Author Topic: Any resolutions to FTL paradoxes?  (Read 28365 times)

Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #20 on: 07/19/2017 09:51 PM »
In my Warp Drive paper, the warp field effectively negates the effects of SR by changing the length of the ship and the clocks it contains, so that they match the original rest frame where it started from, at all times. In other words, there is no length contraction or time dilation of the accelerated starship. Therefore, the motion of the ship is not relativistic, it's Newtonian. Lorentz transformations do not apply.

Again, how can changing the rate of my clock, moving faster or slower, suddenly give me the ability to travel backwards in time, or send a message backwards in time? It doesn't, it can't. The paradox is only there because SR is not applicable, yet everyone insists it is.
None of what you said changes the scenario I described. When 2 people have a copy of your magic FTL device, what happens when they act out the scenario above?

Remember, GR allows CTCs, just all of the solutions can't be implemented for reasons like needing exotic matter with negative mass. You have not shown that you don't generate CTCs.

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #21 on: 07/20/2017 04:58 AM »
In my Warp Drive paper, the warp field effectively negates the effects of SR by changing the length of the ship and the clocks it contains, so that they match the original rest frame where it started from, at all times. In other words, there is no length contraction or time dilation of the accelerated starship. Therefore, the motion of the ship is not relativistic, it's Newtonian. Lorentz transformations do not apply.

Again, how can changing the rate of my clock, moving faster or slower, suddenly give me the ability to travel backwards in time, or send a message backwards in time? It doesn't, it can't. The paradox is only there because SR is not applicable, yet everyone insists it is.
None of what you said changes the scenario I described. When 2 people have a copy of your magic FTL device, what happens when they act out the scenario above?

Remember, GR allows CTCs, just all of the solutions can't be implemented for reasons like needing exotic matter with negative mass. You have not shown that you don't generate CTCs.

The scenario you put forth has an assumption built into it. That is, in the frame of ship 2 the distance to Earth is shorter AND this makes a difference when the FTL drive is switched on. In my model, when the FTL is switched on, regardless of how fast ship 2 was going relative to the Earth prior to that. After the switch, the length of the ship and the clocks on board are "tuned" to be the same as that on Earth, at all times, regardless of the FTL speed. So the distance to Earth is not what it was before the FTL was turned on. In the case of ship 2, that distance gets longer in the FTL frame. Lorentz transformations go out the window. In other words, there is no FTL frame where the distance to Earth is shorter.

The gamma factor becomes dependent on the refractive index, K.

1/gamma = sqrt((1/K) - K*(v/c)^2) = 1  Where, K is a function of (v) that solves this equation. A ship surrounded by a field where K << 1, can travel at speeds v >> c, and still have dtau/dt = 1. But it still doesn't go backwards in time.

On another note:

Another way to avoid the paradox would be a BSG Jump drive. Regardless of how fast the ship is moving, it can instantaneously jump to another point in space and arrive "at rest" at those coordinates. There would be no way to send the ship back in time, because it didn't take any time to get there.




Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #22 on: 07/20/2017 05:18 AM »
The scenario you put forth has an assumption built into it. That is, in the frame of ship 2 the distance to Earth is shorter AND this makes a difference when the FTL drive is switched on. In my model, when the FTL is switched on, regardless of how fast ship 2 was going relative to the Earth prior to that. After the switch, the length of the ship and the clocks on board are "tuned" to be the same as that on Earth, at all times, regardless of the FTL speed. So the distance to Earth is not what it was before the FTL was turned on. In the case of ship 2, that distance gets longer in the FTL frame. Lorentz transformations go out the window. In other words, there is no FTL frame where the distance to Earth is shorter.
The Earth is 11 light years away in the Earth frame, and around 8 light years away in the ship frame when the ship 2 FTL is switched on. It is utterly nonsensical to say that the ship's reference frame instantly changes to have the same inertial motion as Earth when it turns on. There is nothing special about the Earth frame.

All you have done is created a preferred frame for the entire universe which conveniently is the Earth frame. This has no experimental basis in reality, and instead contradicts everything known about relativity and astrodynamics.

