Any resolutions to FTL paradoxes?

[meberbs]

What third option? I clearly said that observer ship travels at 0.7c. If it had FTL, it would be different, but I said it's 0.7c so why make up options? And I used 0.7c because it was the speed I believe you used yourself in some of the examples. I did understand what he said perfectly.

At school exam, when teacher tasked you to solve some task, where "train goes at 100km/h and ...", did you also try to be smart and say "yeah but it could also go at 120km/h!", sure it could, but that's not the case in situation you've been tasked with, so no point in making such option(s).

Next, I do understand what you said about the observer traveling at 0.7c by the coffee event and THEN using the bubble FTL to go to us. Yes, his bubble encapsulates different time-reference, but the moment he switches off the A-FTL, everything will move away from him at 0.7c. Any message sent will be delayed a bit, and that bit happens to be exactly what would prevent him from sending a message back in time, even by a tiny bit.

You trying to say "but the other ship doesn't have FTL" is simply a poor attempt at avoiding the issue. Ignoring situations that cause paradoxes don't make them go away.

No, no significant delay would happen, they would choose their exit point properly, and depending on the setup could end up many years in the past from Earth's perspective. Go look at the worked examples from the beginning of this thread.

[MikeAtkinson]

There are I think three possible resolutions to FTL paradoxes:

1. FTL is possible but there is no communication possible with the outside world until the light cone has caught up. So for instance, you jump 1 ly away, but then cannot communicate (in any way, in either direction) with the outside world for a year. Although this at first seems a bit pointless, it would allow light speed travel, which is much better than we can do now.

2. FTL travel moves you into a parallel universe, no paradoxes are possible within that stack of universes. Perhaps you could return to your own universe/origin, but only if no paradoxes have been created in any frame of reference.

3. Paradoxes are not possible because of some unknown physical principle. Although we can create paradoxes with thought experiments, this unknown principle means that those thought experiments cannot be realized.

[kamill85]

What third option? I clearly said that observer ship travels at 0.7c. If it had FTL, it would be different, but I said it's 0.7c so why make up options? And I used 0.7c because it was the speed I believe you used yourself in some of the examples. I did understand what he said perfectly.

At school exam, when teacher tasked you to solve some task, where "train goes at 100km/h and ...", did you also try to be smart and say "yeah but it could also go at 120km/h!", sure it could, but that's not the case in situation you've been tasked with, so no point in making such option(s).

Next, I do understand what you said about the observer traveling at 0.7c by the coffee event and THEN using the bubble FTL to go to us. Yes, his bubble encapsulates different time-reference, but the moment he switches off the A-FTL, everything will move away from him at 0.7c. Any message sent will be delayed a bit, and that bit happens to be exactly what would prevent him from sending a message back in time, even by a tiny bit.

You trying to say "but the other ship doesn't have FTL" is simply a poor attempt at avoiding the issue. Ignoring situations that cause paradoxes don't make them go away.

No, no significant delay would happen, they would choose their exit point properly, and depending on the setup could end up many years in the past from Earth's perspective. Go look at the worked examples from the beginning of this thread.

No, I was just pointing out that making such case was not the point of given example. Now, like I said later on, even if that observer ship used bubble FTL, it would result in no paradoxes at all.

Let me make it more clear to you, the moment such ship a million ly away witnesses the coffee break event, no matter what speed it is traveling at, its reference frame is counting time FROM that moment onwards, and since the ship is not moving faster than light through space, it cannot travel backwards in time. Lets make a timeline:

1) Ship1 leaves point X at 10:00, travels for 10 minutes 1 million light years away to point Y, where at 10:10 has a 5 min coffee break until 10:15, jumps back, 10minutes later arrives back at point X, its now 10:25.
2) Ship2 was passing by point Y at 0.99c, saw coffee break event, due to his speed, the event appeared to be shorter, taking only 1 minute (5x less).
3) Ship2 decided to use a similar bubble FTL engine like on Ship1, and in his 10 minutes of time, arrived at point X.
4) Ship2 time-reference being different, made the travel shorter, so after the coffee break event was over, it traveled to X in 10/5=2minutes of time instead of 10 minutes like Ship1. Ship2 arrived at point X at 10:17.


