Something I don't understand about FTL travel

[AndromedaRXJ]

Okay first of all, I know it's impossible to travel faster than light. But they say that IF... IF you could, then you would arrive at your destination before you left.

That's what I don't understand.

Like for example, it takes light 8 minutes to get to us from the Sun.

So if a person left Earth at 6:00 and arrived at the Sun at 6:07, he traveled faster than light. But that doesn't sound like he arrived there before leaving. It just sounds like he arrived 7 minutes LATER. Faster than expected of light, but still LATER.

Can someone explain this?

 

[Matterwave]

In some valid reference frame which is in motion with respect to the Earth-Sun system, it will be that you arrived before you left because any two events which are space-like separated (you leaving and you arriving would be 2 events which are space-like separated) can be found to change order by making a lorentz boost. I will let someone else show the math because I'm lazy.

 

[stevendaryl]

Okay first of all, I know it's impossible to travel faster than light. But they say that IF... IF you could, then you would arrive at your destination before you left.

It has to do with the way time transforms in Special Relativity. Suppose you have some faster-than-light ship that travels at some speed $U > c$. So pick two frames F and F' with relative speed v. Have your FTL ship travel from $x_1=0, t_1=0$ to some point $x_2=UT, t_2 = T$. Under Lorentz transforms, we can compute the coordinates in frame F' as follows:

$x_1' = 0$
$t_1' = 0$
$x_2' = \gamma (x_2 - v t_2) = \gamma (U-v)T$
$t_2' = \gamma (t_2 - \dfrac{v}{c^2} x_2) = \gamma (1-\dfrac{Uv}{c^2})T$

Note: if $U = \dfrac{c^2}{v}$, then $t_2' = 0$. So if $U > c$ in one frame, then travel time can be instantaneous in another frame. But it gets weirder than that. If $U > \dfrac{c^2}{v}$, then $t_2' < 0$. So in frame F', the faster-than-light ship arrives Before it leaves.

So if faster-than-light travel is possible in one frame, then there are frames in which back-in-time travel is possible.

 

[Fredrik]

Okay first of all, I know it's impossible to travel faster than light. But they say that IF... IF you could, then you would arrive at your destination before you left.

That's what I don't understand.

Like for example, it takes light 8 minutes to get to us from the Sun.

So if a person left Earth at 6:00 and arrived at the Sun at 6:07, he traveled faster than light. But that doesn't sound like he arrived there before leaving. It just sounds like he arrived 7 minutes LATER. Faster than expected of light, but still LATER.

Can someone explain this?

You're right. However, in a coordinate system that's comoving with someone going fast (but <c) in the direction towards the sun, the same sequence of events would be described very differently. I think a spacetime diagram is the best way to explain it. I drew this one in paint, so it's ugly (and not 100% accurate, because the lines don't have the right slopes), but it illustrates the main point well enough.

The t and x axes are the ones used by the observer on Earth. The points on a line that's parallel to the x-axis all have the same t coordinate. The t' and x' axes are the ones used by an observer whose motion is described by the t' axis. The points on a line that's parallel to the x' axis all have the same t' coordinate. Note that it's possible to draw a horizontal line in the diagram below the Sun 6:01 event and above the Earth 6:00 event. This means that the Sun 6:01 event has a later t coordinate than the Earth 6:00 event. But the Earth 6:00 event is above the x' axis, while the Sun 6:01 event is below the x' axis. This means that the former has a later t' coordinate than the latter.

So in the "primed" coordinate system, the thing you think of as going from the Earth to the sun is described as going from the Sun to the Earth. Alternatively, it can be considered going from the Earth to the sun, but arriving before departing (i.e. going back in time).

Edit: I have to add that it doesn't make sense to use a person in the example, because a person moving FTL contradicts SR. So SR plus your assumption is logically inconsistent, and in an inconsistent system, every statement is true (including things like 7=3). It never makes sense to ask what would happen if something that contradicts the theory we're supposed to use to answer the question is true. But it's fine to ask what happens if some weird-*** particle makes this trip, because that doesn't immediately contradict SR. (Apparently we can't say "***". I didn't know that).

