FTL without paradoxes?

[Dave]

Your first reply didn't answer my question, but this one does, thanks -

If you can travel FTL, then you can jump from any point in space to any other without going thru space. And because space-time is a ridged manifold, it mean you can jump between any two points in time. And since there is no preferred order of these points, you can jump forward or backward in time. (Altho with Relativity, forward and backward only makes sense within a light cone.)

Also, if you can jump between any two points in space-time, you can jump between any two velocities. Speed is distance divided by time and you can change them arbitrarily. Which means FTL breaks the First Law of Thermodynamics. (Which is the biggest reason FTL is thought to be impossible.)

 

[goldhawk]

I can now see why so many people are upset by the use of FTL in stories: nearly everyone knows about ridged 4D manifolds....

Don't forget the hyperbolic rotations.

 

[Ursa major]

I'm wincing just thinking about them....

 

[Travis Woodward]

Thanks for all of the replies, especially those who've tried to explain why this isn't workable. I obviously don't understand this as well as I thought (I had read about preferred frames of reference and the idea actually came to me while playing around with light cone diagrams, as everyone I've seen that creates a paradox has involved two-way FTL communication).

I appreciate the suggestions that I could just avoid mentioning paradoxes, and I'm not going for hard sci-fi, but I'd like the universe I'm creating to be logically coherent within itself if possible. The narrative requires both FTL and the time dilation effects of special relativity, but I don't want to allow someone to travel into their own past (and one of the characters would definitely do that if it were possible...). Perhaps that's not achievable, but if so I'd like to understand why.

I probably could have been clearer about what I'm trying to achieve as well. I understand that, if information can travel FTL, there will be a frame of reference where an effect can happen before its cause and so any form of FTL will break causality. What I'm trying to avoid is any possibility of information about the the effect being known by someone who is in a position to influence the cause (e.g. telling the traveler not to depart, because they're going to jump into the middle of a star). And I wanted to do it in an unobtrusive way that doesn't seem too contrived. So the Alastair Reynolds idea of a whole area of space going dark probably doesn't fit the bill.

To help my understanding - let's take the simplest version of the system I described above. Suppose there's just one gateway in existence, and it can send you anywhere in the universe instantaneously (relative to the gateway's frame of reference), but after you've jumped there you're on your own - if you want to go home you have to travel back at relativistic speeds.

For the gateway and traveler's frame of reference (let's say the traveler has to be stationary relative to the gateway when they jump) the journey would happen instantaneously. In some other frames of reference the traveler would arrive before they've left. However, I'd thought that it would still be impossible in any non-FTL frame of reference for information about the traveler's arrival to get back to the gateway before the traveler's departure - i.e. the information would also have to travel back to the gateway at FTL to arrive before the traveler left.

Is that right? If not, can someone explain how the information can get back to the gateway before the traveler leaves?

 

[zmunkz]

I think you can slip around the cases where paradoxes would pop up by simply not mentioning them in your story. You don’t need perfect consistency for a story to stay together.

The issue will still exist, though. Frames in motion relative to one or both endpoints would not agree on the simultaneity of the entry/exit, and if one such frame were able to trigger the gate to close, say, one could contrive a setup where it could close the gate after the arrival of a traveller but also before the departure.

I really don’t think you need to worry too much. Just say its impossible, and the story will move on.

 

[Parson]

I can now see why so many people are upset by the use of FTL in stories: nearly everyone knows about ridged 4D manifolds....

Yeah! you and me both Ursa. We are among the many who knows about rigid 4D manifolds.

 

[Joshua Jones]

Yes, you are mixing classical mechanics with Relativity.

In classical mechanics, space is a ridged 3D manifold and time is governed by a universal clock. Time always flows the same way and by the same amount for everything in the universe. You can travel faster than light and everyone will observe you arriving before you left but you will always arrive after you left because of the universal clock.

But with Special Relativity, space and time form a ridged 4D manifold. When you change your velocity, you cause a hyperbolic rotation within space-time. Time between two events becomes longer while the distance between them becomes smaller. Or vice versa. For events in each other's light cone, time cannot go negative. The hyperbolic rotation prevents this.

If the events are outside of each other's light cone, it is possible for the time between events to go negative. That is, the order of the events reverses. The question: which order of events is the correct one? Or to generalize, which amount of time is the correct one? Because there is no preferred frame of reference, they are all correct.

