Any resolutions to FTL paradoxes?

[KelvinZero]

This is a call for reputable, published scientific speculation on what consistant FTL could look like.

One of my frustrations with FTL proponents is that I have never seen serious attempts to explain what they even mean. What result they expect, how the paradoxes are all avoided. There just doesn't seem to be much interest in this. If I had produced some math that seems to imply FTL, it just seems natural to me that the first thing to try is to investigate what the maths says would happen if I attempt to produce one of the various famous paradoxes. That would explain what the maths actually means in the real world.

(I think the closest I have seen to reputable investigation suggests that things like warp drive can indeed avoid paradoxes.. you just can't ever exit them. Paradox averted :-) Has anyone done better? )

UPDATE (from a message further down):

While not published, an interesting paradox-free FTL while trying to preserve as much as possible of relativity is described here (preferred FTL frame):
http://www.physicsguy.com/ftl/html/FTL_part4.html#subsec:specialframe

https://en.wikipedia.org/wiki/Cosmic_microwave_background#CMBR_dipole_anisotropy

Can anyone think of a clear example that FTL with just one message, or failing that, wrt to just one special reference frame (eg the CMB rest frame), will still create a paradox?

UPDATE 2

I think I just had an interesting insight about the "CMB rest frame as special" solution to FTL paradoxes. It gives me more confidence that it really does avoid all paradoxes.

My insight was that "simultaneous" in this context can be defined as all points where the CMB is the same temperature. For example if we had 'Instantaneous' travel, this would mean we were sliding around an isosurface through space-time where the temperature of the CMB (in the CMB rest frame) is exactly 2.725°. If we were using our FTL 13 billion years ago, the universe would be orange and our instantaneous travel would take us to another point of the universe with the exact same shade of orange.

FTL that is less than instantaneous would deliver you to some point in space time where the temperature is a tiny bit lower.. never higher.

Relativistic flight also obeys this rule.

If our FTL obeys this simple rule, I think we can be confident that no combination of FTL and relativistic flight would ever deliver you back to your starting point before you left.

(This in no way argues that such an FTL feature is shoehorned into physics. The topic was simply about whether we could describe FTL without paradox that renders our description undefined.)

UPDATE 3

The thing I wanted to add was, the CMB rest frame choice isn't merely nice. I think it is special because I think it almost rules out any other choice.. if you are going to chose some frame and label it special it pretty much has to be this one.

Why? because you are either choosing the ONLY definition of "instantaneous" where you are travelling between points of the universe that have the same temperature and entropy, and look pretty similar, or you are choosing ANY OTHER one where travel in one specific arbitrary direction takes you to a younger, hotter universe, and the other direction takes you to a colder one, even though the universe does not look hotter or colder in either of those directions. Only one choice of reference frame is nice, all the others are "yuck". Apart from being "yuck", there are probably horrible exploits you could implement if you could slide freely between entire observable universes at different states of entropy. IMO that makes one choice head and shoulders above any other possible one.

UPDATE 4

https://backreaction.blogspot.it/2015/06/does-faster-than-light-travel-lead-to.html
I think [Sabine Hossenfelder's] point could be summarised by saying that the way to solve such paradoxes is to acknowledge the fact that, for macroscopic objects, there exist a sort of "preferred frame" given by the unidirectionality of the arrow of time that is over-imposed on top of fundamentally time-symmetric interactions.

She also posted a link to an article by Nemiroff and Russell where they calculate explicitly when the closed loop starts going back in time.
https://arxiv.org/abs/1505.07489

[meberbs]

This topic has unsurprisingly come up here before.

The last discussion I saw on it ended up with this comment:

https://forum.nasaspaceflight.com/index.php?topic=41389.msg1597244#msg1597244

It isn't clear to me if there is a set of consistent rules for where wormholes can or can't exist that would always prevent time travel. The argument Nilof made of "just close the wormhole if a closed timelike curve forms" seems compelling, but I feel like this would create situations where you could get FTL information by methods such as checking whether or not you can open a wormhole in a specific situation.

I would like to see a formal investigation of what conditions you could have on wormholes to guarantee that they don't violate causality.

[blasphemer]

There is no resolution as long as Einsteins relativity holds entirely. So we have to modify it.

What is the simplest such modification? Assume that there is an absolute frame of reference for FTL travel.

The most natural such assumption is CMB rest frame. FTL travel will always happen with respect to this frame. The rest of physics can work normally and is unaffected, but any FTL effect will have to happen relative to CMB frame. Your FTL speed will differ depending on which direction with respect to CMB you are going. This cures those temporal paradoxes.

