7 ms·

Does anybody know of a good intuitive explanation for the claim that FTL breaks causality? By intuitive I mean something more than "the numbers in this formula

Does anybody know of a good intuitive explanation for the claim that FTL breaks causality? By intuitive I mean something more than "the numbers in this formula don't add up without breaking causality". I've tried to build a foundation for understanding this concept several times and failed each time. It makes total sense that with FTL, it would be possible to OBSERVE events in the wrong order, but just this alone wouldn't break causality. My intuition is not helping me get any further than this.

maxerickson 3y ago
To get to Mars faster than light, you have to be able to travel backwards in time (you could watch yourself start the trip). If you can travel backwards in time, you can kill a younger instance of yourself.
- sunaurus 3y ago
  Everything you say makes sense if you already presume that FTL implies breaking causality, but I'm missing the explanation for why FTL implies breaking causality in the first place. I mean, it's completely logical that if you get to Mars faster then light, you can watch yourself start the trip, but why does this also mean that you are actually going back in time? Intuitively it would seem that even if you teleport to Mars with no travel time, observe yourself on Earth, then teleport back to Earth, you should arrive the next instant after you left, not before. So time travel does not follow immediately from the fact that you were able to observe yourself in the past.
  - maxerickson 3y ago
    I guess I don't understand your intuition. My intuition: Teleport to Mars. Wait 3 minutes to watch myself go poof on Earth. Teleport to Earth. If I arrive back on Earth just after I went poof, then I'm pretty sure I went backwards in time a couple of minutes.
    - sunaurus 3y ago
      If you wait 3 minutes on Mars, why would an instant teleport back to Earth result in you arriving just after you went poof rather than 3 minutes after you went poof?
      - maxerickson 3y ago
        Well, the point is more that you have to wait 3 minutes on Mars if you want to watch yourself leave. But say instead of waiting you just keep going poof.
        SAI_Peregrinus 3y ago
        They never said they wait to watch themselves leave, just watch themselves on Earth (3 minutes before they left).
        maxerickson 3y ago
        I mean, it's completely logical that if you get to Mars faster then light, you can watch yourself start the trip, but why does this also mean that you are actually going back in time? I'm the one that introduced the 'start the trip' condition, and they used it in their comment.
    - senectus1 3y ago
      >If I arrive back on Earth just after I went poof, then I'm pretty sure I went backwards in time a couple of minutes. How? Teleport in this context is an instant transportation process. but the image of you going poof is not ists a speed of light. Like If I throw a ball at a target first THEN Fire a gun at the same target, the bullet will get there first but it didn't time travel to do that. Lets assume that the teleport process is a wormhole or a folding of space process that reduces the distance between the two locations rather than making you go faster. You could step through onto mars and back again and not see yourself when you arrive back but then go back to mars again and see yourself disappear and re-appear twice. still no time travel. You're just watching a delayed image.
  - chasd00 3y ago
    Causality propagates at the speed of light. “Speed of light” is just a more intuitive way to say the speed of causality. FTL travel is the same as faster than causality travel. So going faster than light exceeds the speed of causality. To me, that means the order of events is no longer predictable so everything about cause and effect breaks down hence breaking causality.
- BobbyJo 3y ago
  > To get to Mars faster than light, you have to be able to travel backwards in time (you could watch yourself start the trip). I think the issue is that seeing something from the past is not the same as time travel. If I yell, then travel faster than sound, then stop, I'll hear my previous yell, but so what? It's not like I can run back faster than sound and stop myself from yelling.
  - maxerickson 3y ago
