I'm still trying to wrap my head around why does FTL violate causality (even in the specific case of "space folding", a theoretical instant jump from one point in space to another).
Let's simplify the problem (take a spherical cow in the vacuum), say we have planets A and B, 100 LY away from each other, time flows at exactly the same rate near both, clear path in between them, they move through space at the same speed and relative direction, etc.
I'm on planet A. I send out a signal towards planet B. I jump to planet B and wait 100 years. I observe the signal.
Now my simplistic assumptions probably suggest that this isn't that much different from sending out a carrier pigeon while I take the train to its destination and wait. Very obviously I'm not Einstein. What am I missing?
I didn’t know either, but this article [0] has some thorough explanations.
I think the basic idea is that when two people are experiencing time dilation, FTL communication makes it possible (according to relativity equations) for a recipient to receive a message, reply to it, and have the original sender receive the reply before the point in time (in the original sender’s point of reference) the original sender sent the initial message, which clearly violates causality.
I think your scenario would not break causality because you are assuming both A and B are experiencing time at the same pace, so there would be no way to take advantage of time dilation.
Time is relative in special relativity. Things do not happen at the same time or the same order. Say FTL jumps are instantaneous for the ship in their frame, this means that ship moving fast will have a different view about when the jump happens.
Ship 1 FTL jumps, transmits message to Ship 2 that is moving relativistically, and then Ship 2 FTL jumps back. Ship 2 can arrive before Ship 1 left, creating a paradox if they give them the message.
This assumes that FTL follows relativity where physics are the same in all frames. If it happens in fixed frame, then there isn't a problem. But that would break physics; I guess FTL would break physics too. We would either need to give up on causality and except weird things happen, or give up on FTL and accept light speed as the speed limit.
Because (at least, according to special and general relativity) when two events U,V are simultaneous (in the sense of “the time coordinate is the same) in one frame, then from another frame U is before V (in the sense of the time coordinate in that frame’s coordinate system) , and in a third frame V is before U.
Hm, that’s probably not a very clear explanation..
Ok, suppose you depict time and one dimension of space on a grid, where traveling at c is depicted with a line that makes a 45 degree angle with the space axis.
Draw two such lines crossing at the t=0, x=0 point.
If you apply a “hyperbolic rotation” aka a “boost”, keeping the origin fixed, these lines will stay fixed, and each point in one of the 4 quadrants made by these lines will remain in that quadrant.
The upper quadrant consists of all events in the absolute future of the event at t=0, x=0 . The bottom quadrant consists of all events in the absolute past of the event at t=0, x=0 .
These boosts are what happens when one changes one’s reference frame by changing velocity. Of course, changing one’s velocity cannot change what events can have a causal effect on what other events, as it only changes one’s perspective.
Any line segment that you draw that would be faster than light speed can be hyperbolically rotated so that the endpoint has an earlier time coordinate in the boosted frame than the start point.
Whereas, the points in the upper quadrant always have positive time coordinates.
Now, if you only allowed one instance of FTL ever, that might not cause any cycles in causation? Maybe even if you only allow it in one direction? But those don’t seem particularly plausible.
If you have it in both directions, and they aren’t separated enough I guess, then one could combine those line segments with ones that go at 45 degrees (I.e. light speed) in the forward-in-time direction, to make a loop.
Uh.
Ok so specifically these hyperbolic rotations, in units where c=1 , are
t’ = t cosh(theta) - x sinh(theta) and x’ = x cosh(theta) - t sinh(theta)
Uhh…
Ok I think if FTL was only possible if the signals are still forward in time with respect to one fixed preferred reference frame, then there’s no issue. It is just when it is possible in both directions in a variety of reference frames that it results in a loop.
I'd love that, but when we have perfected off-planet orbital habitats in the outer solar system, it'd be an interesting endeavor to add engines, make the trip in 1,000 years and say hello to our cabbage-smelling neighbors (who'll probably think the same about us).
In the meantime, we continue to develop new designs for deep space mobile habitats and the expedition can have the newest design to build a couple in their new system.
I imagine a culture that has developed in a deep space habitat would not feel life on a planetary surface very appealing.