If you can travel FTL, then you can jump from any point in space to any other without going thru space. And because space-time is a ridged manifold, it mean you can jump between any two points in time. And since there is no preferred order of these points, you can jump forward or backward in time. (Altho with Relativity, forward and backward only makes sense within a light cone.)

Also, if you can jump between any two points in space-time, you can jump between any two velocities. Speed is distance divided by time and you can change them arbitrarily. Which means FTL breaks the First Law of Thermodynamics. (Which is the biggest reason FTL is thought to be impossible.)

Ah, so you are speaking of FTL of the sort that bypasses a section of space, such as a wormhole or teleportation. Well, yeah, if time is a dimension of space, and you can teleport around space, it seems to be just a nuance to teleport around time. Same for wormholes. I was thinking more about technology which contracts space, rather than bypasses it, or if a ship were to be able to directly accelerate past C (we all know that is impossible, but we are talking what ifs as is...).

But, I think where the light speed cone argument falls is that it is confusing the perception of an event with the happening of an event. This isn't ultimately a matter of preferred frame of reference either; when matter, energy, and whatever else interacts in a particular event, our ability to perceive it at all is an effect of the effect, and our ability to perceive the cause is an effect of the cause. Regardless of when, how, or in what order we perceive something, the actual cause and effect remain. That is what I mean by confusing epistemology with ontology; the actual interactions of the cause and effect are subsequently immutable, but how we see them may vary considerably.

 

[goldhawk]

But, I think where the light speed cone argument falls is that it is confusing the perception of an event with the happening of an event. This isn't ultimately a matter of preferred frame of reference either; when matter, energy, and whatever else interacts in a particular event, our ability to perceive it at all is an effect of the effect, and our ability to perceive the cause is an effect of the cause. Regardless of when, how, or in what order we perceive something, the actual cause and effect remain. That is what I mean by confusing epistemology with ontology; the actual interactions of the cause and effect are subsequently immutable, but how we see them may vary considerably.

The effect must be in the cause's future light cone and the cause must be in the effect's past light cone. If you have FTL, you have effect and cause outside of each other's light cone. Specifically, when you enter FTL flight, this is the cause and you exit, this is the effect. It doesn't matter how FTL works since we're only considering the end points.

Now, the effect, that is you exiting FTL flight, comes after the cause in your old light cone. But you can change your velocity so that cause will be in the past of the effect from your new light cone. From this new velocity, you can do another FTL flight where is is possible to jump back to your old position but in the past before you left.

The thing about Special Relativity is that if two events are outside of each other's light cone, it is impossible to determine which came first. Which comes first depends on your velocity and if you change your velocity, you can change the order. That combined with FTL flight allows you to jump back into your own past.

 

[Onyx]

Thanks for all of the replies, especially those who've tried to explain why this isn't workable. I obviously don't understand this as well as I thought (I had read about preferred frames of reference and the idea actually came to me while playing around with light cone diagrams, as everyone I've seen that creates a paradox has involved two-way FTL communication).

I appreciate the suggestions that I could just avoid mentioning paradoxes, and I'm not going for hard sci-fi, but I'd like the universe I'm creating to be logically coherent within itself if possible. The narrative requires both FTL and the time dilation effects of special relativity, but I don't want to allow someone to travel into their own past (and one of the characters would definitely do that if it were possible...). Perhaps that's not achievable, but if so I'd like to understand why.

I probably could have been clearer about what I'm trying to achieve as well. I understand that, if information can travel FTL, there will be a frame of reference where an effect can happen before its cause and so any form of FTL will break causality. What I'm trying to avoid is any possibility of information about the the effect being known by someone who is in a position to influence the cause (e.g. telling the traveler not to depart, because they're going to jump into the middle of a star). And I wanted to do it in an unobtrusive way that doesn't seem too contrived. So the Alastair Reynolds idea of a whole area of space going dark probably doesn't fit the bill.

To help my understanding - let's take the simplest version of the system I described above. Suppose there's just one gateway in existence, and it can send you anywhere in the universe instantaneously (relative to the gateway's frame of reference), but after you've jumped there you're on your own - if you want to go home you have to travel back at relativistic speeds.

For the gateway and traveler's frame of reference (let's say the traveler has to be stationary relative to the gateway when they jump) the journey would happen instantaneously. In some other frames of reference the traveler would arrive before they've left. However, I'd thought that it would still be impossible in any non-FTL frame of reference for information about the traveler's arrival to get back to the gateway before the traveler's departure - i.e. the information would also have to travel back to the gateway at FTL to arrive before the traveler left.

