It seems the problem is very similar to the Twins Paradox. See attached image I found online. I added the red and orange arrows to represent ship 1 and ship 2. However, this diagram is for 0.6c not 0.7c as we were discussing.I added the direction of both ships after they exit FTL. This diagram shows the perspective from both sides.
FWIW, here's physicist Matthew Buckley's (https://twitter.com/physicsmatt) take on explaining why FTL requires giving up relativity or causality http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel
Another possible solution would be to give up free will.
Sorry. Don't know the reference. If this is a reference to "Mr Robot", no spoilers please because I intend to watch that some time.Does anyone know if you can make a single FTL jump and then always decide to implement a paradox? If not, it seems semi plausible to avoid paradoxes by making FTL only operate if no choice afterwards would cause a paradox. For example, If you have sent an observer along your route at relativistic speeds to create a paradox, it disrupts FTL and you don't make the trip. This is a bit like fate limiting free will, but more palatable since it only happens at this one point, and we are all used to having our free will limited at airports.I realise that on one level that sounds really arbitrary. On the other hand it is not much weirder than the problem of the observer in quantum mechanics collapsing waveforms though the act of observation.
A single FTL jump will not cause a paradox. It will look like time travel to an observer in another frame of reference but you have a space like distance between you and your past so you can't immediately cause a paradox. To cause a paradox you have to accelerate your ship to some relative velocity to your original frame. Then when you jump home you will arrive before you left. That's where the paradoxes start.
Quote from: ppnl on 07/23/2017 04:48 pmA single FTL jump will not cause a paradox. It will look like time travel to an observer in another frame of reference but you have a space like distance between you and your past so you can't immediately cause a paradox. To cause a paradox you have to accelerate your ship to some relative velocity to your original frame. Then when you jump home you will arrive before you left. That's where the paradoxes start.I thought you could impliment a paradox with a single FTL trip, but I couldn't think of an example. If events A and B are synchronized by a pulse of light emitted exactly halfway between them, it does not seem that any lightspeed signal could get from A to B or vice versa in less time.Can anyone else confirm whether or not FTL paradoxes always involve multiple FTL usages to implement?
Well maybe it can if your warp drive can warp to a point in space time that is local in space but back in time. Such a thing is usually just called a time travel machine. Time travel machines can enable effective FTL travel. Just travel back in time eight years and then go to Alpha Centauri at half the speed of light. You will effectively have gotten there instantly.And it depends on what you mean by paradox. If you travel faster than light then an observer will see you as being in two different places at once. That seems like a paradox. But usually the word paradox is used to refer to when you interact with your own past.
The #1 issue with that diagram is the obvious lack of symmetry. You can see that the red line travels backwards in time in the "outbound" frame, but the orange line should therefore be moving backwards in time in the Earth frame. As part of this you do not show the ship 2 as having as fast of FTL in its frame as ship 1 does. You also somehow appear to have ship 2 travelling at light speed or close to it after its FTL leg (in its frame), rather than at rest. To me this mostly is just more evidence you don't know what you are talking about....
The key to resolving the paradox is; the two clocks are compared when ship 1 exits FTL, whoever has elapsed the most time is correct, and the other is wrong.
What causes the paradox is that Special Relative is about the "Special Case" where there is symmetry.
That is when the Lorentz transformations are applied. But it's not always symmetrical. Take two observers with clocks, one far from any massive objects and one hovering near the event horizon of the black hole.
Quote from: WarpTech on 07/24/2017 04:22 amThe key to resolving the paradox is; the two clocks are compared when ship 1 exits FTL, whoever has elapsed the most time is correct, and the other is wrong.What do you not understand about the fact that the Earth frame and the ship 2 initial frame are both correct? Nothing about the ship 1 or Earth frame should cause ship 2 to be unable to FTL in its own frame as fast as ship 1 could in its own frame.
Quote from: WarpTech on 07/24/2017 04:22 amWhat causes the paradox is that Special Relative is about the "Special Case" where there is symmetry.It isn't a special case where there is symmetry, it is the only case. If you find an exception to this, you would literally have to rewrite all of modern physics.
Are you sure that this is a realistic expectation? If we confine this to our own galaxy, then none of the stars that we've observed within our galaxy have speeds anywhere near 0.6c. Even if there were a planet orbiting a black hole, the last stable orbit is only v = 0.5c and any planet at 0.6c orbit would spiral into the event horizon. So I do not believe that such a situation can arise without Ship 2 having accelerated to >0.6c from a relative speed << c, relative to Earth.
