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
...Also, I have no idea why you bring up the concept of rotating reference frames, that is just an irrelevant complication. As for inertial reference frames, we have Michelson-Morley type experiments that show they are all equivalent.
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?Im not worried about how or why such a phenomenon could exist, just if it can be described without a paradox.
Take a quantum entanglement that seems to be instantaneous. Now send one of the charges away at near light speed. When its wave form collapses the signal should instantaneously go into the past (which I doubt). Wait, how do you entangle two charges and have them not exist in the same light cone...
Quote from: WarpTech on 07/25/2017 04:43 amQuote 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."which is like it or not, "identical" to the Twin paradox."This statement disproves your claim that you see why there is a paradox.The twin paradox is not a paradox, it is people misusing special relativity, and not recognizing that there are 3 relevant inertial frames that need to be considered. This situation only involves 2 relevant inertial frames, and really is a paradox if you allow FTL travel.
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.
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.
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.
Quote from: WarpTech on 07/25/2017 04:43 amIn formulating this problem, Ship 1 and Ship 2 are "identical" and both originate from Earth.Both originating from Earth is both optional and irrelevant.Quote from: WarpTech on 07/25/2017 04:43 amIn 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.In ship 2's frame, everything you said about ship 2 is true about ship 1, except the hangar on Earth part. If they started in deep space with no nearby reference points, and the crews of each ship were unconscious during the acceleration, no measurement they could do onboard the ship, or by observing the other ship could tell them which one had accelerated. (They could look at far away stars and see the redshift of course, but those were all moving at different velocities to start with as well, and in no way affect the problem. )I already said this, but I will keep repeating it until you read it, because you did not actually addres this statement:QuoteAfter 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.
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: WarpTech on 07/25/2017 04:43 amQuote 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.Except there is no gravity well in this problem. In this problem as stated, ship 2 does see ship 1's clock running slow. As I said before go setup this problem by sending both ships off in opposite directions at c/3 (to get 0.6 relative). They are all equivalent, and once the acceleration is done, there is no way to tell it ever happened.Quote from: WarpTech on 07/25/2017 04:43 amThe 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.Your so called "solutions" are just to not act out the problem. You have suggested adding a gravity well when there is none. You have also just turned down the effectiveness of the FTL drives to almost nothing, without having the ships actually have enough relative velocity for the given amount of FTL to illustrate the paradox.
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.
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.
there is no difference between gravitational time dilation and SR time dilation.
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.
No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.
Not true. If Ship 2 returns instantaneously to Earth, it would get there in year 5, not year 4 in Earth's frame. The ship's clock is slow, Earth's clock is not, the situation is not symmetrical.
Quote from: WarpTech on 07/25/2017 04:29 pmNo, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.What is the third frame? What velocity is it moving at relative to any other given frame?
The paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?
Quote from: WarpTech on 07/25/2017 04:29 pmNot true. If Ship 2 returns instantaneously to Earth, it would get there in year 5, not year 4 in Earth's frame. The ship's clock is slow, Earth's clock is not, the situation is not symmetrical.You are defining the Earth's frame as the only correct reference frame in the universe, this is simply contradictory to all of relativity.
If Ship 2 returns instantaneously to Earth
Quote from: meberbs on 07/25/2017 04:46 pmQuote from: WarpTech on 07/25/2017 04:29 pmNo, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.What is the third frame? What velocity is it moving at relative to any other given frame?The 3rd frame is the frame in which Ship 2 is now moving "toward" the Earth, not away from it. The velocity can be anything. It can be instantaneous travel taking 0 time, the Earth's clock will still have elapsed more time than Ship 2, which "was" accelerated to 0.6c moving away from Earth.
Quote from: meberbs on 07/25/2017 04:46 pmThe paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?I didn't ignore it. I said that Ship 2 started on Earth and was accelerated to 0.6c moving away from Earth. This "work" that was done to Ship 2 puts it in a higher-energy relative to Earth, in which it's clock runs show. That is what is different about ship 2's frame.
What experiment can they run? I said, they can return to Earth and find that the twin left behind has aged more. That proves the situation is not symmetrical. It can't be done remotely, they have to bring the two clocks back together to ompare them "accurately".
Why would their FTL drive be slower than ship 1's? Because ship 2 was accelerated and has a higher relative mass/energy content than ship 1. Therefore, it takes more Work to accelerate it back toward the Earth, than it does for Ship 1 to leave Earth.
No, that's your assumption. I'm explaining that if you start from rest within our galaxy, you are not moving very fast relative to Earth, v << c to begin with. If you start from rest near "Sagittarius A", that would be your correct reference frame. If you start at rest on Proxima Centauri, then that is your correct reference frame. It's all relative, but they are not all the same! Basically what I'm saying is that you can have inertial reference frames, with different vacuum spectral energy densities, different scaling of rulers, clocks, matter and energy. All inertial frames are NOT created equally.