[KelvinZero]

Im sure I have been on threads discussing this before, I was probably on that one too.. And I think one result was that you can produce a paradox with just a single FTL 'jump'.. If that is true then choosing a single reference frame does not resolve the issue. Maybe someone can confirm that.

The difference from earlier threads is that I wanted to concentrate on published solutions or speculations. Someone must have done this.

(just googled "resolutions to FTL paradoxes", found various "researchgate.net" papers, but I don't know if they are reputable.. I will probably have a go at reading them to at least see what they claim.. not sure I will understand them well enough to even do that.)

[gospacex]

If I had produced some math that seems to imply FTL, it just seems natural to me that the first thing to try is to investigate what the maths says would happen if I attempt to produce one of the various famous paradoxes. That would explain what the maths actually means in the real world.

Well, General Relativity's math already produces paradoxes: closed timelike curves inside Kerr black holes.

They even seem to be physically realizable. Very large (supermassive) rotating black holes exist, and there are no laws of physics preventing a spaceship entering them and flying along a CTC. In a large enough hole the ship built from real, existing matter, not unobtanium, can survive tidal forces.

The ship may never emerge back from black hole, yes, but still, how to explain that while orbiting on that CTC, the ship can return into its own past (previous orbit)

[WarpTech]

Im sure I have been on threads discussing this before, I was probably on that one too.. And I think one result was that you can produce a paradox with just a single FTL 'jump'.. If that is true then choosing a single reference frame does not resolve the issue. Maybe someone can confirm that.

The difference from earlier threads is that I wanted to concentrate on published solutions or speculations. Someone must have done this.

(just googled "resolutions to FTL paradoxes", found various "researchgate.net" papers, but I don't know if they are reputable.. I will probably have a go at reading them to at least see what they claim.. not sure I will understand them well enough to even do that.)

It was published in JBIS, Nov. 2015 issue, (didn't come out until Feb. 2016).

http://www.jbis.org.uk/paper.php?p=2015.68.347

There are no paradoxes here. Another paper I put together earlier also resolved several issues with warp drives.

https://www.researchgate.net/publication/251231464_THE_CONTROLLED_REFRACTIVE_INDEX_WARP_DRIVE

Todd

[KelvinZero]

Well, General Relativity's math already produces paradoxes: closed timelike curves inside Kerr black holes.

I suppose that is true. I know that General relativity has known holes.

But FTL is meant to operate in the real world in the sense that a postman can leap in an FTL ship, fly to alpha centauri, drop of a letter and come back. If that produces a paradox then you haven't actually described what the postman just did. Relativity can have holes in it and still be a great, useful theory. If a proposal for FTL cannot describe FTL, it can't have much value.

[KelvinZero]

There are no paradoxes here. Another paper I put together earlier also resolved several issues with warp drives.

You can't just say "There are no paradoxes here".

You have to be able to explain how the known paradoxes are avoided. If you have avoided paradoxes, you have to describe how your definition of FTL is constrained from the general form, that most definitely produces paradoxes.

The explanation cannot require complicated math to describe. To prove, sure, but not describe.

A person trying to implement one of these paradoxes will not be diverted by a maths storm. They have to experience something. A force. An alternate history. Annihilation. Something.

[WarpTech]

There are no paradoxes here. Another paper I put together earlier also resolved several issues with warp drives.

You can't just say "There are no paradoxes here".

You have to be able to explain how the known paradoxes are avoided. If you have avoided paradoxes, you have to describe how your definition of FTL is constrained from the general form, that most definitely produces paradoxes.

The explanation cannot require complicated math to describe. To prove, sure, but not describe.

A person trying to implement one of these paradoxes will not be diverted by a maths storm. They have to experience something. A force. An alternate history. Annihilation. Something.

Did you read them? There is no paradox because the coordinate speed of light is a variable in the theory. Objects never exceed the speed of light in their own local coordinates. Varying the speed of light changes the scale of rulers (ships) and clocks (atoms).

In "ST Voyager" we see the ship elongate into the distance, then snap away in a bright flash. In this theory, that animation is what it would look like.

[meberbs]

Objects never exceed the speed of light in their own local coordinates.

That is the whole idea of a closed timelike curve, a path that can be traveled moving at lightspeed (or slower) where the thing travelling the path ends up in its own past. It in no way prevents any paradoxes.

[KelvinZero]

Did you read them? There is no paradox because the coordinate speed of light is a variable in the theory.

Apparently I am having difficulty explaining why that answer is extremely unsatisfactory to me. I will try one more time.

I could not possibly understand a theory that proves something that is beyond generally accepted science. If it is correct, it is very very hard.

What I can understand is the general problem, for example how special relativity plus an instantaneous communicator trivially creates a time-travel paradox.

