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

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.

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.

https://backreaction.blogspot.it/2015/06/does-faster-than-light-travel-lead-to.htmlI 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

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.

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.)

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

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

Quote from: WarpTech on 07/18/2017 05:59 pmThere 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.

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

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

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?

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.

Quote from: JasonAW3 on 07/19/2017 02:20 pm 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.

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

Quote from: meberbs on 07/19/2017 03:08 pmQuote from: JasonAW3 on 07/19/2017 02:20 pm 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.

Quote from: WarpTech on 07/19/2017 08:15 pmQuote from: meberbs on 07/19/2017 03:08 pmQuote from: JasonAW3 on 07/19/2017 02:20 pm 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.Quote from: WarpTech on 07/19/2017 08:15 pm 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.