Quote from: WarpTech on 07/25/2017 06:30 pmQuote from: meberbs on 07/25/2017 04:46 pmQuote from: WarpTech on 07/25/2017 04:29 pmNo, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.What is the third frame? What velocity is it moving at relative to any other given frame?The 3rd frame is the frame in which Ship 2 is now moving "toward" the Earth, not away from it. The velocity can be anything. It can be instantaneous travel taking 0 time, the Earth's clock will still have elapsed more time than Ship 2, which "was" accelerated to 0.6c moving away from Earth.Lets assume it is instantaneous for simplicity. What frame is it instantaneous in though? The only sensible answer is the ship 2 frame, but in this frame ship 1 hasn't left yet, so it produces the paradox.Also, despite your claim to the contrary, you still are ignoring considering the problem from any case other than "ship 2 was accelerated." All of the cases have the same result of time travel.Quote from: WarpTech on 07/25/2017 06:30 pmQuote from: meberbs on 07/25/2017 04:46 pmThe paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?I didn't ignore it. I said that Ship 2 started on Earth and was accelerated to 0.6c moving away from Earth. This "work" that was done to Ship 2 puts it in a higher-energy relative to Earth, in which it's clock runs show. That is what is different about ship 2's frame. Ship 2 is at rest in the ship 2 frame, and ship 1 has the higher energy, and nothing is special about Earth.Quote from: WarpTech on 07/25/2017 06:30 pmWhat experiment can they run? I said, they can return to Earth and find that the twin left behind has aged more. That proves the situation is not symmetrical. It can't be done remotely, they have to bring the two clocks back together to ompare them "accurately". All that experiment would tell them is that after they woke up, they accelerated towards Earth.Ship 1 could run the same experiment and accelerate the same amount to "catch up" to ship 2 and they would find that ship 1 had had the slow clock.Quote from: WarpTech on 07/25/2017 06:30 pmWhy would their FTL drive be slower than ship 1's? Because ship 2 was accelerated and has a higher relative mass/energy content than ship 1. Therefore, it takes more Work to accelerate it back toward the Earth, than it does for Ship 1 to leave Earth.No it would take the same amount of work.Quote from: WarpTech on 07/25/2017 06:30 pmNo, that's your assumption. I'm explaining that if you start from rest within our galaxy, you are not moving very fast relative to Earth, v << c to begin with. If you start from rest near "Sagittarius A", that would be your correct reference frame. If you start at rest on Proxima Centauri, then that is your correct reference frame. It's all relative, but they are not all the same! Basically what I'm saying is that you can have inertial reference frames, with different vacuum spectral energy densities, different scaling of rulers, clocks, matter and energy. All inertial frames are NOT created equally.Except the very principle of relativity is that ALL frames are created equally. You cannot claim that Earth and Sagittarius A are both correct and then say that not all are equal.You have put no restriction on how fast your FTL can go, explicitly referencing instantaneous travel. Even the slightest difference in speed will lead to a paradox as you approach instantaneous travel. Try it with the Earth orbital speed (30 km/s) and effectively instantaneous travel between here and some point, say 10 light years away.
KelvinZero,Clearly what you need is a way to visualize spacetime geometry so that you can answer these questions for yourself....Now can a single instantaneous message or trip cause a paradox? No because the only points available for you to go to are the points in your now slice. In order to time travel you have to accelerate to some velocity with respect to that now slice. Then your now slice has a tilt with respect to the original now slice. This will allow you to travel to your own past. Paradox.Can you prevent time travel by limiting your FTL to with respect to a single frame of reference? Well yes but that's like having a time traveling machine in the room and just deciding not to use it. It will not for example prevent aliens from using time travel to screw with our past. FTL travel makes time travel possible under relativity. Choosing not to use it does not change anything. Paradoxes are but a decision away.Can we avoid paradoxes if the physics of the universe established a universal frame of reference? Well yes but then it makes no sense to worry about what relativity has to say about it since relativity is wrong. Also just about all of modern physics would be horribly wrong. Could you do it while reproducing all the correct predictions of our current wrong physics? Maybe but it would be horribly complex and very very difficult to do. I wouldn't even know where to begin.
Can we avoid paradoxes if the physics of the universe established a universal frame of reference? Well yes but then it makes no sense to worry about what relativity has to say about it since relativity is wrong. Also just about all of modern physics would be horribly wrong. Could you do it while reproducing all the correct predictions of our current wrong physics? Maybe but it would be horribly complex and very very difficult to do. I wouldn't even know where to begin.
I don't mean "I am ok with any hypothetical universe, so long as it is self consistent". It absolutely must not contradict what we already observe about the real world, ie relativity.Given that, Im prepared to entertain all sorts of arbitrary rules to prevent paradoxes, such as impenetrable walls suddenly appearing, preventing relativistic travel in a defined region/period. Postulating a wall is not the same as pretending relativity is no longer a thing.It just has to be describable in this universe without having paradoxes that mean you haven't really described anything.
In the problem formulated my way and not all the other ways you're trying to drag us into;
the clock on Ship 2 runs slow. The clock on Earth/Ship 1 does not. (Again, assuming my FTL warp drive in my JBIS paper where, when FTL is engaged, the rate of the clock on the ship does not change rate relative to it's rate before FTL was engaged.)