If your theory has any meaning in the real world, you must be able to explain how it changes the experience of someone attempting to produce one of these simple paradoxes.

If you cannot answer this, lets end this conversation here.

[blasphemer]

While not published, an interesting paradox-free FTL while trying to preserve as much as possible of relativity is described here (preferred FTL frame):

http://www.physicsguy.com/ftl/html/FTL_part4.html#subsec:specialframe

[JasonAW3]

What bothers me is simply; When there is a certain segment of time that passes from the starting time at the origin point and the destination point, in a progression towards entropy, no matter how short the duration, even though a significant distance is traveled, everyone insists that it's a form of time travel.

    This puzzles me.  If a train from New York to Washington DC only takes a few hours to travel the distance, while walking on foot between the two would take several days or weeks, is the train a form of time traveling device?

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

     If the same amount of time passes for the craft, the starting point and the destination, I don't see an issue.  Optically, the people at the target location would not see the launch from the starting point for eleven years, minus the travel time, while the starting point wouldn't see the craft arrive for eleven years minus the travel time.  People on the craft MAY experience a different time rate from the time observed by both the starting point and destination point, but will still have a forwards progression of time.

      So long as action precedes causation, I don't see a paradox here.

[meberbs]

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

You are entirely ignoring relativity. There are reference frames where The ship will be moving backwards. This is not "apparent" backwards motion, but actual backwards motion after accounting for speed of light delays in sensing. This is what creates the paradox. To illustrate:

Someone in such a frame passing by Ross 128 when  at (just estimating) 0.7 c towards Earth could receive a message from the first craft just as they arrive at Ross128, "we ran out of chocolate." The second craft then activates its own equivalent FTL drive. Since it started in a frame where the distance between Earth and Ross 128 is smaller, its trip will be shorter, and since the first ship will be travelling backwards in that frame, the second ship can arrive before the first ship left, and then give them extra chocolate so they don't run out.

[ppnl]

What bothers me is simply; When there is a certain segment of time that passes from the starting time at the origin point and the destination point, in a progression towards entropy, no matter how short the duration, even though a significant distance is traveled, everyone insists that it's a form of time travel.

    This puzzles me.  If a train from New York to Washington DC only takes a few hours to travel the distance, while walking on foot between the two would take several days or weeks, is the train a form of time traveling device?

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

     If the same amount of time passes for the craft, the starting point and the destination, I don't see an issue.  Optically, the people at the target location would not see the launch from the starting point for eleven years, minus the travel time, while the starting point wouldn't see the craft arrive for eleven years minus the travel time.  People on the craft MAY experience a different time rate from the time observed by both the starting point and destination point, but will still have a forwards progression of time.

      So long as action precedes causation, I don't see a paradox here.

Well it wouldn't look like time travel to any of those points of view. It would look like time travel to another observer in motion relative to those observers. This is because velocity not only causes length contraction it causes clocks at different points to be out of sync.

Imagine trying to put a 20 foot rocket inside a box only five feet thick. Does not fit right? But say we accelerate the rocket to a velocity such that it is only one foot long. Fly it into the box and simultaneously close the front and back of the box. For a tiny fraction of a second the rocket is fully inside the box and the front and back are closed. Then you must simultaneously open the front and back to let the rocket out.

But now lets imagine what that looks like from the point of view of someone riding on the nose of the rocket. From their point of view it is the box that is length contracted. How do they fit in a box less than a foot thick? From their perspective they don't. From their perspective the front and back of the box is never closed at the same time. They do not see themselves ever enclosed by the box. If you put a clock on the front of the box and the back of the box they will show the same time in one frame but will show different times in another frame.

Now imagine you have a teleporter that can instantaneously transport you from the front of the box to the back of the box and you do this at the exact time that the rocket is fully enclosed.  The rocket is fully enclosed and the front and back are still closed when you arrive. no problem right?

But again look at it from the point of view of the person on the rocket. From this point of view the front and back are never closed at the same time. So if they see you teleport from the front when the door is closed to the back when the door is closed then you have teleported from one point in time to another point in time.

Different observers can see events that are simultaneous in one frame as happening in a different order in another. And in relativity this is not an illusion. There is no absolute frame and so there is no absolute order that the events took place in as long as the events are far enough apart in space and close enough in time that a light beam cannot connect the events. As long as you do not violate the speed of light there is no paradox.   



 

[bad_astra]

I'm not sure there really is a resolution to the problem short of "many worlds"
This would imply that any conceivable FTL travel is in essence interuniversal.