    Yeah, if you use a false analogy it doesn't make any sense. Traveling faster than light isn't the same as (or rather, wouldn't be similar to) traveling faster than sound.
    - BobbyJo 3y ago
      Yes, and that is, specifically, the part that is not apparent. What makes it not the same other than one being light/faster and the other sound/slower?
- CyberDildonics 3y ago
  Do you think that light moves instantly?
  - maxerickson 3y ago
    Do you?
    - CyberDildonics 3y ago
      I didn't say that traveling faster than light was the same as traveling backwards in time and then, for some reason, that that includes being able to kill a younger version of yourself.
      - maxerickson 3y ago
        But why didn't you? The speed of light is a fundamental aspect of space-time. Time isn't separate from space-time, it is bound up with space into space-time. And then if you goof the rules, goofy things happen. If you look down in the cousin comments to yours, I had already posted a comment making it clear that I don't think light propagates instantly (3 minutes to Mars and all that). It's certainly possible that someone will come up with a theory that allows us to set aside the idea of space-time, but it's not worth worrying about until it happens. Think of it this way: photons don't have to exist, they might just be a model for the propagation of information. In the reference frame of a photon, propagation is instantaneous.
        CyberDildonics 3y ago
        To be clear, you are saying if someone can make it to mars in under three minutes, they can kill their younger self because of the laws of physics that say "if you goof the rules, goofy things happen" ?
        maxerickson 3y ago
        To get to Mars in less than 3 minutes you have to either convert mass into energy and back or invent entirely new physics. It'd be pretty cool if either of those things happen.
mr_mitm 3y ago
There is nothing intuitive about special relativity. If you want to understand SR (or GR or QM), you must throw intuition out the window and strictly follow the rules of the theory. The best explanation for why FTL breaks causality that I have seen is the tachyonic antitelephone: https://en.wikipedia.org/wiki/Tachyonic_antitelephone https://en.wikipedia.org/wiki/Tachyonic_antitelephone Drawing a bunch of spacetime diagrams might help as well.
- sunaurus 3y ago
  Thanks, that's what I was afraid of. I guess I've been trying to look for a shortcut, but in the end I'll have to dive much deeper and learn much more to really understand this topic. I've read the tachyonic antitelephone article several times over the years, but the problem is that (as far as I understand it), this thought experiment exactly boils down to "the numbers don't add up without breaking causality", without really explaining why that is in any intuitive way for me.
  - hgsgm 3y ago
    Please define "causality", as precisely as you can. Presumably you'll need a "clock" of some kind, so please describe a clock in a way that it is independent of the speed of light and any particular frame of reference (unless you believe there is a preferred frame of reference. If so, which one is / which ones are?) Remember that the theory and experiment of special relativity state and show that the speed of light is always measured to be a constant, no matter who measures it and how they are moving with respect to anyone else.
- dataflow 3y ago
  Just because there's one unintuitive step that doesn't mean everything following that is incomprehensible without math though. The fact that the speed of light is constant might be unintuitive, but once you accept that, the fact (for example) that you can never reach it is intuitive. As is the fact that it would require infinite energy to do so. It's perfectly fair for someone to seek an intuitive explanation even with an unintuitive assumption. I have no idea whether there is one in this case, but it doesn't seem true that there's nothing intuitive about special relativity.
arnoldb0620 3y ago
I am just a lay person but I tend to think about FTL travel in terms of traveling faster than the speed of sound. There is a sight dimension in which we can see the object before we hear it. Is there another dimension that we can observe the object traveling FTL?
maxbond 3y ago