I just gave you the basis of such a model. Starting from the BH at the center of the milky way, there is a "baseline" for the rate at which time passes in our galaxy, our solar system, our planet. The "local" baseline is our preferred frame and motion relative to it causes increased damping of the quantum oscillators, leading to time dilation and length contraction such that all observers measure the same value of "c", independent of their relative velocity. It doesn't rewrite ANY physics, it only re-interprets what we know based on QED, instead of the classical, fictitious geometry of empty space. You only need to consider it with an open mind.
Quote from: WarpTech on 07/24/2017 07:54 pmAre you sure that this is a realistic expectation? If we confine this to our own galaxy, then none of the stars that we've observed within our galaxy have speeds anywhere near 0.6c. Even if there were a planet orbiting a black hole, the last stable orbit is only v = 0.5c and any planet at 0.6c orbit would spiral into the event horizon. So I do not believe that such a situation can arise without Ship 2 having accelerated to >0.6c from a relative speed << c, relative to Earth. High mass ratio photon rockets powered by matter-antimatter reactions should be able to reach such high velocities, and the relativistic velocity needed to produce a paradox also depends on the speed of your FTL, and it could be quite low. You are trying to solve this by saying "just don't do the thing that causes a paradox." This is just a non-answer.
Quote from: WarpTech on 07/24/2017 07:54 pmI just gave you the basis of such a model. Starting from the BH at the center of the milky way, there is a "baseline" for the rate at which time passes in our galaxy, our solar system, our planet. The "local" baseline is our preferred frame and motion relative to it causes increased damping of the quantum oscillators, leading to time dilation and length contraction such that all observers measure the same value of "c", independent of their relative velocity. It doesn't rewrite ANY physics, it only re-interprets what we know based on QED, instead of the classical, fictitious geometry of empty space. You only need to consider it with an open mind.You are the one who needs to open up your mind and go learn the basics of special relativity. If you pick one frame to be special, then the speed of light would not be constant between frames. You listed multiple different frames, none of which are "the one special frame", which is obvious from you having listed multiple of them. If you did actually pick a special frame, you would have to rewrite a lot of physics, and you would have a lot of experimental results that you would find impossible to explain.Please don't talk about a theory of quantum gravity when you don't even get special relativity, it makes you sound both arrogant and ignorant.
That's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.
There is no "one special frame". They are all relative.
Our "local" frame is our preferred frame, because it sets the rate at which time passes on Earth.
there is no difference between gravitational time dilation and SR time dilation.
Quote from: WarpTech on 07/24/2017 10:24 pmThat's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.And don't bring up the so-called "twin paradox." That is a case where people who arrive at a paradox fail to account for the effect of the acceleration on the time experienced by the twin who is accelerating. In this case, the paradox does not care if the people on the ship their trip as lasting 1 million years, or 1 second. All that matters is that a drive exists that can move between 2 space-like separated points.Quote from: WarpTech on 07/24/2017 10:24 pmThere is no "one special frame". They are all relative.Exactly.Quote from: WarpTech on 07/24/2017 10:24 pmOur "local" frame is our preferred frame, because it sets the rate at which time passes on Earth.Special frame and preferred frame mean exactly the same thing in this context. There is no preferred frame.You state one of the basic principles of relativity and contradict it in the next sentence. You don't understand why FTL is time travel even after being shown diagrams that demonstrate it clearly, when every competent physicist on the planet understands this. It would be a waste of time to read anything you write about actually complicated topics like general relativity or quantum mechanics. Quote from: WarpTech on 07/24/2017 10:24 pmthere is no difference between gravitational time dilation and SR time dilation.General relativity is just the full version of special relativity, of course time dilation is the same thing in both. You treating this statement like it is some kind of revelation or thinking that it changes anything I have already said is just further evidence that you don't understand the relevant topics.
The rotation thus measured is an absolute rotation, that is, the platform's rotation with respect to an inertial reference frame.
Satellites ring. An idea to verify the GR corrections to the Sagnac effectis to make use of a ring of orbiting satellites (such as those belonging to theGPS or to the future European Galileo system). A stationary ring configurationof satellites can be the way to force the light beams to run in a closed circuitaround the Earth, both in co-rotating and counter-rotating direction. The timedifference in the propagation times should reproduce the effect expressed by formula(42)-(47), once the much bigger classical Sagnac effect has been subtractedout. Of course here too the technical details need to be thoroughly worked out.