That being said, we are making a big assumption for "warp bubbles", such that space it self has no volume, for example, perhaps, warping at 0.7c to from Y to X is 1.42 times more energy-consuming, hence in reality the drive was just working that much harder to arrive there in 2 minutes instead of 10. I guess we might never know. However, it is irrelevant to the problems within this thread. There are no paradoxes with Apparent FTL.

[meberbs]

Let me make it more clear to you, the moment such ship a million ly away witnesses the coffee break event, no matter what speed it is traveling at, its reference frame is counting time FROM that moment onwards, and since the ship is not moving faster than light through space, it cannot travel backwards in time. Lets make a timeline:

1) Ship1 leaves point X at 10:00, travels for 10 minutes 1 million light years away to point Y, where at 10:10 has a 5 min coffee break until 10:15, jumps back, 10minutes later arrives back at point X, its now 10:25.
2) Ship2 was passing by point Y at 0.99c, saw coffee break event, due to his speed, the event appeared to be shorter, taking only 1 minute (5x less).
3) Ship2 decided to use a similar bubble FTL engine like on Ship1, and in his 10 minutes of time, arrived at point X.
4) Ship2 time-reference being different, made the travel shorter, so after the coffee break event was over, it traveled to X in 10/5=2minutes of time instead of 10 minutes like Ship1. Ship2 arrived at point X at 10:17.

Mostly fine up until step 4.
There is no absolute time reference, so ship 2 would arrive some hundreds of thousands of years before ship 1 originally left point X.

Did you read the examples I worked out at the beginning of this thread yet?

[kamill85]

Let me make it more clear to you, the moment such ship a million ly away witnesses the coffee break event, no matter what speed it is traveling at, its reference frame is counting time FROM that moment onwards, and since the ship is not moving faster than light through space, it cannot travel backwards in time. Lets make a timeline:

1) Ship1 leaves point X at 10:00, travels for 10 minutes 1 million light years away to point Y, where at 10:10 has a 5 min coffee break until 10:15, jumps back, 10minutes later arrives back at point X, its now 10:25.
2) Ship2 was passing by point Y at 0.99c, saw coffee break event, due to his speed, the event appeared to be shorter, taking only 1 minute (5x less).
3) Ship2 decided to use a similar bubble FTL engine like on Ship1, and in his 10 minutes of time, arrived at point X.
4) Ship2 time-reference being different, made the travel shorter, so after the coffee break event was over, it traveled to X in 10/5=2minutes of time instead of 10 minutes like Ship1. Ship2 arrived at point X at 10:17.

Mostly fine up until step 4.
There is no absolute time reference, so ship 2 would arrive some hundreds of thousands of years before ship 1 originally left point X.

Did you read the examples I worked out at the beginning of this thread yet?

It would not, as it started witnessing the event at lets call it TIME_X, from which, their respective clocks continue ticking onwards but at different rates. At TIME_X, the events such as Ship1 leaving the point X have already happened, regardless of any time-reference frame. Doesn't matter at what speed Ship2 is traveling at through space, it cannot revisit that time/space coordinate anymore without breaking causality (via traveling FTL through-space for example). It is traveling FTL using a warp bubble, without ever going beyond C in space. It makes a huge difference.

Let me put it in a different way - just because Ship2 can see the event, it means the event of Ship1 leaving point X has already happened, even in time reference of Ship2. Ship2 is not a time traveler, no matter how fast it will go to point X, it will not arrive there before Ship1 has left.

[meberbs]

It would not, as it started witnessing the event at lets call it TIME_X, from which, their respective clocks continue ticking onwards but at different rates. At TIME_X, the events such as Ship1 leaving the point X have already happened, regardless of any time-reference frame.

This is simply false, the event that ship 1 left point X happens a long time in the future according to someone at the coffee break travelling with some velocity relative to ship 1.

Doesn't matter at what speed Ship2 is traveling at through space, it cannot revisit that time/space coordinate anymore without breaking causality (via traveling FTL through-space for example). It is traveling FTL using a warp bubble, without ever going beyond C in space. It makes a huge difference.

It makes no difference whatsoever. All that matters are the events in spacetime (each ship departing/arriving). What method they used to FTL is irrelevant. The breaking of causality would happen with any form of FTL including wormholes.

Let me put it in a different way - just because Ship2 can see the event, it means the event of Ship1 leaving point X has already happened, even in time reference of Ship2. Ship2 is not a time traveler, no matter how fast it will go to point X, it will not arrive there before Ship1 has left.