 

[AndromedaRXJ]

Thanks everyone for answering. I've read all your posts.

I'm not that great in understanding mathematics, however. So in other words, not all observers will see the ships arrival before it's departure? Only the one moving towards the Sun?

Is the way I described it in my first post assumes that time and simultaneity are absolute and not relative? Or is there at least one observer who would see it that way?

It has to do with the way time transforms in Special Relativity. Suppose you have some faster-than-light ship that travels at some speed $U > c$. So pick two frames F and F' with relative speed v. Have your FTL ship travel from $x_1=0, t_1=0$ to some point $x_2=UT, t_2 = T$. Under Lorentz transforms, we can compute the coordinates in frame F' as follows:

$x_1' = 0$
$t_1' = 0$
$x_2' = \gamma (x_2 - v t_2) = \gamma (U-v)T$
$t_2' = \gamma (t_2 - \dfrac{v}{c^2} x_2) = \gamma (1-\dfrac{Uv}{c^2})T$

Note: if $U = \dfrac{c^2}{v}$, then $t_2' = 0$. So if $U > c$ in one frame, then travel time can be instantaneous in another frame. But it gets weirder than that. If $U > \dfrac{c^2}{v}$, then $t_2' < 0$. So in frame F', the faster-than-light ship arrives Before it leaves.

So if faster-than-light travel is possible in one frame, then there are frames in which back-in-time travel is possible.

Also, what is the capital T in these equations?

 

[Fredrik]

I'm not that great in understanding mathematics, however.

You should focus on spacetime diagrams then.

So in other words, not all observers will see the ships arrival before it's departure? Only the one moving towards the Sun?

Correct.

Is the way I described it in my first post assumes that time and simultaneity are absolute and not relative? Or is there at least one observer who would see it that way?

The Earth observer sees it that way. A thing is only "absolute" if all observers agree about it.

Also, what is the capital T in these equations?

It's the time coordinate of the arrival event in the coordinate system comoving with Earth. Since the departure event has time coordinate 0, it's also the travel time in that same coordinate system.

 

[Whovian]

Someone in a certain reference frame will see you arrive before you left, but they'll see you arrive as a flying purple telephone made of strawberry sausage since the journey took you 5i years.

 

[georgir]

Someone in a certain reference frame will see you arrive before you left, but they'll see you arrive as a flying purple telephone made of strawberry sausage since the journey took you 5i years.

No, imaginery durations or coordinates are the result of the observer himself moving at above c, but in this case we are talking about a subluminal observer observing superluminal-separated (spacelike separated) events. He will just see a reversed order of events.

 

[georgir]

I think the distinction between spacelike-separated, timelike-separated and null-separated events is good to point out here.

If a velocity under the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is also always the same in all reference frames. Such events are called "timelike separated", and because of the invariance of their relative order, causal relation between them is possible.

If a velocity above the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is not the same in all reference frames. In some frames they are simultaneous, in others one preceeds the other, and in others yet their order is reversed. Such events are called "spacelike separated" and because of the undefiniteness of their relative order, causal relation between them is considered impossible. In other words, they can not belong on a single "worldline", or be events concerning a single object.

If a velocity exactly equal the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is also always the same in all reference frames. Such events are called "null separated", causal relation between them is possible, but only as electromagnetic or gravity field changes, not massive particle travel.

 

[vemvare]

Do I read Fredrik's diagram correctly if I conclude that the fast-moving observer will see the "FTL" ship moving backwards, but due to the distances between Earth and sun and the observer moving slower than light it could never interfere, fr. ex by first seeing the ship leaving (backwards) the sun and then sending a message to tell the ship not to start the journey in the first place.

Oh, this is hard to put to words, but my point is, is there some kind of difference between a scenario leading to a paradox where an observer would observe an effect leading to a cause (=time going backwards) but not being able to interfere due to the limits of lightspeed, and an observer being able to either contact his own past, or convey a message from the sun to Earth backwards in time?

Are both scenarios "equally impossible?"