Quote from: WarpTech on 07/24/2017 10:24 pmThat's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.And don't bring up the so-called "twin paradox." That is a case where people who arrive at a paradox fail to account for the effect of the acceleration on the time experienced by the twin who is accelerating. In this case, the paradox does not care if the people on the ship their trip as lasting 1 million years, or 1 second. All that matters is that a drive exists that can move between 2 space-like separated points.
Quote from: WarpTech on 07/24/2017 10:24 pmthere is no difference between gravitational time dilation and SR time dilation.General relativity is just the full version of special relativity, of course time dilation is the same thing in both. You treating this statement like it is some kind of revelation or thinking that it changes anything I have already said is just further evidence that you don't understand the relevant topics.
Quote from: meberbs on 07/24/2017 11:03 pmQuote from: WarpTech on 07/24/2017 10:24 pmThat's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.And don't bring up the so-called "twin paradox." That is a case where people who arrive at a paradox fail to account for the effect of the acceleration on the time experienced by the twin who is accelerating. In this case, the paradox does not care if the people on the ship their trip as lasting 1 million years, or 1 second. All that matters is that a drive exists that can move between 2 space-like separated points.Quote from: WarpTech on 07/24/2017 10:24 pmThere is no "one special frame". They are all relative.Exactly.Quote from: WarpTech on 07/24/2017 10:24 pmOur "local" frame is our preferred frame, because it sets the rate at which time passes on Earth.Special frame and preferred frame mean exactly the same thing in this context. There is no preferred frame.You state one of the basic principles of relativity and contradict it in the next sentence. You don't understand why FTL is time travel even after being shown diagrams that demonstrate it clearly, when every competent physicist on the planet understands this. It would be a waste of time to read anything you write about actually complicated topics like general relativity or quantum mechanics. Quote from: WarpTech on 07/24/2017 10:24 pmthere is no difference between gravitational time dilation and SR time dilation.General relativity is just the full version of special relativity, of course time dilation is the same thing in both. You treating this statement like it is some kind of revelation or thinking that it changes anything I have already said is just further evidence that you don't understand the relevant topics.I won't refer to them all but there are better ways than to throw insults. If the conversion could continue without the need to justify oneself, by insulting others, it would be of benefit to the forum. Thanks.
Quote from: meberbs on 07/24/2017 11:03 pmQuote from: WarpTech on 07/24/2017 10:24 pmThat's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.And don't bring up the so-called "twin paradox." That is a case where people who arrive at a paradox fail to account for the effect of the acceleration on the time experienced by the twin who is accelerating. In this case, the paradox does not care if the people on the ship their trip as lasting 1 million years, or 1 second. All that matters is that a drive exists that can move between 2 space-like separated points.Apparently we have different assumptions (realistic vs false) regarding the setup of this problem. Which is why you insist there is a paradox. You are wrong in that I do see why there is a paradox AND how to resolve it. You see only a symmetrical problem, which is like it or not, "identical" to the Twin paradox. What I'm saying that the interpretation you have is wrong. The past does not exist for anyone to travel backwards in time. Causality only requires that there be a finite coordinate speed of light, GR says that the coordinate speed of light is not constant, it's a variable around massive objects. The speed of light in high orbit is "faster" than it is on the surface of the Earth. No causality is broken by this, yet relative to a light signal in vacuum on Earth, the same signal in space far from matter travels a little faster.
In formulating this problem, Ship 1 and Ship 2 are "identical" and both originate from Earth.
In accelerating Ship 2 to 0.6c, it's relative mass/energy has increased to 125% of that of Ship 1, it's clock has slowed down and it's length has contracted. Nothing changed on Ship 1, it's still in the hanger on Earth. This is not a symmetrical problem.
After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.
Quote from: meberbs on 07/24/2017 11:03 pmQuote from: WarpTech on 07/24/2017 10:24 pmthere is no difference between gravitational time dilation and SR time dilation.General relativity is just the full version of special relativity, of course time dilation is the same thing in both. You treating this statement like it is some kind of revelation or thinking that it changes anything I have already said is just further evidence that you don't understand the relevant topics.It specifically contradicts your belief that there is symmetry in this problem, because in GR, if Ship 2 is in a gravity well and it's clock runs slow, it does not look up at Ship 1 and see it's clock there running slow. It runs fast. Which is identical to the temporal relationship between Ship 1 and Ship 2 when Ship 2 was accelerated to 0.6c.
The space-time diagrams that I provided last night shows the trip of Ship 1 and Ship 2, at the speed "c". If these paths are slightly faster than c, Ship 2 may get to Earth at year 7 on Earth's clock instead of year 8 but, it does not cause a paradox. The paradox only occurs when you "assume" the problem is symmetrical in both frames, when in reality, it is not.