Is that right? If not, can someone explain how the information can get back to the gateway before the traveler leaves?

You can construct a solitary situation that doesn't seem to violate the rules, but there is nothing in the rules that would keep that situation unique.

So if people could build "gateways" and relativistic space ships, there is nothing to prevent the two being used in a way that would create a paradox.

Regardless of when, how, or in what order we perceive something, the actual cause and effect remain. That is what I mean by confusing epistemology with ontology; the actual interactions of the cause and effect are subsequently immutable, but how we see them may vary considerably.

I've tried for a long time to express what the light cone diagrams depict, but English is not built to express things that mathematical in nature. But English is very good at making impossible things sound reasonable. What you wrote above is the latter.

There is no universal time scale to say that anything happens at X:XX time. None. That doesn't fit with the way language treats time, cause and effect. So just saying it is so, isn't.

 

[Joshua Jones]

You can construct a solitary situation that doesn't seem to violate the rules, but there is nothing in the rules that would keep that situation unique.

So if people could build "gateways" and relativistic space ships, there is nothing to prevent the two being used in a way that would create a paradox.



I've tried for a long time to express what the light cone diagrams depict, but English is not built to express things that mathematical in nature. But English is very good at making impossible things sound reasonable. What you wrote above is the latter.

There is no universal time scale to say that anything happens at X:XX time. None. That doesn't fit with the way language treats time, cause and effect. So just saying it is so, isn't.

What I said doesn't require a universal time scale; only that matter, energy, and forces have actual interactions with one another. These interactions are then perceived by observers in their reference frames. But, again, just because Observer A sees X proceed Y and Observer B sees Y before X doesn't mean X and Y's actual interactions are altered. Perception is how we understand reality, but it is not reality itself. Hence, my argument that such paradoxes are relativistic illusions, rather than actual paradoxes.

 

[Joshua Jones]

The effect must be in the cause's future light cone and the cause must be in the effect's past light cone. If you have FTL, you have effect and cause outside of each other's light cone. Specifically, when you enter FTL flight, this is the cause and you exit, this is the effect. It doesn't matter how FTL works since we're only considering the end points.

Now, the effect, that is you exiting FTL flight, comes after the cause in your old light cone. But you can change your velocity so that cause will be in the past of the effect from your new light cone. From this new velocity, you can do another FTL flight where is is possible to jump back to your old position but in the past before you left.

But that only happens in a certain reference frame, and is negated in a different reference frame. If Ship A departs Alpha Centauri at 2C, it will arrive at Earth when the light is 1/2 way across the distance. If it then reversed course and returned to Alpha Centauri, it would cross paths with the light from its first event at 3/4, and as it crosses the light history of Alpha Centauri, it will catch up with what has happened on Alpha Centauri in the intervening time. So, relative to Alpha Centauri, roughly 4 years will elapse in the round trip, and likewise relative to Earth. The only frame of reference where that is different is when the ship is in transit, because of time dilation at speeds in excess of C. But, unless I am mistaken, time never actually changes direction of flow with time dilation; it only slows further and further to smaller fractions. Hence my argument that travel into the future is possible, but not the past.

The thing about Special Relativity is that if two events are outside of each other's light cone, it is impossible to determine which came first. Which comes first depends on your velocity and if you change your velocity, you can change the order. That combined with FTL flight allows you to jump back into your own past.

Yes, but this is which is perceived first, not which actually comes first. If matter, energy, and forces have actual interactions, perception is just this, even if we have no access to the actuality.

 

[goldhawk]

Yes, but this is which is perceived first, not which actually comes first. If matter, energy, and forces have actual interactions, perception is just this, even if we have no access to the actuality.

In Relativity, perception is reality. If you can change the order of events by changing your velocity, then the order of the events is changed.

 

[Joshua Jones]

In Relativity, perception is reality. If you can change the order of events by changing your velocity, then the order of the events is changed.

I need to reread my primary sources on the matter... if your assessment is accurate, it may lead to my rejecting Relativity as a viable theory, or at least that implication from it (not that my rejecting means much in the final analysis...). Epistemological Relativity is viable, and Relativity as it relates to velocity and distance is viable, but total Ontological Relativity is self-contradictory and unsustainable in any possible universe, regardless of FTL.

