity in particular. An unqualified "instantenous reply" is inherently ambiguous--does it mean the reply is received at the same time it is sent in A's frame of reference (line AB in the diagram below, parallel to x-axis) or in B's frame of reference (line BC, parallel to x'-axis). Without this qualification, your scenario is too ambiguous to make any predictions.

[Cthulhuvong]

Ok, I have to put in my 2 cents, as this has been bugging me lately.

When A talks to B, B does not get the message instantly, no matter how close B is to A. It takes a fraction of a second to get the message from A to B due to the speed of sound, the distance between A and B, the speed at which B compiles the sound. Thus you are always talking into the future, and a message is never recieved at the same time as it is sent. No matter what we can come up with, we cannot go faster than the speed of time. Every message sent is always recieved after it is sent.

In the nova question, he sent a message to a person at the same time, twice as fast as light (2c). The message was sent to the future. It wouldn't have mattered how fast the message was because time would have to reverse for a message to be revcieved in the past, as time is always moving forward.

If I understand correctly gamma, light, infrared, and radio waves all move at the same speed, c. Even so, it takes time for messages to go around the globe. If you were able to send a message to the person next to you at the speed of sound, it would arrive near instantly. Now if you used one at the speed of light, it would still be near instantly heard. This is becaue time does not move at c, and c will always be slower than time. Time is instantaneous, we have never seen anything be instantaneous besides time. Even light moving 1 nanometer takes time, even if its so small we have to calculate it because our instruments cannot measure it.

[Adrian Laguna]

I came up with an explanations to go around the causality problem if one is really interesting in having FTL in a fictional universe and explaining how it works to some extent. Naturally, it involves fucking with Einstein, various other scientists, and much of modern science.

The Universe forbids violations of causality, end of story. I cannot, and will not, reciever information about my future. The closest to that it can get is information about my present. A warning about getting hit by lightning if I go outside will arrive, at best, as the lightning is hitting me. So causality is never violated. As for observers seeing otherwise, they either obsever false information, or they don't observe this at all. So back to the the chart, when A sends a message to B, the primed observers sees the information going back in time. Since this is impossible, what he sees is incorrect. The 'true' version of events could be said to be what is wittenesed by observers in the same frame of reference as the event.

Comment about Kuronko's chart: I don't see how a violation of causality could occur, if A sends a message to B who sends it to C who sends it back to A, and all of this happens instantanously. Then wouldn't A just be recieving his own message the instant he sent it. No violation of causality, the primed observer sees the message travelling backwards in time, as does A, but what does it matter what he sees. What is happening never actually violates causality does it? I feel like such an idiot for not getting this... perhaps it has something to do with people spending years in college to study this stuff.

The quoted area can be ignored. I wrote this, and cannot be bring my self to delete it. I like the second to last two sentences too much. Think of it as a rough draft that was thrown out for being too bullshitty.

From any frame of reference, you are bound to see things that appear to be violations of causality, (thanks to FTL travel) but aren't. What you are seeing is inccorect, false information. The only frame of reference from which everything you see is the 'correct' vesion of events is one at an absolute standstill and that only exists at the point that is the very center of the universe. The place where the singularity that exploded into the Big Bang used to be. So, while Observer A is seeing Observer B get info on her future from Observer C, B never gets the info until the event has come to pass, and this agrees with what a hypothetical Observer at the center of the Universe will be seeing. However, this opens a horrid can of worms by saying that space-time is, to an extent, absolute. Perhaps a can of worms best not opened for the sake of mantianing SoD with the audience.

[Adrian Laguna]

I just can't resist to edit something if I feel there is even a slight chance that I might be missunderstood.

I like the second to last two sentences too much.

Should not have that "second to" there. So the proper sentence should be:

I like the last two sentences too much.

[Wyrm]

The Universe forbids violations of causality, end of story. I cannot, and will not, reciever information about my future. The closest to that it can get is information about my present. A warning about getting hit by lightning if I go outside will arrive, at best, as the lightning is hitting me. So causality is never violated. As for observers seeing otherwise, they either obsever false information, or they don't observe this at all. So back to the the chart, when A sends a message to B, the primed observers sees the information going back in time. Since this is impossible, what he sees is incorrect. The 'true' version of events could be said to be what is wittenesed by observers in the same frame of reference as the event.

Mmmyes, you've certainly shown that you're not quite grasping what is happening.

The thing is that both the unprimed observer, O, and the primed observer, O', will agree on several things. One of these things is the relative ordering of the events. They will both agree that the event B is in the absolute elsewhere of events A and C, and they will agree that the event A is in the absolute future of C and C is in the absolute past of A. Furthermore, they may not agree along which leg the FTL signal is propagating backward in time, but they will agree that some FTL signal propagates backward in time.

This is not an illusion! Information really is traveling backward in time in Kuroneko's diagram! It comes from the fact that everyone agrees that A transmits real information to B who transmits the same information to C, and C lies in the absolute past of A! (That's why it's called the "absolute past" -- events in the absolute past in one reference frame are in the absolute past of all reference frames!)

Comment about Kuronko's chart: I don't see how a violation of causality could occur, if A sends a message to B who sends it to C who sends it back to A, and all of this happens instantanously. Then wouldn't A just be recieving his own message the instant he sent it.