Another way to avoid the paradox would be a BSG Jump drive. Regardless of how fast the ship is moving, it can instantaneously jump to another point in space and arrive "at rest" at those coordinates. There would be no way to send the ship back in time, because it didn't take any time to get there.
You apparently have never read the first page of any description of relativity. The very first point is that there is no such things as an arbitrary "at rest." No reference frame is special. For an instantaneous jump drive, the ship would just have to accelerate back in the direction it came sufficiently quickly, before reengaging the drive. It accelerating into a different frame would mean that it is now in a frame where the time it departed from is in the future. If all they want is to send a message back in time, it is even easier, just have someone already moving fast at the destination.

Offline Nomadd

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Re: Any resolutions to FTL paradoxes?
« Reply #23 on: 07/20/2017 05:23 AM »
Im sure I have been on threads discussing this before, I was probably on that one too.. And I think one result was that you can produce a paradox with just a single FTL 'jump'.. If that is true then choosing a single reference frame does not resolve the issue. Maybe someone can confirm that.

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

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

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

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

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

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

Todd
That thing reads like the Entabulator video.

Offline aceshigh

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Re: Any resolutions to FTL paradoxes?
« Reply #24 on: 07/20/2017 01:17 PM »
Warptech, lightspeed should be called Causality Speed. That would clear many problems of understanding it.

Watch these two videos which explain with spacetime diagrams why FTL is time travel.








Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #25 on: 07/20/2017 06:07 PM »
The scenario you put forth has an assumption built into it. That is, in the frame of ship 2 the distance to Earth is shorter AND this makes a difference when the FTL drive is switched on. In my model, when the FTL is switched on, regardless of how fast ship 2 was going relative to the Earth prior to that. After the switch, the length of the ship and the clocks on board are "tuned" to be the same as that on Earth, at all times, regardless of the FTL speed. So the distance to Earth is not what it was before the FTL was turned on. In the case of ship 2, that distance gets longer in the FTL frame. Lorentz transformations go out the window. In other words, there is no FTL frame where the distance to Earth is shorter.
The Earth is 11 light years away in the Earth frame, and around 8 light years away in the ship frame when the ship 2 FTL is switched on. It is utterly nonsensical to say that the ship's reference frame instantly changes to have the same inertial motion as Earth when it turns on. There is nothing special about the Earth frame.

All you have done is created a preferred frame for the entire universe which conveniently is the Earth frame. This has no experimental basis in reality, and instead contradicts everything known about relativity and astrodynamics.

Another way to avoid the paradox would be a BSG Jump drive. Regardless of how fast the ship is moving, it can instantaneously jump to another point in space and arrive "at rest" at those coordinates. There would be no way to send the ship back in time, because it didn't take any time to get there.
You apparently have never read the first page of any description of relativity. The very first point is that there is no such things as an arbitrary "at rest." No reference frame is special. For an instantaneous jump drive, the ship would just have to accelerate back in the direction it came sufficiently quickly, before reengaging the drive. It accelerating into a different frame would mean that it is now in a frame where the time it departed from is in the future. If all they want is to send a message back in time, it is even easier, just have someone already moving fast at the destination.

You have many preconceived notions and assumptions! Keep an open mind.

The Alcubierre warp drive had the feature that dtau=dt, the proper time aboard the ship matched the same time as the folks back home. That is the "Goal"! It is what my drive was designed to do. Earth is only preferred, because that is where we come from. It could just as easily be tuned to a different home-clock, but what clock you choose is irrelevant. Time is relative to where you call "home".

I never said "at rest" in a preferred frame. What I meant was "at rest with respect to the target coordinates", regardless of what speed the ship was moving relative to those coordinates when the BSG Jump Drive was activated.

Now, if you talk to Marc Millis or some other advocates, then the CMB represents a preferred "rest frame" of the Universe. How do you feel about that? I don't agree with it, but it is what it is. We can detect doppler shift and therefore, motion relative to the CMB.






Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #26 on: 07/20/2017 06:24 PM »
As you say the only frame that matters is the frame that the person with the FTL drive is in. Instead of randomly switching from the ship 2 frame to the Earth frame, let ship 2 stay in the ship2 frame and see what happens.

"at rest with respect to the target coordinates" is nonsensical. The "target coordinates" would be an event in space-time. An event does not have a velocity, and can be described in any arbitrary frame with any velocity.