Comments
just gotta crack that pesky FTL travel
I'm still trying to wrap my head around why does FTL violate causality (even in the specific case of "space folding", a theoretical instant jump from one point in space to another).
Let's simplify the problem (take a spherical cow in the vacuum), say we have planets A and B, 100 LY away from each other, time flows at exactly the same rate near both, clear path in between them, they move through space at the same speed and relative direction, etc.
I'm on planet A. I send out a signal towards planet B. I jump to planet B and wait 100 years. I observe the signal.
Now my simplistic assumptions probably suggest that this isn't that much different from sending out a carrier pigeon while I take the train to its destination and wait. Very obviously I'm not Einstein. What am I missing?
I didn’t know either, but this article [0] has some thorough explanations.
I think the basic idea is that when two people are experiencing time dilation, FTL communication makes it possible (according to relativity equations) for a recipient to receive a message, reply to it, and have the original sender receive the reply before the point in time (in the original sender’s point of reference) the original sender sent the initial message, which clearly violates causality.
I think your scenario would not break causality because you are assuming both A and B are experiencing time at the same pace, so there would be no way to take advantage of time dilation.
[0] https://en.m.wikipedia.org/wiki/Tachyonic_antitelephone
Time is relative in special relativity. Things do not happen at the same time or the same order. Say FTL jumps are instantaneous for the ship in their frame, this means that ship moving fast will have a different view about when the jump happens.
Ship 1 FTL jumps, transmits message to Ship 2 that is moving relativistically, and then Ship 2 FTL jumps back. Ship 2 can arrive before Ship 1 left, creating a paradox if they give them the message.
This assumes that FTL follows relativity where physics are the same in all frames. If it happens in fixed frame, then there isn't a problem. But that would break physics; I guess FTL would break physics too. We would either need to give up on causality and except weird things happen, or give up on FTL and accept light speed as the speed limit.
Because (at least, according to special and general relativity) when two events U,V are simultaneous (in the sense of “the time coordinate is the same) in one frame, then from another frame U is before V (in the sense of the time coordinate in that frame’s coordinate system) , and in a third frame V is before U.
Hm, that’s probably not a very clear explanation..
Ok, suppose you depict time and one dimension of space on a grid, where traveling at c is depicted with a line that makes a 45 degree angle with the space axis. Draw two such lines crossing at the t=0, x=0 point. If you apply a “hyperbolic rotation” aka a “boost”, keeping the origin fixed, these lines will stay fixed, and each point in one of the 4 quadrants made by these lines will remain in that quadrant.
The upper quadrant consists of all events in the absolute future of the event at t=0, x=0 . The bottom quadrant consists of all events in the absolute past of the event at t=0, x=0 .
These boosts are what happens when one changes one’s reference frame by changing velocity. Of course, changing one’s velocity cannot change what events can have a causal effect on what other events, as it only changes one’s perspective.
Any line segment that you draw that would be faster than light speed can be hyperbolically rotated so that the endpoint has an earlier time coordinate in the boosted frame than the start point.
Whereas, the points in the upper quadrant always have positive time coordinates.
Now, if you only allowed one instance of FTL ever, that might not cause any cycles in causation? Maybe even if you only allow it in one direction? But those don’t seem particularly plausible. If you have it in both directions, and they aren’t separated enough I guess, then one could combine those line segments with ones that go at 45 degrees (I.e. light speed) in the forward-in-time direction, to make a loop.
Uh.
Ok so specifically these hyperbolic rotations, in units where c=1 , are t’ = t cosh(theta) - x sinh(theta) and x’ = x cosh(theta) - t sinh(theta)
Uhh…
Ok I think if FTL was only possible if the signals are still forward in time with respect to one fixed preferred reference frame, then there’s no issue. It is just when it is possible in both directions in a variety of reference frames that it results in a loop.
I'd love that, but when we have perfected off-planet orbital habitats in the outer solar system, it'd be an interesting endeavor to add engines, make the trip in 1,000 years and say hello to our cabbage-smelling neighbors (who'll probably think the same about us).
In the meantime, we continue to develop new designs for deep space mobile habitats and the expedition can have the newest design to build a couple in their new system.
I imagine a culture that has developed in a deep space habitat would not feel life on a planetary surface very appealing.