There is no transmission from A to C. C evolves into A. Kuroneko's chart is a spacetime diagram, not a space diagram. Up and down is a displacement in time, not space, and "down" means earlier in time. C and A have the same space coordinates, but C has an earlier time coordinate than A.

No violation of causality, the primed observer sees the message travelling backwards in time, as does A, but what does it matter what he sees. What is happening never actually violates causality does it?

Yes, it does.

It's been fairly well verified (on paper) that, in a certain sense, relativistic FTL travel and time travel are one and the same. A method of sending signals (or traveling) FTL either obeys causality strictly, or it obeys relativity strictly -- it cannot do both.

[Wyrm]

GRRR! Ghetto Edit: I mean to say that all observers will agree whether any given event takes place in the absolute past, absolute elsewhere, and absolute future of any other event. (They will not agree, in the case of events in the absolute elsewhere, whether one event occurs in the "past" or "future" of another -- that is, which event has the earlier time coordinate. They will agree on the ordering in the case of absolute past and absolute future; that's why they're "absolute.")

[General Trelane (Retired)]

Comment about Kuronko's chart: I don't see how a violation of causality could occur, if A sends a message to B who sends it to C who sends it back to A, and all of this happens instantanously. Then wouldn't A just be recieving his own message the instant he sent it. No violation of causality, the primed observer sees the message travelling backwards in time, as does A, but what does it matter what he sees.

That would be true if none of the observers (A, B, C) were moving at relativistic speeds. But as soon as one or more of them are, then they have different reference frames, and if they're separated by any distance, the concept of simultaneity (and instantaneously) breaks down, and now FTL can result in paradoxes such as this.

I find the following website to be a good primer:
http://www.physicsguy.com/ftl/html/FTL_intro.html

It's still quite lengthy (it even explains light cones), but the math is pared down; try skipping to the relevant chapter (chapter 8 ) and if it doesn't make sense, read the earlier sections to get the fundamentals.

The only solution I've come up with is a partial FTL drive. From the point of view of a ship and its crew, travel between two distant points is instantaneous (and since it uses non-Newtonian methods, no propellant is needed for the interstellar portion of the trip), but from the point of view of an observer at point B, it took exactly as long for them to travel the distance as it would have if they'd moved at exactly c.

This would be no different than actually travelling at exactly c. Note that time dilation and length contraction are two sides of the same coin. So while one may say that time stops for something travelling at c, from the PoV of that something, time continues normally, but the distance (any distance) in the direction of travel has been contracted to nothing, so it took no time to journey however far it went.

[Ariphaos]

Impressive claim, but it doesn't seem to hold up to scrutiny.

I did a hunt for this awhile ago, and even bugged a physicist friend of mine about it (working on his doctorate), and still stumped him, so I dunno.

Of course they must be at the same spacetime location; that's what the Lorentz transformation requries by definition. If they weren't, one would use the Poincaré transformation rather than the Lorentz one. Why is this a problem? There is certainly no conceptual difficulty, as the distance between two observers can be made arbitrarily small, particularly relative to the communication distance, making the Lorentz transformation valid to arbitrarily high precision.

Some people go to say, Everything2, and read the argument there, which uses the Lorentz transformations but starts them 20 minutes apart.

I've never seen one use the Poincare transformation, so if you can come up with one feel free to convince me.

Instantaneous in which reference frame?

That's what I was getting across with the three possibilities. Which reference frame gets to define instant.

I suppose there's a fourth possibility, which would suggest that the FTL message flies off to lala land.

What does it mean to "emulate" relativity? Which frame are you referring to? One of the ships, some frame inbetween...?

If matter is an extension of the fabric of space, then matter's progress towards entropy is its own perception of time, rather than 'real' time as perceived by the universe itself. This would mean that there is a standard frame of reference, but it would be impossible to perceive using currently known laws of physics.

Dunno if I explained that too well.

You are simply conflating frames of reference, the notion of simultaneity in particular. An unqualified "instantenous reply" is inherently ambiguous--does it mean the reply is received at the same time it is sent in A's frame of reference (line AB in the diagram below, parallel to x-axis) or in B's frame of reference (line BC, parallel to x'-axis). Without this qualification, your scenario is too ambiguous to make any predictions.

Let's say A just sends an 'instantanious' message to B. Depending on what 'instantanious' means, B might get it at 7.5 seconds (instantanious to A's frame of reference) or at 30 seconds (instantanious to it's own frame of reference).

Now, if we're to accept the Twin Paradox, the particle that does not undergo acceleration does the aging, and not vise versa. Thus, when A sends its 'instantanious' message to B, B's reference frame is what should be considered 'instant' and not A's, because the message is an effective acceleration back to B.

That better?

[RedImperator]

The thing that really cracks my brain about all this is that A and B are simultaneous, B and C are simultaneous, but C takes place prior to A. I accept Kuroneko's model because he's demonstrated numerous times in the past he knows what he's talking about when it comes to this stuff, but I really really can't get my head around that concept the way I can stuff like evolution or electrons. Is this a personal limitation, or are humans just not wired to understand this stuff any way but mathmatically? I suspect the former, and it's a shot to the ego.