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #27 on: 07/20/2017 07:21 PM »
As you say the only frame that matters is the frame that the person with the FTL drive is in. Instead of randomly switching from the ship 2 frame to the Earth frame, let ship 2 stay in the ship2 frame and see what happens.

"at rest with respect to the target coordinates" is nonsensical. The "target coordinates" would be an event in space-time. An event does not have a velocity, and can be described in any arbitrary frame with any velocity.

You are far too nit-picky! You just like to argue and be right.

If I'm the pilot of ship 2 and I want to be home on time for dinner, I had better have my clock synchronized with my wife's and when I engage my BSG Jump Drive, I want to arrive home, with my ship parked in the garage. Hence, "at rest with respect to the target coordinates" is far from "nonsensical"!


Online Phil Stooke

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Re: Any resolutions to FTL paradoxes?
« Reply #28 on: 07/20/2017 07:28 PM »
But how do you synchronize the clocks?  Personally I think this discussion shows the paradoxes cannot be resolved.

Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #29 on: 07/20/2017 09:13 PM »
As you say the only frame that matters is the frame that the person with the FTL drive is in. Instead of randomly switching from the ship 2 frame to the Earth frame, let ship 2 stay in the ship2 frame and see what happens.

"at rest with respect to the target coordinates" is nonsensical. The "target coordinates" would be an event in space-time. An event does not have a velocity, and can be described in any arbitrary frame with any velocity.

You are far too nit-picky! You just like to argue and be right.

If I'm the pilot of ship 2 and I want to be home on time for dinner, I had better have my clock synchronized with my wife's and when I engage my BSG Jump Drive, I want to arrive home, with my ship parked in the garage. Hence, "at rest with respect to the target coordinates" is far from "nonsensical"!
Are you even reading what you are writing?  As Phil Stooke asked, what do you even mean by "synchronized clocks? And don't try to say "its obvious" because it is one of the most basic results of relativity that clocks cannot be synchronized in general. The target coordinates still don't have a velocity.

And why not just leave your clock as is so that you can make it for lunch years ago instead of dinner today? Choosing not to act out a paradox causing situation doesn't change the fact that your device can cause paradoxes.

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #30 on: 07/20/2017 09:20 PM »
But how do you synchronize the clocks?  Personally I think this discussion shows the paradoxes cannot be resolved.

"I'm from Earth, I only work in space." ;) It was synchronized before I left the house. Since neither my warp drive nor my jump drive cause time dilation, our clocks remain synchronized until I get home for dinner.

Physicists have been trying to resolve the issue of CTL paradoxes for decades. It's probably not going to be resolved on a usenet group. IMO, Lorentz transformations are the cause of the problem, because when using them, moving reference frames are arbitrary and indistinguishable. These are Math assumptions. Reality, where accelerations are used to change speed, works differently. IMO, changing the rate of my clock does not allow me to send messages backwards in time.


Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #31 on: 07/20/2017 09:45 PM »
But how do you synchronize the clocks?  Personally I think this discussion shows the paradoxes cannot be resolved.

"I'm from Earth, I only work in space." ;) It was synchronized before I left the house. Since neither my warp drive nor my jump drive cause time dilation, our clocks remain synchronized until I get home for dinner.
Not even relevant. Go read the original scenario I described again. Making up some different scenario doesn't change mine.

IMO, Lorentz transformations are the cause of the problem, because when using them, moving reference frames are arbitrary and indistinguishable. These are Math assumptions.
They are not math assumptions, they are very fundamental and experimentally confirmed principles.

Reality, where accelerations are used to change speed, works differently. IMO, changing the rate of my clock does not allow me to send messages backwards in time.
It isn't the changing clock speeds that cause time travel, it is the FTL device. Accelerations to some extent can be handled in special relativity, at least for simple cases including resolving the "twin paradox" which really is just recognizing there are 3 inertial reference frames involved, not 2.

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #32 on: 07/20/2017 10:33 PM »

Reality, where accelerations are used to change speed, works differently. IMO, changing the rate of my clock does not allow me to send messages backwards in time.
It isn't the changing clock speeds that cause time travel, it is the FTL device. Accelerations to some extent can be handled in special relativity, at least for simple cases including resolving the "twin paradox" which really is just recognizing there are 3 inertial reference frames involved, not 2.