You can think of the speed of light as the speed at which causes produce effects. In the same way that the speed of sound[1] is the speed at which one air molecule can tell another air molecule that it's been been moved, the speed of light is the speed at which one piece of spacetime can tell another piece of spacetime that something has happened to it. Light just happens to move as fast as it is possible to move, the speed of light might be better described as the speed of causality. This speed defines the "happens before" relation in spacetime, like a Lamport clock defines the "happens before" relation in a distributed system. Event A "happens before" event B if all the information about B was known when A happened. Otherwise B happens at the same time or later than A. If you can travel faster than light (faster than causality), there's nothing stopping you from constructing a scenario where A happens before B and B happens before A. And that's what it means to violate causality. [1] To head off a potential confusion, note that while a jet may be able to move faster than sound, the sound of that jet passing by does not.
- eis 3y ago
  To an observer who is only able to sense sound, in his reality nothing should be able to move faster than the speed of sound because otherwise he'd observe event B happening before event A. Of course in our reality moving faster than the speed of sound is possible. And in terms of sound we hear the object actually moving back in time. That is we hear it first when it's at our location and then we hear the sound it made further and further back in time. From the jets point of view though he was not moving backwards in sound-time. For us, the same would apply to something moving faster than the speed of light. We would observe it moving backwards in time but that does not mean it actually does from its point of view. Point being we have to be very careful about distinguishing between when we observe something happening and when it actually happens. Observing something going backwards in time is fine while actually traveling backwards in time probably is not.
  - maxbond 3y ago
    Point taken. Thanks for the explanation, that helped me a achieve a deeper understanding & blew my mind. This animation of a tachyon goes well with your explanation: https://commons.m.wikimedia.org/wiki/File:Tachyon04s.gif#mw-jump-to-license https://commons.m.wikimedia.org/wiki/File:Tachyon04s.gif#mw-... I think you can observe this effect in the high speed Schlieren footage of a whip in this video https://youtube.com/watch?v=AnaASTBn_K4 https://youtube.com/watch?v=AnaASTBn_K4 (you can skip to around 8 minutes) but I'm not sure, I keep going back and forth on it.
ben_w 3y ago
Ok, so, at 14:45 in the video she shows some spacetime diagrams. The "normal" interpretation is that the distortions shown, including the event-ordering flip she shows, represent reality. Relativistic motion is actual time dilation and not merely your perception of someone else's motion. This is backed up by evidence in a lot of extreme cases. I don't have the skills to know if one is really "allowed" to say that there exists some frame of reference that is preferred or if that breaks something else, but I think that any such frame where time must always go forwards would do what she's saying here. Possibly. Unfortunately, I know this is an area where not only does my intuition often fail me, but where I can easily have the wool pulled over my eyes with plausible sounding but erroneous maths.
- hgsgm 3y ago
  > Relativistic motion is actual time dilation and not merely your perception of someone else's motion. What distinction are you drawing? What is the difference between "actual" and "what [every] observer observes? Part of the concept of relativity is that there is no preferred clock. That's why it is called "relativity".
  - ben_w 3y ago
    Alice, Bob, initially at rest, Bob accelerates to relative motion of 0.5c, turns around, returns, decelerates to rest with respect to Alice, both agree Bob experienced less time. No clock is preferred, but the dilation is real. That the Alcubierre metric is supposed to avoid dilation made me ask ages ago if it also avoided the usual paradoxes, but everyone I asked insisted it didn't help at all with that.
sigmoid10 3y ago
>It makes total sense that with FTL, it would be possible to OBSERVE events in the wrong order, but just this alone wouldn't break causality. There seems to be a general misunderstanding here. A different order of events can easily be observed without FTL, but only for events outside of our own light-cone. If we could observe events within our own light-cone without causal ordering, they could still affect us and thus would easily create paradoxes. However, if you are limited by the speed of light, this can't happen.