FTL of any sort is time travel, and it is simply inconsistent with relativity to make the claim that the ship 1 leaving is an event that had already happened in the ship 2 frame.

You still appear to have not read the examples I already provided, after repeated requests for you to do so. At this point not doing so is extremely rude. You seem to be new here, so you might not know this, but moderators don't appreciate rudeness here, so if you continue trying to communicate with me without going back to read the examples I worked out, you can expect your posts to disappear.

[kamill85]

It would not, as it started witnessing the event at lets call it TIME_X, from which, their respective clocks continue ticking onwards but at different rates. At TIME_X, the events such as Ship1 leaving the point X have already happened, regardless of any time-reference frame.

This is simply false, the event that ship 1 left point X happens a long time in the future according to someone at the coffee break travelling with some velocity relative to ship 1.

Uh, stop right here. That's not true and there is no math that could back this up. When you SEE the event-B (coffee break) that is an outcome of an event-A happening (Ship1 leaving point X), it means, logically, that regardless of your speed, event-A is already in your past. Sorry man, that's how causality works.

Edit: To publicly address some private note - no, I don't feel like I'm doing a logical fallacy here, proving causality isn't broken by assuming it cannot be broken, no.

I think we all agree causality is pretty much broken the moment something could move faster than the causality speed (lets just say c) through space.  That is why it is called causality speed after all. Now, with Apparent FTL, where we do not move faster than c through space, logically, do not break causality. If we see a star explosion on the sky, do an instant FTL jump there, we would still arrive X (=ly distance) many years after the event, not a day before, not a day after (ignoring space expansion here). If someone witnessed our visit, while moving at some relativistic speed, and did an FTL jump back with us, would still arrive after we have left to see it, it's that simple.

PS. Yes I have read your examples, they are inadequate IMO. Just to point out some error, Observer1 at A sees distance from A to B to be 10ly, Observer2, traveling at relativistic speed of 0.7c passing A towards B would tell its a different distance; and to him, it would be. It is how relativity works. You ignored that completely in your calculations.

[meberbs]

It would not, as it started witnessing the event at lets call it TIME_X, from which, their respective clocks continue ticking onwards but at different rates. At TIME_X, the events such as Ship1 leaving the point X have already happened, regardless of any time-reference frame.

This is simply false, the event that ship 1 left point X happens a long time in the future according to someone at the coffee break travelling with some velocity relative to ship 1.

Uh, stop right here. That's not true and there is no math that could back this up. When you SEE the event-B (coffee break) that is an outcome of an event-A happening (Ship1 leaving point X), it means, logically, that regardless of your speed, event-A is already in your past. Sorry man, that's how causality works.

Edit: To publicly address some private note - no, I don't feel like I'm doing a logical fallacy here, proving causality isn't broken by assuming it cannot be broken, no.

This directly is circular logic, or "begging the question." You are saying that ship 1 leaving must be in the past because of causality, therefore causality is preserved.

I think we all agree causality is pretty much broken the moment something could move faster than the causality speed (lets just say c) through space.  That is why it is called causality speed after all.

No, no one including me has been able to come up with an example of causality breaking from a single FTL jump. If you can, please share.

Now, with Apparent FTL, where we do not move faster than c through space, logically, do not break causality. If we see a star explosion on the sky, do an instant FTL jump there, we would still arrive X (=ly distance) many years after the event, not a day before, not a day after (ignoring space expansion here). If someone witnessed our visit, while moving at some relativistic speed, and did an FTL jump back with us, would still arrive after we have left to see it, it's that simple.

Your last sentence is simply wrong, and ignores that in the reference frame of the other ship, the event of the first ship leaving can be in the future, because it is a spacelike separated event. This means that it can jump back to before the first ship left.

PS. Yes I have read your examples, they are inadequate IMO. Just to point out some error, Observer1 at A sees distance from A to B to be 10ly, Observer2, traveling at relativistic speed of 0.7c passing A towards B would tell its a different distance; and to him, it would be. It is how relativity works. You ignored that completely in your calculations.

I explicitly remember showing that effect, and I always accounted for it, because it is built directly into the Lorentz transformations. Please point me to the post where you think I didn't. (Right click on the post title and copy link, or just quote the post, which creates a link)

[kamill85]

Now, with Apparent FTL, where we do not move faster than c through space, logically, do not break causality. If we see a star explosion on the sky, do an instant FTL jump there, we would still arrive X (=ly distance) many years after the event, not a day before, not a day after (ignoring space expansion here). If someone witnessed our visit, while moving at some relativistic speed, and did an FTL jump back with us, would still arrive after we have left to see it, it's that simple.