You keep missing the point. My FTL device works by changing the rate of "my clock" and changing the length of "my ship". This what the warp field generated around my ship does. It compensates for time dilation and length contraction and thereby allows it to travel FTL without any affects of length contraction or time dilation typical of SR. Again, altering the space around my ship does not allow me to send the ship or any signals backwards in time. Your imaginary FTL device may allow it, but the one I wrote about in my paper does not. It's not relativistic, it's Newtonian. dtau=dt on this ship, my proper time matches that of my wife at home, all day, regardless of my speed. That's how FTL is done "right". :)



« Last Edit: 07/20/2017 10:33 PM by WarpTech »

Offline ppnl

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Re: Any resolutions to FTL paradoxes?
« Reply #33 on: 07/21/2017 12:09 AM »

The Alcubierre warp drive had the feature that dtau=dt, the proper time aboard the ship matched the same time as the folks back home. That is the "Goal"! It is what my drive was designed to do. Earth is only preferred, because that is where we come from. It could just as easily be tuned to a different home-clock, but what clock you choose is irrelevant. Time is relative to where you call "home".



But what if you change what your ship is tuned to? Wouldn't that enable time travel?

Ok, let's say you are out tooling around in your shiny new ship and you meet some aliens in deep space. Let's say you agree to warp to earth and meet up there. Problem, their ship is tuned to their home system which has a very high relative velocity with respect to earth. That causes them to arrive at earth years before you were even born. They accidentally land on your grandfather thus insuring that you were never born to invent your warp drive. 

Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #34 on: 07/21/2017 12:20 AM »

Reality, where accelerations are used to change speed, works differently. IMO, changing the rate of my clock does not allow me to send messages backwards in time.
It isn't the changing clock speeds that cause time travel, it is the FTL device. Accelerations to some extent can be handled in special relativity, at least for simple cases including resolving the "twin paradox" which really is just recognizing there are 3 inertial reference frames involved, not 2.

You keep missing the point. My FTL device works by changing the rate of "my clock" and changing the length of "my ship". This what the warp field generated around my ship does. It compensates for time dilation and length contraction and thereby allows it to travel FTL without any affects of length contraction or time dilation typical of SR. Again, altering the space around my ship does not allow me to send the ship or any signals backwards in time. Your imaginary FTL device may allow it, but the one I wrote about in my paper does not. It's not relativistic, it's Newtonian. dtau=dt on this ship, my proper time matches that of my wife at home, all day, regardless of my speed. That's how FTL is done "right". :)
You STILL have not addressed what would happen with your device when used in the scenario I had described.

Note: the below example re-defines light-year to be distance light travels in 50 weeks (and 1 year = 50 weeks) to make the math easier.

Let me break it down with numbers. Define that Ship 1 is at rest in the Earth frame at t= 0, x = 0. At this time ship 1 activates its FTL drive, allowing it to arrive at a location in the earth frame of x = 10 light years, at time t = 5 weeks, (apparent speed of roughly 100 c). It will take 10 years before a signal from the ship upon arrival would reach Earth, but this doesn't change the time coordinate I listed in the Earth Frame for the ship's arrival. I do not know or care how much apparent time or distance was experienced by the people on ship 1, only the space-time coordinates of where ship 1 entered and exited FTL.

Now lets take another spaceship travelling away from Earth at 0.7 c. (I think I got towards/away mixed up earlier) as is traditional for simplicity, define t'=0 and x'=0 to be the coordinates in the ship2 frame of ship 1 when it had entered FTL. (Making the origins overlap is just simpler.) Now we calculate the coordinates when ship 1 exits FTL in this frame. These are x' = 13.9 light years, and t' = -483 weeks (-9.66 years).

At this point it should be obvious where the problem is going to be, but lets continue. First we should remember that as far as ship 2 cares, ship 2 is stationary, and both Earth and ship 1 are travelling away from it at 0.7c.