- hgsgm 3y ago
  How do you observe an event outside your lightcone?
  - sigmoid10 3y ago
    "Observe" in the sense of someone who can see coordinate times, e.g. if you draw a space-time diagram and then perform a Lorentz transformation.
wiml 3y ago
It's because "simultaneous" is relative in the same way that "in the same place" is relative. You can bounce a ball against the same spot repeatedly, but if you're on an airplane and another observer isn't, the places the ball hits are separated by a large distance in their reference frame. Most concretely, the FTL-breaks-causality conclusion comes from: If special relativity holds (it does), and you have FTL travel, and there is no universal privileged frame of reference affecting your FTL drive, then it's possible to get back to your starting point before you leave by making multiple FTL hops. You have to be able to make the two hops in different reference frames, that is, you need to do a bit of conventional acceleration between hop 1 and hop 2. From everything we know about the universe it seems unlikely that there's a special preferred frame out there, but if for example you're developing a hard-science-fiction setting and want FTL without causality violations, you can throw in that background detail to keep the physicists happy. > it would be possible to OBSERVE events in the wrong order True, but of course that's possible even in normal earth-bound newtonian physics. All of the discussions about relativity assume that all the observers are taking speed-of-light delays into account when they're observing.
- neurobashing 3y ago
  One of the Xeelee Sequence novels deals with this problem specifically: a pilot in an FTL space fighter uses multiple hops to defeat an enemy, and ends up back before he left. It's a Xeelee Sequence book, grimdark of grimdark, so hilarity does not ensue.
wyager 3y ago
Say we're in a universe with a +- metric signature. We're looking at tx, ignoring yz. Rotating within a 45 degree cone (which hides the hyperbolic geometry of +- space) is easy. That's just normal acceleration. Rotating more than 45 degrees is the hard part. That corresponds to going FTL. It's hard because of the hyperbolic structure of +-. Once you're going FTL, changing your direction to point backwards in time is trivial; you just turn your engines on and accelerate. Read Greg Egan's "Clockwork Rocket" and "Dichronauts" books and support material on his website to develop an intuitive understanding of spacetimes with ++++ and ++-- signatures and (by contrast) our own spacetime with a +--- signature.
bmacho 3y ago
FTL in SR does not break causality. Some FTL travel is "allowed", at least causality allows it. A natural model for SR + FTL that is consistent with causality, is that SR is an emerging phenomenon / effective theory over a Galilean space time. If you can, say, send information in the Galilean space time with arbitrary velocity, then you can send information FTL, but causality is total cool with it. It is also possible, that you can move with arbitrary speeds in this Galilean spacetime (but I believe we haven't observed anything in the universe that moves FTL). However, arbitrary FTL would mean you can send information from anywhere and anywhen to anywhere and anywhen, which breaks causality.
- hgsgm 3y ago
  I don't get it. What is non-arbitrary FTL? How does sendding information FTL not violate causality? What is the speed of light in the reference frame of the traveling information? Or does the information teleport? What is the speed of light in the reference frame of light traveling at the speed of light?
  - bmacho 3y ago
    Some people can move FTL, some people can't. The time coordinate increases with causality. (Same as in Newtonian physics.) If you want SR to hold, then yes, information teleports. If you want to travel FTL, then SR can't hold obviously.
  - Ono-Sendai 3y ago
    Have a look at https://forwardscattering.org/post/36 https://forwardscattering.org/post/36
rendall 3y ago
I found this video to be helpful. "Why Going Faster-Than-Light Leads to Time Paradoxes" from the Cool Worlds channel https://youtu.be/an0M-wcHw5A https://youtu.be/an0M-wcHw5A