So, thanks for giving me a reason to reread some science!

 

[zmunkz]

Yes, but this is which is perceived first, not which actually comes first. If matter, energy, and forces have actual interactions, perception is just this, even if we have no access to the actuality.

This is where your error is occurring. When you say which “actually comes first” you are mistakenly choosing one particular frame as the true reference, and judging the rest to be altered perceptions of that reference. In fact, every different frame has a different moment when any given event “actually” occurred, and there is no way to say one is actual. They are all valid.

Think about it. What point of reference are you claiming is actual? A frame in motion with one of the bodies? Why did you choose this one?

There are no ontological issues because everything remains consistent within any given frame. What “actually” happened in that frame is actual to that frame, and causality is not violated. Paradoxes only occur when you allow information from different frames to interact at super luminal speeds. I recommend physicsforums.com if you really want someone to break it down. A lot of PhDs and physics professors hang out there and are quite accustomed to explaining various relativistic paradoxes.

 

[Joshua Jones]

This is where your error is occurring. When you say which “actually comes first” you are mistakenly choosing one particular frame as the true reference, and judging the rest to be altered perceptions of that reference. In fact, every different frame has a different moment when any given event “actually” occurred, and there is no way to say one is actual. They are all valid.

Think about it. What point of reference are you claiming is actual? A frame in motion with one of the bodies? Why did you choose this one?

There are no ontological issues because everything remains consistent within any given frame. What “actually” happened in that frame is actual to that frame, and causality is not violated. Paradoxes only occur when you allow information from different frames to interact at super luminal speeds. I recommend physicsforums.com if you really want someone to break it down. A lot of PhDs and physics professors hang out there and are quite accustomed to explaining various relativistic paradoxes.

I will certainly take a look there, as I am certainly open to being wrong.

That said, I don't see how I am preferring one frame of reference. Using the situation from the article shared a bit back, I am not saying either the observer on Earth, Alpha Centauri, or the ship has the "correct" observation of the event. For the sake of discussion, let's say it was a supernova. There is an actual internal sequence happening in the star causing the supernova. Each of the observers may see it differently, but that doesn't change the internal sequence in actuality. Yes, each of the observers have an equally valid (or invalid) perspective, but a failure to identify which perspective is more accurate does not mean that there isn't an actual physical process happening which is the basis of these perceptions.

In other words, I don't see how general or special Relativity negates a correspondence theory of truth, as the inability to directly access anything other than perception doesn't negate the veracity of those other things.

But, again, I am open to being proven wrong, so I will take a look at the link you sent. Thanks!

 

[zmunkz]

There is an actual internal sequence happening in the star causing the supernova. Each of the observers may see it differently, but that doesn't change the internal sequence in actuality. Yes, each of the observers have an equally valid (or invalid) perspective, but a failure to identify which perspective is more accurate does not mean that there isn't an actual physical process happening which is the basis of these perceptions.

I think you just have to take a step back to see the philosophical picture. Take your example: realtive to the star (a frame at rest), you could identify the places and moments that iron and other heavy elements started forming (within the blur of uncertainty). You could plot the movements and timings of those atoms as the cascade continues and the pressure in the star begins the path towards explosion.

The thing is, relative to (say) another star, which our subject is zipping past, advanced instruments could be taking the same measurements. They would see slightly different times and places (and order) that the various elements appeared. They would see slightly different trajectories and timing, and their view would fully consistently explain the ensuing supernova.

And another observer still relative to the galaxy CoM? Again, all slightly different times and locations and vectors, all consistent and causal, resulting in the expected nova.

The problem is that no cause-effect exists, first, outside of relativity. It is already a part of a chain of cause-events which can find no fundamental reference starting point, and must be described, ab initio, from arbitrary reference frames. Thus the entire causal chain depends on the frame you use.

I think you are only considering the reference frames from the supposed moment of an event and forward, but if you pull back on the cause-effect chain, I think you’ll see what some of us are trying to describe.

 

[Joshua Jones]

I think you just have to take a step back to see the philosophical picture. Take your example: realtive to the star (a frame at rest), you could identify the places and moments that iron and other heavy elements started forming (within the blur of uncertainty). You could plot the movements and timings of those atoms as the cascade continues and the pressure in the star begins the path towards explosion.

The thing is, relative to (say) another star, which our subject is zipping past, advanced instruments could be taking the same measurements. They would see slightly different times and places (and order) that the various elements appeared. They would see slightly different trajectories and timing, and their view would fully consistently explain the ensuing supernova.