 

[Fredrik]

Do I read Fredrik's diagram correctly if I conclude that the fast-moving observer will see the "FTL" ship moving backwards, but due to the distances between Earth and sun and the observer moving slower than light it could never interfere, fr. ex by first seeing the ship leaving (backwards) the sun and then sending a message to tell the ship not to start the journey in the first place.

The world line of the "fast-moving" observer is the t' axis. As you can see, it intersects the world line of the FTL object. So they actually meet at that event, and can do things to each other. Suppose e.g. that a short time before that event, the "fast-moving" ship drops an empty fuel tank or something, that collides with and destroys the FTL object. This would eliminate the part of the FTL object's world line that's to the right of the explosion event, not the part that's to the left. From the fast-moving ship's point of view, this is what happened: It dropped a fuel tank, which subsequently exploded, and out of the explosion came an object that was moving FTL towards Earth.

Oh, this is hard to put to words, but my point is, is there some kind of difference between a scenario leading to a paradox where an observer would observe an effect leading to a cause (=time going backwards) but not being able to interfere due to the limits of lightspeed, and an observer being able to either contact his own past, or convey a message from the sun to Earth backwards in time?

To get an actual contradiction, you must consider two devices that are moving at different velocities, and are both capable of receiving and emitting FTL particles. See this post to find out how the ability to send messages that have infinite speed in your own rest frame leads to a contradiction.

 

[stevendaryl]

Do I read Fredrik's diagram correctly if I conclude that the fast-moving observer will see the "FTL" ship moving backwards, but due to the distances between Earth and sun and the observer moving slower than light it could never interfere, fr. ex by first seeing the ship leaving (backwards) the sun and then sending a message to tell the ship not to start the journey in the first place.

Oh, this is hard to put to words, but my point is, is there some kind of difference between a scenario leading to a paradox where an observer would observe an effect leading to a cause (=time going backwards) but not being able to interfere due to the limits of lightspeed, and an observer being able to either contact his own past, or convey a message from the sun to Earth backwards in time?

Are both scenarios "equally impossible?"

What I think you might be getting at is that travel back in time doesn't necessarily lead to a paradox. What is paradoxical is a closed time loop. If I can send a message to my own younger self, then that would lead to a paradox, because I can tell myself "Don't send this message".

But if FTL is possible, and all frames are equivalent (the relativity principle), then it is possible to send a message to your own younger self. Send a back-in-time message from yourself to a colleague, and have the colleague send a back-in-time message back to you.

 

[Fredrik]

But FTL is possible, and all frames are equivalent (the relativity principle), then it is possible to send a message to your own younger self. Send a back-in-time message from yourself to a colleague, and have the colleague send a back-in-time message back to you.

This is a bit of an oversimplification. I would describe it like this: Send a FTL message to a colleague who is moving away from you at a speed close to c, and have him send a FTL reply back to you. If the speeds and distances involved are great enough, then you will receive the reply before you sent the message.

 

[Dadface]

What am I missing here? Andromeda RXJ seems to be asking ...What would the outcome be if you did something that's impossible to do?

 

[stevendaryl]

This is a bit of an oversimplification. I would describe it like this: Send a FTL message to a colleague who is moving away from you at a speed close to c, and have him send a FTL reply back to you. If the speeds and distances involved are great enough, then you will receive the reply before you sent the message.

But you can prove that if it is possible to send FTL messages between two observers, then it is possible to send back-in-time messages between the same two observers.

 

[stevendaryl]

What am I missing here? Andromeda RXJ seems to be asking ...What would the outcome be if you did something that's impossible to do?

It's not possible to do something that is impossible.

 

[Dadface]

It's not possible to do something that is impossible.

That's exactly my point. If FTL is impossible then why discuss the consequences of moving at FTL speeds? The question is contradictory and doesn't make sense.

 

[Fredrik]

But you can prove that if it is possible to send FTL messages between two observers, then it is possible to send back-in-time messages between the same two observers.

To produce a message that's going back in time in all inertial coordinate systems, you need two devices that can send and receive FTL messages, and there must be a large velocity difference or large distance between them.

 

[Fredrik]

That's exactly my point. If FTL is impossible then why discuss the consequences of moving at FTL speeds? The question is contradictory and doesn't make sense.