maxerickson 3y ago

To get to Mars faster than light, you have to be able to travel backwards in time (you could watch yourself start the trip). If you can travel backwards in time, you can kill a younger instance of yourself.

sunaurus 3y ago
Everything you say makes sense if you already presume that FTL implies breaking causality, but I'm missing the explanation for why FTL implies breaking causality in the first place. I mean, it's completely logical that if you get to Mars faster then light, you can watch yourself start the trip, but why does this also mean that you are actually going back in time? Intuitively it would seem that even if you teleport to Mars with no travel time, observe yourself on Earth, then teleport back to Earth, you should arrive the next instant after you left, not before. So time travel does not follow immediately from the fact that you were able to observe yourself in the past.
- maxerickson 3y ago
  I guess I don't understand your intuition. My intuition: Teleport to Mars. Wait 3 minutes to watch myself go poof on Earth. Teleport to Earth. If I arrive back on Earth just after I went poof, then I'm pretty sure I went backwards in time a couple of minutes.
  - sunaurus 3y ago
    If you wait 3 minutes on Mars, why would an instant teleport back to Earth result in you arriving just after you went poof rather than 3 minutes after you went poof?
    - maxerickson 3y ago
      Well, the point is more that you have to wait 3 minutes on Mars if you want to watch yourself leave. But say instead of waiting you just keep going poof.
      - SAI_Peregrinus 3y ago
        They never said they wait to watch themselves leave, just watch themselves on Earth (3 minutes before they left).
        maxerickson 3y ago
        I mean, it's completely logical that if you get to Mars faster then light, you can watch yourself start the trip, but why does this also mean that you are actually going back in time? I'm the one that introduced the 'start the trip' condition, and they used it in their comment.
  - senectus1 3y ago
    >If I arrive back on Earth just after I went poof, then I'm pretty sure I went backwards in time a couple of minutes. How? Teleport in this context is an instant transportation process. but the image of you going poof is not ists a speed of light. Like If I throw a ball at a target first THEN Fire a gun at the same target, the bullet will get there first but it didn't time travel to do that. Lets assume that the teleport process is a wormhole or a folding of space process that reduces the distance between the two locations rather than making you go faster. You could step through onto mars and back again and not see yourself when you arrive back but then go back to mars again and see yourself disappear and re-appear twice. still no time travel. You're just watching a delayed image.
- chasd00 3y ago
  Causality propagates at the speed of light. “Speed of light” is just a more intuitive way to say the speed of causality. FTL travel is the same as faster than causality travel. So going faster than light exceeds the speed of causality. To me, that means the order of events is no longer predictable so everything about cause and effect breaks down hence breaking causality.
BobbyJo 3y ago
> To get to Mars faster than light, you have to be able to travel backwards in time (you could watch yourself start the trip). I think the issue is that seeing something from the past is not the same as time travel. If I yell, then travel faster than sound, then stop, I'll hear my previous yell, but so what? It's not like I can run back faster than sound and stop myself from yelling.
- maxerickson 3y ago
  Yeah, if you use a false analogy it doesn't make any sense. Traveling faster than light isn't the same as (or rather, wouldn't be similar to) traveling faster than sound.
  - BobbyJo 3y ago
    Yes, and that is, specifically, the part that is not apparent. What makes it not the same other than one being light/faster and the other sound/slower?
CyberDildonics 3y ago
Do you think that light moves instantly?
- maxerickson 3y ago
  Do you?
  - CyberDildonics 3y ago
    I didn't say that traveling faster than light was the same as traveling backwards in time and then, for some reason, that that includes being able to kill a younger version of yourself.
    - maxerickson 3y ago
      But why didn't you? The speed of light is a fundamental aspect of space-time. Time isn't separate from space-time, it is bound up with space into space-time. And then if you goof the rules, goofy things happen. If you look down in the cousin comments to yours, I had already posted a comment making it clear that I don't think light propagates instantly (3 minutes to Mars and all that). It's certainly possible that someone will come up with a theory that allows us to set aside the idea of space-time, but it's not worth worrying about until it happens. Think of it this way: photons don't have to exist, they might just be a model for the propagation of information. In the reference frame of a photon, propagation is instantaneous.
      - CyberDildonics 3y ago
        To be clear, you are saying if someone can make it to mars in under three minutes, they can kill their younger self because of the laws of physics that say "if you goof the rules, goofy things happen" ?
        maxerickson 3y ago
        To get to Mars in less than 3 minutes you have to either convert mass into energy and back or invent entirely new physics. It'd be pretty cool if either of those things happen.

mr_mitm 3y ago

There is nothing intuitive about special relativity. If you want to understand SR (or GR or QM), you must throw intuition out the window and strictly follow the rules of the theory. The best explanation for why FTL breaks causality that I have seen is the tachyonic antitelephone: https://en.wikipedia.org/wiki/Tachyonic_antitelephone https://en.wikipedia.org/wiki/Tachyonic_antitelephone Drawing a bunch of spacetime diagrams might help as well.

sunaurus 3y ago
Thanks, that's what I was afraid of. I guess I've been trying to look for a shortcut, but in the end I'll have to dive much deeper and learn much more to really understand this topic. I've read the tachyonic antitelephone article several times over the years, but the problem is that (as far as I understand it), this thought experiment exactly boils down to "the numbers don't add up without breaking causality", without really explaining why that is in any intuitive way for me.
- hgsgm 3y ago
  Please define "causality", as precisely as you can. Presumably you'll need a "clock" of some kind, so please describe a clock in a way that it is independent of the speed of light and any particular frame of reference (unless you believe there is a preferred frame of reference. If so, which one is / which ones are?) Remember that the theory and experiment of special relativity state and show that the speed of light is always measured to be a constant, no matter who measures it and how they are moving with respect to anyone else.
dataflow 3y ago
Just because there's one unintuitive step that doesn't mean everything following that is incomprehensible without math though. The fact that the speed of light is constant might be unintuitive, but once you accept that, the fact (for example) that you can never reach it is intuitive. As is the fact that it would require infinite energy to do so. It's perfectly fair for someone to seek an intuitive explanation even with an unintuitive assumption. I have no idea whether there is one in this case, but it doesn't seem true that there's nothing intuitive about special relativity.