An interesting idea. Why bother colonizing your galaxy on trips well below light speed if your culture reaches a technological ability to farm and colonize other universes for whatever it needs going back to the earliest period possible/useful and regions using stable wormhole gateways. You won't be altering the future for whatever might have happened in that part of the universe. It simply will never have happened in that reality.

That's not to say this sort of universal past mining might not be without consequences. https://arxiv.org/pdf/1505.05952.pdf
 Beyond me, though.

We really should take another look at the WMAP Cold Spot



 

[WarpTech]

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

You are entirely ignoring relativity. There are reference frames where The ship will be moving backwards. This is not "apparent" backwards motion, but actual backwards motion after accounting for speed of light delays in sensing. This is what creates the paradox. To illustrate:

Someone in such a frame passing by Ross 128 when  at (just estimating) 0.7 c towards Earth could receive a message from the first craft just as they arrive at Ross128, "we ran out of chocolate." The second craft then activates its own equivalent FTL drive. Since it started in a frame where the distance between Earth and Ross 128 is smaller, its trip will be shorter, and since the first ship will be travelling backwards in that frame, the second ship can arrive before the first ship left, and then give them extra chocolate so they don't run out.

Please provide a math example of how a ship can "physically" move backwards in time. Or a signal for that matter. These paradoxes arise for the same reason the Twin paradox arises. Ignoring which frame (clock/ruler) actually accelerated to the speed v, and which did not. Special Relativity is the special case where two "identical" inertial reference fames are passing each other at a relative speed, v. It says nothing about the history of how they got that way, or the physical effects of acceleration that "caused" one system's clock to run slower than the other, as in the Twin paradox.

In GR, the coordinate speed of light is a variable, it's not a constant. It's not absolute in any sense, as it is in SR. Two inertial reference frames at different gravitational potentials, with different conformal scaling, are not identical. Lorentz transformation do not apply.

In my model, which is a conformal scaling of the metric due to a relative refractive index, K. It simply changes the scale of local rulers and clocks, which are used to measure space and time in the region affected by the metric potentials. Changes affecting local rulers and clocks does not suddenly allow you to send messages backwards in time. It just changes the rate at which these effected clocks move forward in time. No paradoxes can occur in this case, and it still conforms with GR. It also conforms with SR, but ONLY in the "special case" where the two inertial frames have the same identical potential. SR is not generally true for every conceivable situation! That is why you get paradoxes.

[JasonAW3]

I'm not sure there really is a resolution to the problem short of "many worlds"
This would imply that any conceivable FTL travel is in essence interuniversal.

An interesting idea. Why bother colonizing your galaxy on trips well below light speed if your culture reaches a technological ability to farm and colonize other universes for whatever it needs going back to the earliest period possible/useful and regions using stable wormhole gateways. You won't be altering the future for whatever might have happened in that part of the universe. It simply will never have happened in that reality.

That's not to say this sort of universal past mining might not be without consequences. https://arxiv.org/pdf/1505.05952.pdf
 Beyond me, though.

We really should take another look at the WMAP Cold Spot

The "Many Worlds" theory is one of the only ones that I have ever found that resolves the majority of time travel issues.

     Essentially, if one were to go backwards in time, one would wind up leaving their original universe and shunt over to one NEARLY identical to one's origin universe, so any actions taken in THIS new universe, would have no effect on your home universe.  (ie, the old "Killing one's grandfather before one's father was born" paradox)

     Whether or not this would would resolve the "Time Travel vs. FTL" debate is problematic, as we, at present, have no way of testing this out.  If, indeed, this FTL travel causes a shunt to another universe, then the FTL trip back would return one to a SECOND universe, virtually identical to the one, one started in.

     Of course, this is also assuming that other versions of one's self are likewise shunting between universes.  This would avoid all sorts of messy problems with mass variations between universes and the same matter occupying the same space/time, but in two different locations.  (This also brings to mind the possibility of quantum interaction with one's self at a distance.  Would one become entangles with one's self over a vast distance?)

     If this is a case of universe shunting, then one would notice differences from one's home universe after a significant number of "FTL flights", but likely could write off minor differences as memory lapses.

     Overall, I tend to think that distance and velocity are only relevant to time in relativistic flight.  Moving Space itself, or shunting outside of normal Time/Space, or even some sort of wormhole drive, should not violate "time's arrow" unless the arrival at the destination happens before the departure from the origin point, relative to the reference frame of both the origin and the destination points.

      Even some form of spacial fold shouldn't violate "time's arrow", as the actual transition would still take at least Planck Time to actually occur.