And another observer still relative to the galaxy CoM? Again, all slightly different times and locations and vectors, all consistent and causal, resulting in the expected nova.

The problem is that no cause-effect exists, first, outside of relativity. It is already a part of a chain of cause-events which can find no fundamental reference starting point, and must be described, ab initio, from arbitrary reference frames. Thus the entire causal chain depends on the frame you use.

I think you are only considering the reference frames from the supposed moment of an event and forward, but if you pull back on the cause-effect chain, I think you’ll see what some of us are trying to describe.

Let me see if I can make my point a little more clear. If a tree falls in the forest, and no one is around to observe it, does it still fall? To ask the question is to answer it; there is nothing within gravity, biology, and whatever force (let's say wind in this case) which requires an observer to interact. It doesn't make a sound, because sound is how the brain interacts with the sound waves produced by the tree falling, but it still falls. Whether it fall forward or backward, left or right depends on the observer, as does when the sound reaches the observer and how exactly it sounds (because of echos and the like), but there is an actual physical event transpiring. And, this physical event transpires whether there are no observers or a billion observers. The actual physical event happens, and for lack of better expression, sends out waves of data which are then interpreted by observers, regardless of if those observers are standing within the tree, north or south of the tree, 1 meter or a kilometer away. But, berift of observers, the physical event still happens.

This is true regardless of what the physical event is and what force transmits the data which is interpreted. Now, when we are in an exotic frame of reference, our perceptions may cause us to observe things in odd ways, but that doesn't mean the physical event actually changes.

But, again, I will take a look at the resource recommended and go from there.

 

[zmunkz]

That is a very interesting way to outline the problem, and I see what you’re getting at. I still think it comes down to an embedded assumption that frames of reference are added after-the-fact, and not fundamental to all of causality.

Keep in mind I’m not necessarily talking about human observers. Observer just means anything that becomes causally linked to an earlier event by way of passive interaction. Every event has such observers. For instance, a passing comet, struck by a photon from the said supernova explosion. This comet would never know exactly what had transpired to send that photon at it and it’s never going to do the math. Same is true of a different comet going in another direction, struck by a similar photon. The two would have no notes to compare, but if they did, they would find they heartily disagreed on the order of events and placement of events that led to the supernova and the two photon striking them. What is more, all subsequent events within each of their frames would remain consistent with their own “view“ of what transpired, despite the fact the two would be, unbeknownst to any conscious thing, slightly different.

As with the tree, nobody needs to be there to observe this, it is just a way physics unfolds.

If you wouldn’t mind, I would be very curious to hear your final interpretations after you’ve researched further. This is interesting topic.

 

[goldhawk]

I will certainly take a look there, as I am certainly open to being wrong.

That said, I don't see how I am preferring one frame of reference.

When you change velocity, you change the frame of reference. Everything that was true in the old frame is no longer true in the new one. For two events not in each other's light cone, changing the frame may result in them changing their order. The order they were in the old frame is not longer true. Only what is measured in the new frame is true. You cannot mix measurements from one frame with another.

 

[Onyx]

What I said doesn't require a universal time scale; only that matter, energy, and forces have actual interactions with one another. These interactions are then perceived by observers in their reference frames. But, again, just because Observer A sees X proceed Y and Observer B sees Y before X doesn't mean X and Y's actual interactions are altered. Perception is how we understand reality, but it is not reality itself. Hence, my argument that such paradoxes are relativistic illusions, rather than actual paradoxes.

I think what may be tripping you up is that FTL is not real, so all the paradoxes only exist when you impose this fake idea on the real universe.

The Ladder paradox - Wikipedia is another FTL type problem. It isn't stated as FTL, but it effectively is because it assumes that an observer can hop between two reference points simultaneously to measure where the ladder "is" at a single precise moment. But the relativistic universe doesn't have those kind of reference points and moments.

There are no actual paradoxes in our universe, just ways to use language that suggest paradox if the language were accurate. But if you couldn't say or think something false like "faster than light" or insist on a concept as problematic as "simultaneously", there wouldn't be a "problem". We're the problem, not relativity, because our internal physics model and the language that has grown from that understanding causes us to ask non-relativistic questions all the time, like "I wonder what she's doing right now?" or "What if you could go faster than the fastest speed that is possible?"