arnoldb0620 3y ago

I am just a lay person but I tend to think about FTL travel in terms of traveling faster than the speed of sound. There is a sight dimension in which we can see the object before we hear it. Is there another dimension that we can observe the object traveling FTL?

maxbond 3y ago

You can think of the speed of light as the speed at which causes produce effects. In the same way that the speed of sound[1] is the speed at which one air molecule can tell another air molecule that it's been been moved, the speed of light is the speed at which one piece of spacetime can tell another piece of spacetime that something has happened to it. Light just happens to move as fast as it is possible to move, the speed of light might be better described as the speed of causality. This speed defines the "happens before" relation in spacetime, like a Lamport clock defines the "happens before" relation in a distributed system. Event A "happens before" event B if all the information about B was known when A happened. Otherwise B happens at the same time or later than A. If you can travel faster than light (faster than causality), there's nothing stopping you from constructing a scenario where A happens before B and B happens before A. And that's what it means to violate causality. [1] To head off a potential confusion, note that while a jet may be able to move faster than sound, the sound of that jet passing by does not.

eis 3y ago
To an observer who is only able to sense sound, in his reality nothing should be able to move faster than the speed of sound because otherwise he'd observe event B happening before event A. Of course in our reality moving faster than the speed of sound is possible. And in terms of sound we hear the object actually moving back in time. That is we hear it first when it's at our location and then we hear the sound it made further and further back in time. From the jets point of view though he was not moving backwards in sound-time. For us, the same would apply to something moving faster than the speed of light. We would observe it moving backwards in time but that does not mean it actually does from its point of view. Point being we have to be very careful about distinguishing between when we observe something happening and when it actually happens. Observing something going backwards in time is fine while actually traveling backwards in time probably is not.
- maxbond 3y ago
  Point taken. Thanks for the explanation, that helped me a achieve a deeper understanding & blew my mind. This animation of a tachyon goes well with your explanation: https://commons.m.wikimedia.org/wiki/File:Tachyon04s.gif#mw-jump-to-license https://commons.m.wikimedia.org/wiki/File:Tachyon04s.gif#mw-... I think you can observe this effect in the high speed Schlieren footage of a whip in this video https://youtube.com/watch?v=AnaASTBn_K4 https://youtube.com/watch?v=AnaASTBn_K4 (you can skip to around 8 minutes) but I'm not sure, I keep going back and forth on it.

ben_w 3y ago

Ok, so, at 14:45 in the video she shows some spacetime diagrams. The "normal" interpretation is that the distortions shown, including the event-ordering flip she shows, represent reality. Relativistic motion is actual time dilation and not merely your perception of someone else's motion. This is backed up by evidence in a lot of extreme cases. I don't have the skills to know if one is really "allowed" to say that there exists some frame of reference that is preferred or if that breaks something else, but I think that any such frame where time must always go forwards would do what she's saying here. Possibly. Unfortunately, I know this is an area where not only does my intuition often fail me, but where I can easily have the wool pulled over my eyes with plausible sounding but erroneous maths.

hgsgm 3y ago
> Relativistic motion is actual time dilation and not merely your perception of someone else's motion. What distinction are you drawing? What is the difference between "actual" and "what [every] observer observes? Part of the concept of relativity is that there is no preferred clock. That's why it is called "relativity".
- ben_w 3y ago
  Alice, Bob, initially at rest, Bob accelerates to relative motion of 0.5c, turns around, returns, decelerates to rest with respect to Alice, both agree Bob experienced less time. No clock is preferred, but the dilation is real. That the Alcubierre metric is supposed to avoid dilation made me ask ages ago if it also avoided the usual paradoxes, but everyone I asked insisted it didn't help at all with that.