[meberbs]

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

You are entirely ignoring relativity. There are reference frames where The ship will be moving backwards. This is not "apparent" backwards motion, but actual backwards motion after accounting for speed of light delays in sensing. This is what creates the paradox. To illustrate:

Someone in such a frame passing by Ross 128 when  at (just estimating) 0.7 c towards Earth could receive a message from the first craft just as they arrive at Ross128, "we ran out of chocolate." The second craft then activates its own equivalent FTL drive. Since it started in a frame where the distance between Earth and Ross 128 is smaller, its trip will be shorter, and since the first ship will be travelling backwards in that frame, the second ship can arrive before the first ship left, and then give them extra chocolate so they don't run out.

Please provide a math example of how a ship can "physically" move backwards in time.

A ship can't physically move backwards in time for the same reason it can't travel faster than the speed of light.

You ask for the math. The math is the Lorentz transformations. For any hypothetical object travelling FTL, it is trivial to find a reference frame where it travels the path backwards.

Or a signal for that matter. These paradoxes arise for the same reason the Twin paradox arises. Ignoring which frame (clock/ruler) actually accelerated to the speed v, and which did not. Special Relativity is the special case where two "identical" inertial reference fames are passing each other at a relative speed, v. It says nothing about the history of how they got that way, or the physical effects of acceleration that "caused" one system's clock to run slower than the other, as in the Twin paradox.

But they didn't accelerate in the above example except for engaging FTL, which should work the same in either frame. There are only 4 spacetime points that matter. When ship 1 entered and exited FTL and when ship 2 entered and exited FTL. Ship 1 enters FTL where ship 2 exits and vice versa (give or take the width of the ship to avoid a crash). Ship 1 exits FTL before ship 2 enters it, but ship 1 entered FTL after ship 2 exited it.

Only special relativity is needed to describe the above situation, and the explanation of independent of whatever magic generates the FTL.

None of your comments about general relativity apply. Special relativity is a special case of general relativity, so if it is a problem in special relativity, it still is in general relativity.

[WarpTech]

     By this notion, if a craft, traveling at the velocity of light would take eleven years to go from here to Ross 128, as an example, would using a technique that would allow a craft to make that same trip, in weeks, relative to both the starting point and the destination, STILL be a time machine?

You are entirely ignoring relativity. There are reference frames where The ship will be moving backwards. This is not "apparent" backwards motion, but actual backwards motion after accounting for speed of light delays in sensing. This is what creates the paradox. To illustrate:

Someone in such a frame passing by Ross 128 when  at (just estimating) 0.7 c towards Earth could receive a message from the first craft just as they arrive at Ross128, "we ran out of chocolate." The second craft then activates its own equivalent FTL drive. Since it started in a frame where the distance between Earth and Ross 128 is smaller, its trip will be shorter, and since the first ship will be travelling backwards in that frame, the second ship can arrive before the first ship left, and then give them extra chocolate so they don't run out.

Please provide a math example of how a ship can "physically" move backwards in time.

A ship can't physically move backwards in time for the same reason it can't travel faster than the speed of light.

You ask for the math. The math is the Lorentz transformations. For any hypothetical object travelling FTL, it is trivial to find a reference frame where it travels the path backwards.

Or a signal for that matter. These paradoxes arise for the same reason the Twin paradox arises. Ignoring which frame (clock/ruler) actually accelerated to the speed v, and which did not. Special Relativity is the special case where two "identical" inertial reference fames are passing each other at a relative speed, v. It says nothing about the history of how they got that way, or the physical effects of acceleration that "caused" one system's clock to run slower than the other, as in the Twin paradox.

But they didn't accelerate in the above example except for engaging FTL, which should work the same in either frame. There are only 4 spacetime points that matter. When ship 1 entered and exited FTL and when ship 2 entered and exited FTL. Ship 1 enters FTL where ship 2 exits and vice versa (give or take the width of the ship to avoid a crash). Ship 1 exits FTL before ship 2 enters it, but ship 1 entered FTL after ship 2 exited it.

Only special relativity is needed to describe the above situation, and the explanation of independent of whatever magic generates the FTL.

None of your comments about general relativity apply. Special relativity is a special case of general relativity, so if it is a problem in special relativity, it still is in general relativity.

In my Warp Drive paper, the warp field effectively negates the effects of SR by changing the length of the ship and the clocks it contains, so that they match the original rest frame where it started from, at all times. In other words, there is no length contraction or time dilation of the accelerated starship. Therefore, the motion of the ship is not relativistic, it's Newtonian. Lorentz transformations do not apply.

Again, how can changing the rate of my clock, moving faster or slower, suddenly give me the ability to travel backwards in time, or send a message backwards in time? It doesn't, it can't. The paradox is only there because SR is not applicable, yet everyone insists it is.