At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
IMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.
As for a consistent way to implement FTL, I have not done the math to fully work this out yet, but here are my thoughts:I believe it is correct that it can be done by picking one reference frame to be the ultimate arbiter of "forward in time" for the entire universe. Every experiment we have done says that this is not out universe, but restricting it so that no FTL drive can move backwards in time in the preferred frame should prevent paradoxes. This also contradicts the most basic principle in relativity, so I am not sure exactly what else would have to change in physics, probably things like the speed of light would only truly be constant in one frame (or maybe the concept of aether would need to be brought back), also relativistic effects if they still exist at all would probably have to be tied to velocity in the special frame. If you are just writing interstellar hard sci-fi, picking a preferred frame for FTL should be good enough. (If you are going to pick a special frame, the center of the galaxy is the closest object you could tie it to that would seem believable, really it should just be some arbitrary frame that even our galaxy has some velocity relative to.)
Quote from: WarpTech on 07/25/2017 07:56 pmAt the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.You are defining instantaneous differently for the 2 ships.
In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.
Quote from: WarpTech on 07/25/2017 07:56 pmIMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.General relativity introduces more ways to get paradoxes, and reduces to special relativity in the relevant cases we are discussing (The GR paradoxes are all currently excluded from implementation by things like event horizons and the need for exotic (negative mass) matter). The assumption that all inertial reference frames are equal is also part of general relativity. It is a very realistic assumption because it has been experimentally observed to be true.
Quote from: meberbs on 07/25/2017 11:29 pmQuote from: WarpTech on 07/25/2017 07:56 pmAt the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.You are defining instantaneous differently for the 2 ships.Yes, that is correct, because the situation is not symmetrical.Quote from: meberbs on 07/25/2017 11:29 pmIn the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4. ... and that observation is incorrect, it is an illusion.Can we agree that the symmetry is the cause of the paradox please? I put forward that the paradox cannot happen, because the symmetrical scenario which results in a paradox is not physically possible within the confines of our galaxy, or local cluster.I repeat... Quote from: meberbs on 07/25/2017 11:29 pmQuote from: WarpTech on 07/25/2017 07:56 pmIMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.General relativity introduces more ways to get paradoxes, and reduces to special relativity in the relevant cases we are discussing (The GR paradoxes are all currently excluded from implementation by things like event horizons and the need for exotic (negative mass) matter). The assumption that all inertial reference frames are equal is also part of general relativity. It is a very realistic assumption because it has been experimentally observed to be true.GR is perfectly consistent with inertial reference frames having different rates of time passage. By insisting on having symmetry, what you are saying is that when Ship 2 accelerates away from earth, (not FTL) to 0.6c, it's clock rate is unaffected. It is still the same as it was on Earth. As such, you expect the situation to be symmetrical and therefore you end up with a paradox. I'm saying, the clock on the ship really is slower than the clock on Earth, not vis-versa. It is not symmetrical, and it can't be symmetrical within our galaxy.Anyone: Please give a "realistic" example of how Ship 2 came to be moving at 0.6c relative to the Earth where, it did not previously accelerate to that speed. Given that there have been no observations of stars or planets in our galaxy that are moving more than a little over 100 km/s. Nowhere near 0.6c, and there are no worlds orbiting stars or BH's at 0.6c either. The fastest stable orbit around a BH is .5c and it oscillates relative to Earth. So the situation in which Ship 2 has always been moving 0.6c relative to the Earth is unrealistic (if not impossible). Therefore, the symmetry required to cause a paradox, does not exist.
Quote from: meberbs on 07/25/2017 11:29 pmQuote from: WarpTech on 07/25/2017 07:56 pmAt the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.You are defining instantaneous differently for the 2 ships.Yes, that is correct, because the situation is not symmetrical.Quote from: meberbs on 07/25/2017 11:29 pmIn the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4. ... and that observation is incorrect, it is an illusion.
Can we agree that the symmetry is the cause of the paradox please?
I put forward that the paradox cannot happen, because the symmetrical scenario which results in a paradox is not physically possible within the confines of our galaxy, or local cluster.
GR is perfectly consistent with inertial reference frames having different rates of time passage. By insisting on having symmetry, what you are saying is that when Ship 2 accelerates away from earth, (not FTL) to 0.6c, it's clock rate is unaffected.
Anyone: Please give a "realistic" example of how Ship 2 came to be moving at 0.6c relative to the Earth where, it did not previously accelerate to that speed.
Quote from: WarpTech on 07/26/2017 01:54 amQuote from: meberbs on 07/25/2017 11:29 pmQuote from: WarpTech on 07/25/2017 07:56 pmAt the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.You are defining instantaneous differently for the 2 ships.Yes, that is correct, because the situation is not symmetrical.Quote from: meberbs on 07/25/2017 11:29 pmIn the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4. ... and that observation is incorrect, it is an illusion.No, it is not an illusion.