Ship 2 happens to be at the same place as ship 1 when ship 1 exits FTL. Ship 1 send a message to ship2. Ship 2 Then activates its FTL in the direction of Earth. Since Earth is travelling towards the origin of the ship2 frame with speed, 0.7c and will reach the origin when t'=0, the current location of Earth in the ship2 frame is x' = 6.76 light years at t' = -483 weeks, This makes Earth 7.14 light years away from ship 2. Ship 2 can cover this distance in 3.57 weeks using the same type of FTL drive that ship1 has. Lets say it is a bit slower (and account for the Earth moving away from it, and say 4 weeks.) Ship 2 exits FTL in its frame at t'=-479, and x' =6.706 (Earth has moved). In The Earth frame this corresponds to x=0 (it is at Earth) and t= -244 weeks.

Ship 2 can now send the message to that ship 1 sent to Earth nearly 5 years before ship 1 departs Earth to begin with.

You cannot just wish this problem away, and nothing you have said addresses it. Ship 2 has no reason to have "synchronized"  anything with Earth, and is just relaying a message before it continues to move away from Earth/allow Earth to move away from it at 0.7 c. Neither the Earth frame nor the ship2 frame is any more valid, so the behavior of any FTL drive must be the same in both. Also note that there is no reference to what the people on either ship experience because it doesn't matter. (When talking about the ship2 frame, I am referring to a pure inertial frame of some observer initially commoving with ship2.)

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #35 on: 07/21/2017 02:25 AM »
...
You cannot just wish this problem away, and nothing you have said addresses it. Ship 2 has no reason to have "synchronized"  anything with Earth, and is just relaying a message before it continues to move away from Earth/allow Earth to move away from it at 0.7 c. Neither the Earth frame nor the ship2 frame is any more valid, so the behavior of any FTL drive must be the same in both. Also note that there is no reference to what the people on either ship experience because it doesn't matter. (When talking about the ship2 frame, I am referring to a pure inertial frame of some observer initially commoving with ship2.)

In the unprimed frame, ship 1 enters FTL at Earth, t=0, x=0, and exits FTL at t=5 weeks and x = 10 light years distance. With my proposed warp drive, the clock on ship 1 always runs at the same rate as the clock on Earth. When the ship exits FTL, Earth AND ship 1 have advanced 5 weeks into the future.

Ship 2 is moving at 0.7c and is at the same location in space-time, where ship 1 exits FTL. This is where the two ships are at the same place "at the same time", so this is where the two coordinate systems (primed and unprimed) are coincident at t=t'=0. Earth has already advanced 5 weeks into the future. So at this point, no matter how fast ship 2 goes, it can never get to Earth before ship 1 left.

edit more..
Ship 1 sends a message to ship 2 saying "we arrived". At this point, ship 2 enters FTL from their frame. In that frame, the trip only takes say t = ~3 weeks and when they exit FTL, they are at Earth and still moving at 0.7c relative to Earth. Ship 2 sends the message "we arrived", and Earth receives it, ~8 weeks after ship 1 left on the Earth calendar.





« Last Edit: 07/21/2017 03:12 AM by WarpTech »

Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #36 on: 07/21/2017 06:25 AM »

Ship 2 is moving at 0.7c and is at the same location in space-time, where ship 1 exits FTL. This is where the two ships are at the same place "at the same time", so this is where the two coordinate systems (primed and unprimed) are coincident at t=t'=0. Earth has already advanced 5 weeks into the future. So at this point, no matter how fast ship 2 goes, it can never get to Earth before ship 1 left.

It is not t=0 in either frame when ship 1 exits FTL. You just effectively introduced 2 new frames without fully defining them, since you also have to redefine where x=0, and then you would find in the new primed frame, ship 1 left more than 9 years in the future from when it arrived. Stick to just the 2 frames, the new ones just differ from the ones I used by straight constants, and if you actually did everything consistently, the net result wouldn't change. According to Ship 2 when ship 1 exits FTL, it is still years before ship 1 had entered FTL, no matter where you choose the origin of this frame.
« Last Edit: 07/21/2017 06:46 AM by meberbs »

Online WarpTech

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Re: Any resolutions to FTL paradoxes?
« Reply #37 on: 07/21/2017 03:51 PM »

Ship 2 is moving at 0.7c and is at the same location in space-time, where ship 1 exits FTL. This is where the two ships are at the same place "at the same time", so this is where the two coordinate systems (primed and unprimed) are coincident at t=t'=0. Earth has already advanced 5 weeks into the future. So at this point, no matter how fast ship 2 goes, it can never get to Earth before ship 1 left.