It's contradictory and doesn't make sense, but only because the OP used the word "person" instead of "tachyon". Since there was an easy way to change the question into one that does make sense, I chose to answer the question that made sense instead. See my comment in the "Edit" part of post #4.

 

[Dadface]

It's contradictory and doesn't make sense, but only because the OP used the word "person" instead of "tachyon". Since there was an easy way to change the question into one that does make sense, I chose to answer the question that made sense instead. See my comment in the "Edit" part of post #4.

If there is a real possibility that a particle can move FTL then the question can make sense. Sorry for not noticing your edit.

 

[stevendaryl]

That's exactly my point. If FTL is impossible then why discuss the consequences of moving at FTL speeds? The question is contradictory and doesn't make sense.

The point of discussing what would happen if there were FTL is to prove that it is impossible. Logically, to prove something is impossible means showing that it leads to a contradiction.

 

[Thinker007]

Andromeda RXJ seems to be asking ...What would the outcome be if you did something that's impossible to do?

I don't see the question like that. I believe he's saying that in one IRF (the IRF he's most familiar with - approximately at rest relative to Earth/Sun) FTL travel seems to create no paradoxes of the type he's heard about (arrival before departure, etc.)

The answers seem to me to be just about right on point - explaining what FTL travel looks like in other IRFs.

I'm certainly not convinced that SR, standing alone, rules out FTL. I'm not convinced that physics today rules out time travel. For all I know, some combination of the Many Worlds Theory of QM coupled with SR would obviate all the contradictions that appear. The contradictions are separated into different split-off worlds. As such, understanding the contradictions from FTL is an important step.

Shifting away from the MWT idea- when I think about the meaning of "now" in the Andromeda Galaxy, I'm often tugged towards the idea that the future is fixed and unchangeable - that free will is nothing but an illusion. In such a universe there can be no time paradoxes of the type that challenge us when thinking about FTL. The message to kill my grandfather never arrives, etc.

Or perhaps there are tachyons, but they are on the other side of a light speed barrier and just can't interact with an STL universe.

The question was quite reasonable from my point of view. We all have to start somewhere and we all can travel farther down the road of knowledge from where we are now.

 

[Fredrik]

The point of discussing what would happen if there were FTL is to prove that it is impossible. Logically, to prove something is impossible means showing that it leads to a contradiction.

That's not what we've been doing in most of this thread. If we replace the word "person" with "some weird particle" in the OP's question (in order to make sense of the question), it's just asking whether a particle that moves FTL from Earth to the Sun is really moving back in time. And the answer is that that it's only going back in time in some coordinate systems. In others, like the inertial coordinate system that's comoving with Earth, the particle reaches the Sun after it left Earth.

A theory of both FTL matter and normal matter in Minkowski spacetime would have to have some counterintuitive features, but I don't think there's a theorem that says that all such theories can be ruled out.

 

[nitsuj]

In all this hypothetical FTL talk; how would the natural units for time & length change?

I always find FTL talk really strange as they often are discussed in a context where c is a constant, and the metric is still +++-.

To say "On this Mink' diagram you see the message has arrived sometime before it was sent." seems to completely ignore the relationship, or representation of orthogonal time & length axis on said diagram and from where it was derived.

To say that different, c is a geometric constant as much as an invariant speed limit.

 

[stevendaryl]

That's not what we've been doing in most of this thread. If we replace the word "person" with "some weird particle" in the OP's question (in order to make sense of the question), it's just asking whether a particle that moves FTL from Earth to the Sun is really moving back in time. And the answer is that that it's only going back in time in some coordinate systems. In others, like the inertial coordinate system that's comoving with Earth, the particle reaches the Sun after it left Earth.

A theory of both FTL matter and normal matter in Minkowski spacetime would have to have some counterintuitive features, but I don't think there's a theorem that says that all such theories can be ruled out.

It seems to me that you couldn't prevent closed time-loops if FTL were possible in all reference frames. If it's possible to send a particle from the Earth to the Sun that is backward in time relative to one frame, then what would prevent sending one back-in-time relative to the Earth's frame? And if it's possible to send a message back-in-time from the Earth to the Sun, what would prevent sending a message back-in-time from the Sun to the Earth? It seems to me that FTL + relativity implies the possibility of closed time loops. I don't see what could prevent it.