Your last sentence is simply wrong, and ignores that in the reference frame of the other ship, the event of the first ship leaving can be in the future, because it is a spacelike separated event. This means that it can jump back to before the first ship left.

Again, if ship2 witnessed the event-B, then regardless of its reference frame, event-A must be in its past. Cannot be in the future.

Let's dig deeper. Lets say Oberserver 1 clock ticks 1time for 1min, its current tick count at event-A is 1000, at event-B is 1010. Journey home, clock is at 1025 (after 5 ticks for coffee break).

Observer 2 clock is ticking way slower, relatively to Observer 1, let's just say it's been like that forever. At the event-A, Observer2's clock is at 200, and at 202 when event-B starts. This conjunction of 2 different clocks running at different rates happens when event-B occurs. Now, Observer 2, watches the event, which is 1 tick long to him then takes 2 ticks of his clock to travel the distance of points Y->X. Arrives at point X on tick 205, while to point X Observers, Observer2 arrives at tick 1025. They both arrive at the same time.

[meberbs]

Again, if ship2 witnessed the event-B, then regardless of its reference frame, event-A must be in its past. Cannot be in the future.

Again, this is simply inconsistent with the Lorentz transforms that underlie special relativity. If A and B are spacelike separated events you can always find a reference frame in which they occur in whatever order you choose. FTL travel is by definition travel between spacelike separated events.

Let's dig deeper. Lets say Oberserver 1 clock ticks 1time for 1min, its current tick count at event-A is 1000, at event-B is 1010. Journey home, clock is at 1025 (after 5 ticks for coffee break).

Observer 2 clock is ticking way slower, relatively to Observer 1, let's just say it's been like that forever. At the event-A, Observer2's clock is at 200, and at 202 when event-B starts.

This is wrong. You have already defined the situation to be inconsistent with special relativity. The time of events A and B in frame 2 need to be calculated using the Lorentz transformations, which take into account the distance between the events.

[dustinthewind]

There are I think three possible resolutions to FTL paradoxes:

1. FTL is possible but there is no communication possible with the outside world until the light cone has caught up. So for instance, you jump 1 ly away, but then cannot communicate (in any way, in either direction) with the outside world for a year. Although this at first seems a bit pointless, it would allow light speed travel, which is much better than we can do now.

2. FTL travel moves you into a parallel universe, no paradoxes are possible within that stack of universes. Perhaps you could return to your own universe/origin, but only if no paradoxes have been created in any frame of reference.

3. Paradoxes are not possible because of some unknown physical principle. Although we can create paradoxes with thought experiments, this unknown principle means that those thought experiments cannot be realized.

Probably number 3.  Any instant jump would probably have to be with respect to a rest frame, not a relativistic one.  This kind of jump would be independent from relativity.

Where you run into problems with jumping instantaneously from point to point is energy/momentum conservation.  If FTL is possible then it probably isn't instantaneous jumps from point to point.

[KelvinZero]

2. FTL travel moves you into a parallel universe, no paradoxes are possible within that stack of universes. Perhaps you could return to your own universe/origin, but only if no paradoxes have been created in any frame of reference.

I just wanted to comment on this case. It may be weirder than you think.

Im going to ignore the possibility of slipping back to your previous universe. In that case you just have 3:

3. Paradoxes are not possible because of some unknown physical principle. Although we can create paradoxes with thought experiments, this unknown principle means that those thought experiments cannot be realized.

(ie some other as yet unspecified solution to FTL.)

If you don't have 3 then you just have branching universes as a solution to FTL and time travel in general. You can go back in time and murder your grandfather, no problem. From your POV your history and memory is uninterrupted. From the POV of your destination universe you are just a stranger.

The weirdness is, I think you are now in a scenario where non-travellers do not see people performing FTL, ie beginning a voyage at A and reappearing at B. Like the grandfather killer, anyone that appears is a stranger.