sigmoid10 3y ago

>It makes total sense that with FTL, it would be possible to OBSERVE events in the wrong order, but just this alone wouldn't break causality. There seems to be a general misunderstanding here. A different order of events can easily be observed without FTL, but only for events outside of our own light-cone. If we could observe events within our own light-cone without causal ordering, they could still affect us and thus would easily create paradoxes. However, if you are limited by the speed of light, this can't happen.

hgsgm 3y ago
How do you observe an event outside your lightcone?
- sigmoid10 3y ago
  "Observe" in the sense of someone who can see coordinate times, e.g. if you draw a space-time diagram and then perform a Lorentz transformation.

wiml 3y ago

It's because "simultaneous" is relative in the same way that "in the same place" is relative. You can bounce a ball against the same spot repeatedly, but if you're on an airplane and another observer isn't, the places the ball hits are separated by a large distance in their reference frame. Most concretely, the FTL-breaks-causality conclusion comes from: If special relativity holds (it does), and you have FTL travel, and there is no universal privileged frame of reference affecting your FTL drive, then it's possible to get back to your starting point before you leave by making multiple FTL hops. You have to be able to make the two hops in different reference frames, that is, you need to do a bit of conventional acceleration between hop 1 and hop 2. From everything we know about the universe it seems unlikely that there's a special preferred frame out there, but if for example you're developing a hard-science-fiction setting and want FTL without causality violations, you can throw in that background detail to keep the physicists happy. > it would be possible to OBSERVE events in the wrong order True, but of course that's possible even in normal earth-bound newtonian physics. All of the discussions about relativity assume that all the observers are taking speed-of-light delays into account when they're observing.

neurobashing 3y ago
One of the Xeelee Sequence novels deals with this problem specifically: a pilot in an FTL space fighter uses multiple hops to defeat an enemy, and ends up back before he left. It's a Xeelee Sequence book, grimdark of grimdark, so hilarity does not ensue.

wyager 3y ago

Say we're in a universe with a +- metric signature. We're looking at tx, ignoring yz. Rotating within a 45 degree cone (which hides the hyperbolic geometry of +- space) is easy. That's just normal acceleration. Rotating more than 45 degrees is the hard part. That corresponds to going FTL. It's hard because of the hyperbolic structure of +-. Once you're going FTL, changing your direction to point backwards in time is trivial; you just turn your engines on and accelerate. Read Greg Egan's "Clockwork Rocket" and "Dichronauts" books and support material on his website to develop an intuitive understanding of spacetimes with ++++ and ++-- signatures and (by contrast) our own spacetime with a +--- signature.

bmacho 3y ago

FTL in SR does not break causality. Some FTL travel is "allowed", at least causality allows it. A natural model for SR + FTL that is consistent with causality, is that SR is an emerging phenomenon / effective theory over a Galilean space time. If you can, say, send information in the Galilean space time with arbitrary velocity, then you can send information FTL, but causality is total cool with it. It is also possible, that you can move with arbitrary speeds in this Galilean spacetime (but I believe we haven't observed anything in the universe that moves FTL). However, arbitrary FTL would mean you can send information from anywhere and anywhen to anywhere and anywhen, which breaks causality.

hgsgm 3y ago
I don't get it. What is non-arbitrary FTL? How does sendding information FTL not violate causality? What is the speed of light in the reference frame of the traveling information? Or does the information teleport? What is the speed of light in the reference frame of light traveling at the speed of light?
- bmacho 3y ago
  Some people can move FTL, some people can't. The time coordinate increases with causality. (Same as in Newtonian physics.) If you want SR to hold, then yes, information teleports. If you want to travel FTL, then SR can't hold obviously.
- Ono-Sendai 3y ago
  Have a look at https://forwardscattering.org/post/36 https://forwardscattering.org/post/36

rendall 3y ago

I found this video to be helpful. "Why Going Faster-Than-Light Leads to Time Paradoxes" from the Cool Worlds channel https://youtu.be/an0M-wcHw5A https://youtu.be/an0M-wcHw5A