It is not t=0 in either frame when ship 1 exits FTL. You just effectively introduced 2 new frames without fully defining them, since you also have to redefine where x=0, and then you would find in the new primed frame, ship 1 left more than 9 years in the future from when it arrived. Stick to just the 2 frames, the new ones just differ from the ones I used by straight constants, and if you actually did everything consistently, the net result wouldn't change. According to Ship 2 when ship 1 exits FTL, it is still years before ship 1 had entered FTL, no matter where you choose the origin of this frame.

Correction: Ship 1 entered FTL at t=-5 weeks, and exited FTL at t=0. This EVENT is coincident in both frames. Ship 1 and ship 2 are at the same place, at the same time, t=t'=0. With my FTL warp drive, the clock on ship 1 is the same as the clock on Earth. What you said;

Quote
According to Ship 2 when ship 1 exits FTL, it is still years before ship 1 had entered FTL, no matter where you choose the origin of this frame.

is logically and physically impossible. If this is what the Lorentz transformation is telling you, you're doing something wrong.

Online meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #38 on: 07/21/2017 04:20 PM »

Ship 2 is moving at 0.7c and is at the same location in space-time, where ship 1 exits FTL. This is where the two ships are at the same place "at the same time", so this is where the two coordinate systems (primed and unprimed) are coincident at t=t'=0. Earth has already advanced 5 weeks into the future. So at this point, no matter how fast ship 2 goes, it can never get to Earth before ship 1 left.

It is not t=0 in either frame when ship 1 exits FTL. You just effectively introduced 2 new frames without fully defining them, since you also have to redefine where x=0, and then you would find in the new primed frame, ship 1 left more than 9 years in the future from when it arrived. Stick to just the 2 frames, the new ones just differ from the ones I used by straight constants, and if you actually did everything consistently, the net result wouldn't change. According to Ship 2 when ship 1 exits FTL, it is still years before ship 1 had entered FTL, no matter where you choose the origin of this frame.

Correction: Ship 1 entered FTL at t=-5 weeks, and exited FTL at t=0. This EVENT is coincident in both frames. Ship 1 and ship 2 are at the same place, at the same time, t=t'=0. With my FTL warp drive, the clock on ship 1 is the same as the clock on Earth. What you said;

Quote
According to Ship 2 when ship 1 exits FTL, it is still years before ship 1 had entered FTL, no matter where you choose the origin of this frame.

is logically and physically impossible. If this is what the Lorentz transformation is telling you, you're doing something wrong.
The only thing logically impossible is FTL. You seem to claim that the difference between the time ship 1 enters FTL and the time ship1 exits FTL is the same in both frames even though time is flowing differently in both frames (earth frame and ship 2 initial frame). That is illogical.

To get from my unprimed frame to yours, just subtract 5 weeks from t and 10 light years from x. To get from my primed frame to yours, add 483 weeks to t' and subtract 13.902 lightyears from x'. As they should, the effect of the results does not depend on the choice of origin.

Since you insist, lets use your 2 coordinate systems. The coordinates of the event "ship 1 enters FTL" in the unprimed frame at x = -500 light-weeks (10 light-years), t = -5 weeks

(c = 1 light-week per week)
t' = 1.4*(-5 - 0.7c*-500/c^2) = 1.4*(-5+0.7*500) = 483
x' = 1.4*(-500-0.7*-5) = -695.1 light-weeks = -13.902 light-years

Unsurprisingly, this result is exactly equivalent to what I calculated before.
The switching of past and future is expected, because FTL entrances and exits occur in a space-like interval, not a time-like one. This causes no logical problems as long as you don't have FTL travel.
« Last Edit: 07/21/2017 04:21 PM by meberbs »

Offline JasonAW3

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Re: Any resolutions to FTL paradoxes?
« Reply #39 on: 07/21/2017 04:43 PM »

The only thing logically impossible is FTL.


Never say something is impossible because sooner or later, someone or something comes along and proves you wrong.
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