Long ago, I read a paper that resolved the paradoxes from closed time loops by invoking noise. If you try to communicate with yourself in the past using tachyons, then you will find, on the receiving end, that there will be tachyon "noise" that will drown out any message that you might receive from your own future. I couldn't figure out whether this made sense, or not.

 

[PeterDonis]

It seems to me that FTL + relativity implies the possibility of closed time loops. I don't see what could prevent it.

You could prevent it by introducing a preferred frame into the law that determines the worldlines of FTL particles: in other words, an FTL particle's velocity is not defined relative to the emitter, but relative to the same preferred frame regardless of the emitter's state of motion. This arguably violates the principle of relativity, but it could be modeled within the framework of SR; the model would just have an ugly "privileged" frame in it.

 

[stevendaryl]

You could prevent it by introducing a preferred frame into the law that determines the worldlines of FTL particles: in other words, an FTL particle's velocity is not defined relative to the emitter, but relative to the same preferred frame regardless of the emitter's state of motion. This arguably violates the principle of relativity, but it could be modeled within the framework of SR; the model would just have an ugly "privileged" frame in it.

Yeah. I would consider that a violation of the "spirit" of relativity, which is the equivalence of all inertial frames. If you are willing to give up that equivalence, then FTL doesn't necessarily lead to a contradiction.

 

[Fredrik]

It seems to me that you couldn't prevent closed time-loops if FTL were possible in all reference frames. If it's possible to send a particle from the Earth to the Sun that is backward in time relative to one frame, then what would prevent sending one back-in-time relative to the Earth's frame? And if it's possible to send a message back-in-time from the Earth to the Sun, what would prevent sending a message back-in-time from the Sun to the Earth? It seems to me that FTL + relativity implies the possibility of closed time loops. I don't see what could prevent it.

Think about what we do when we use SR to find the the correct final ages in the twin paradox scenario. All we do is to consider Minkowski spacetime and two curves in it. Physics is usually like this. We use an extremely idealized theory that doesn't describe everything that's going on in the real world. In this case, the theory describes a universe that's empty save for two particles, one of which changes its direction at one point, for reasons not explained by the theory. So the theory doesn't even fully describe the scenario we're trying to study. In addition to things that are left out of the theory by choice, there are also things in the real world that can't exist in the fictional universe described by the theory. For example, a classical theory of point particles in Minkowski spacetime can't describe an atomic clock.

If we try to describe the "message back in time" scenario with an idealized classical theory of point particles, like we did with the twin paradox, and the real world contains objects like emitters and receivers of FTL particles, devices that can't exist in the theory we're using, as well as humans who are willing and able to do all the things we've talked about, then we run into the problem that you see. By assumption, there's nothing that prevents us from doing something self-contradictory, like sending a message that starts a chain of events that prevents us from sending that message in the first place.

I think that this line of reasoning rules out a large class of idealized theories, but maybe not all. You mentioned noise as a way out. I haven't heard that one, but yeah, why not? There could be other ways out, like having the time it takes to reliably detect a particle grow linearly with the distance it has traveled, or something like that. Maybe that's essentially the same idea, because what does noise do other than make it harder to detect the particle?

There's also a tiny chance that a theory of all the matter in the universe could involve FTL particles. In this case, since a theory wouldn't be a "theory" if it's logically inconsistent, the equations of motion would only have solutions in which none of these paradoxial experiments we have thought of is ever carried out. (If it's a quantum theory, that possibility is assigned probability 0). I know that this sounds ridiculous, but it's logically possible. There could be a solution in which humans never discover the technology. There could be a solution in which we do, but never choose to use it. There could be a solution in which we decide to use it, and then get wiped out by a meteor that's been on its way towards us for billions of years, before we have had a chance to finish the experiment. But there can't exist a solution in which we invent the technology, choose to use it, and then do the experiment, because a "solution" with a paradox isn't actually a solution. It's just nonsense.