Im not sure if you would have a situation where
(a) there was often a similarity between the person who began the voyage and the person who returns, and only sometimes no similarity at all, as in the grandfather killer who was never born, or

(b) whether you would have branching universes who only ever experienced one successful-ish FTL flight returnee, namely you, and all other FTL flights simply vanish to some other universe, never to return. The travellers might experience a typical star-hopping experience, but every universe they arrived in would see them as absolutely unique, and no universe would bother to have an FTL economy because no one comes back.

[sghill]

Side note: Speaking of FTL experimentation, wave-function collapse problem, quantum effects etc., perhaps there is a way to construct an experiment that encapsulates some time-loop event but we only learn its outcome afterwards? (where causality is not broken/threatened). Some setup that would allow to prove that some particle went back in time, and changed state of something before it was used, but in such way that it would be impossible for us to act upon said change of state? For example (simplified/layman version): Blackbox where dice is dropped, regardless of its result, an event A is executed if the number is odd, event B of it's even. At the same time, before dice touches the ground, event C is executed. Event A is a light sent through A slit inside the Blackbox onto a detector. Event B is null, no light being sent. Event C is light sent through slit B inside the Blackbox onto a detector. Everything is recorded and available only after the experiment took place. Expected result, perhaps after 1000's of tries, would show some slight interference pattern being detected? This of course is just simple double-slit event experiment. Perhaps there are some other events that are suspected to produce particles that could possibly go back in time, and base the Blackbox setup on that. Anyway, general idea is to make a setup where event A or B happens regardless of C and A B C take place before ANY action can be made by observers.

Been done.

https://www.nbcnews.com/science/weird-science/great-scott-reverse-causality-experiment-ends-quantum-muddle-n336766

[aceshigh]

Please play nice. Polite questions and answers are the soul of NSF. If we wanted romper room, we'd take it to Reddit.

Play nice? First post in the forum and the guy comes treating everyone as morons. He didnīt read a single page of this thread. Just comes and say "it's all a big misunderstanding" and the proceeds to say a lot of things already talked and debunked before here. Says we are confused and thinks he cleared things up when we have been talking about those same things the past 12 pages!

Your first post in the forum, thinking you are wiser than everyone else while not even attempting to read past pages: THAT is what is not playing nice.

[KelvinZero]

Suppose we have solved the grandfather paradoxes, (eg by using the rule that the CMB temperature cannot be hotter at your destination, ie the universe cannot be 'younger')

Is it possible for mass to just vanish at one point and appear at another without violating any conservation law?

I just thought of a possible problem: You would have jumped back in time from some frames of reference even if you have avoided grandfather paradoxes. Does this mean that from THAT frame of reference there are two of you existing simultaneously? and there is more mass in the universe, more gravity and so on?

(In the worst case, I think you could solve these conservation issues by your 'stargate' having some sort of mass that you add to when you enter and subtract from when you exit, but it might put a damper on 'warp travel' style FTL.)

[kamill85]

Please play nice. Polite questions and answers are the soul of NSF. If we wanted romper room, we'd take it to Reddit.

Play nice? First post in the forum and the guy comes treating everyone as morons. He didnīt read a single page of this thread. Just comes and say "it's all a big misunderstanding" and the proceeds to say a lot of things already talked and debunked before here. Says we are confused and thinks he cleared things up when we have been talking about those same things the past 12 pages!

Your first post in the forum, thinking you are wiser than everyone else while not even attempting to read past pages: THAT is what is not playing nice.

I did read all pages before posting, and the only viable option to me was that there is some misunderstanding of what WarpTech had in mind and what was being debated.

Nothing what I said was debunked, how can you debunk something related to FTL or A-FTL if we have neither to put on to a test? We can only speculate and there is a disagreement, that's all to it.

[kamill85]

Again, if ship2 witnessed the event-B, then regardless of its reference frame, event-A must be in its past. Cannot be in the future.

Again, this is simply inconsistent with the Lorentz transforms that underlie special relativity. If A and B are spacelike separated events you can always find a reference frame in which they occur in whatever order you choose. FTL travel is by definition travel between spacelike separated events.

Let's dig deeper. Lets say Oberserver 1 clock ticks 1time for 1min, its current tick count at event-A is 1000, at event-B is 1010. Journey home, clock is at 1025 (after 5 ticks for coffee break).

Observer 2 clock is ticking way slower, relatively to Observer 1, let's just say it's been like that forever. At the event-A, Observer2's clock is at 200, and at 202 when event-B starts.

This is wrong. You have already defined the situation to be inconsistent with special relativity. The time of events A and B in frame 2 need to be calculated using the Lorentz transformations, which take into account the distance between the events.

That's a small detail. Given what you've said, if there was no Ship2 (Observer2), but Ship1 had ability to quickly accelerate to 0.7c, and jump back to Point X, he would end up in its past. Why? Because if there was a Ship2 and saw the event while going at 0.7c, and after event took place, just waited a short while, during which Ship1 matched it speed of 0.7c, and then they both jumped back to point X, they would end up at point X at the same time in space, which wouldn't be in the past by the way.

[RotoSequence]

This is a great primer for what the Lorentz Transformations are, and what the Speed of Light actually is.

[meberbs]

Again, if ship2 witnessed the event-B, then regardless of its reference frame, event-A must be in its past. Cannot be in the future.

Again, this is simply inconsistent with the Lorentz transforms that underlie special relativity. If A and B are spacelike separated events you can always find a reference frame in which they occur in whatever order you choose. FTL travel is by definition travel between spacelike separated events.

Let's dig deeper. Lets say Oberserver 1 clock ticks 1time for 1min, its current tick count at event-A is 1000, at event-B is 1010. Journey home, clock is at 1025 (after 5 ticks for coffee break).

Observer 2 clock is ticking way slower, relatively to Observer 1, let's just say it's been like that forever. At the event-A, Observer2's clock is at 200, and at 202 when event-B starts.

This is wrong. You have already defined the situation to be inconsistent with special relativity. The time of events A and B in frame 2 need to be calculated using the Lorentz transformations, which take into account the distance between the events.

That's a small detail.

Consistency with the theory of relativity is not a "small detail"

Given what you've said, if there was no Ship2 (Observer2), but Ship1 had ability to quickly accelerate to 0.7c, and jump back to Point X, he would end up in its past. Why? Because if there was a Ship2 and saw the event while going at 0.7c, and after event took place, just waited a short while, during which Ship1 matched it speed of 0.7c, and then they both jumped back to point X, they would end up at point X at the same time in space,

Yes if Ship 1 had the ability to quickly accelerate to 0.7 c, it could make a jump and end up in its own past. This is an unavoidable consequence of special relativity + FTL (of any sort).

which wouldn't be in the past by the way.

I already did the math that demonstrates that this would very much be in ship 1's past. Do you have any specific disputes with that math?

[kamill85]

Again, if ship2 witnessed the event-B, then regardless of its reference frame, event-A must be in its past. Cannot be in the future.

Again, this is simply inconsistent with the Lorentz transforms that underlie special relativity. If A and B are spacelike separated events you can always find a reference frame in which they occur in whatever order you choose. FTL travel is by definition travel between spacelike separated events.

Let's dig deeper. Lets say Oberserver 1 clock ticks 1time for 1min, its current tick count at event-A is 1000, at event-B is 1010. Journey home, clock is at 1025 (after 5 ticks for coffee break).

Observer 2 clock is ticking way slower, relatively to Observer 1, let's just say it's been like that forever. At the event-A, Observer2's clock is at 200, and at 202 when event-B starts.

This is wrong. You have already defined the situation to be inconsistent with special relativity. The time of events A and B in frame 2 need to be calculated using the Lorentz transformations, which take into account the distance between the events.

That's a small detail.

Consistency with the theory of relativity is not a "small detail"

Given what you've said, if there was no Ship2 (Observer2), but Ship1 had ability to quickly accelerate to 0.7c, and jump back to Point X, he would end up in its past. Why? Because if there was a Ship2 and saw the event while going at 0.7c, and after event took place, just waited a short while, during which Ship1 matched it speed of 0.7c, and then they both jumped back to point X, they would end up at point X at the same time in space,

Yes if Ship 1 had the ability to quickly accelerate to 0.7 c, it could make a jump and end up in its own past. This is an unavoidable consequence of special relativity + FTL (of any sort).

which wouldn't be in the past by the way.

I already did the math that demonstrates that this would very much be in ship 1's past. Do you have any specific disputes with that math?

I'll bite. Please provide math that supports this short story:

1. Ship uses A-FTL to (instantly) jump 100 light years away from point X, to point Y
2. At point Y, accelerates to 0.7c (instantly)
3. Ship uses A-FTL to jump (instantly) back from point Y to point X, ends up in its own past.