Any resolutions to FTL paradoxes?

[meberbs]

  Okay then, back to the Twin Paradox. The twin on Earth calculates his brother traveling at 0.6c will age 8 years, the traveling twin calculates that his brother at home will age 6.4 years. One is right, the other is wrong. It's not symmetrical, their calculations are not even the same. The one who gets it wrong sees an illusion, because when he gets home he finds that his brother aged 10 years, not 6.4 years. "His" clock rate was slow, his brother's on Earth was not. Again, the rates are not physically symmetrical, so what he measures based on his slow clock is wrong.

An observer in the earth frame sees the traveler's clock as slow both outbound and inbound.
An observer in the outbound frame sees the Earth clock as slow the whole time, the outbound traveler's clock as normal speed, but slowing down greatly after turning around, to the net effect of being slower on average.
An observer in the inbound frame sees the Earth clock as slow, the outbound clock as really slow, and the inbound clock as normal.

Everyone agrees that the travelling twin experienced less time passing, and no one gets it wrong. The only "asymmetry" is that one twin accelerated half way through and the other didn't. The effects the travelling twin experienced as they accelerated to turn around include a lot of everyone else's clocks changing speed, or even "rewinding" to match his new frame. The lesson is to stick to inertial frames when doing the calculations. Some of your mistakes that are leading you to claim "no paradox" in time travel causing situations seem to be related to you not understanding this lesson.

Now can you get to the rest of my post where I pointed out some of the ways you directly are contradicting yourself?

[WarpTech]

  Okay then, back to the Twin Paradox. The twin on Earth calculates his brother traveling at 0.6c will age 8 years, the traveling twin calculates that his brother at home will age 6.4 years. One is right, the other is wrong. It's not symmetrical, their calculations are not even the same. The one who gets it wrong sees an illusion, because when he gets home he finds that his brother aged 10 years, not 6.4 years. "His" clock rate was slow, his brother's on Earth was not. Again, the rates are not physically symmetrical, so what he measures based on his slow clock is wrong.

An observer in the earth frame sees the traveler's clock as slow both outbound and inbound.
An observer in the outbound frame sees the Earth clock as slow the whole time, the outbound traveler's clock as normal speed, but slowing down greatly after turning around, to the net effect of being slower on average.
An observer in the inbound frame sees the Earth clock as slow, the outbound clock as really slow, and the inbound clock as normal.

Everyone agrees that the travelling twin experienced less time passing, and no one gets it wrong. The only "asymmetry" is that one twin accelerated half way through and the other didn't. The effects the travelling twin experienced as they accelerated to turn around include a lot of everyone else's clocks changing speed, or even "rewinding" to match his new frame. The lesson is to stick to inertial frames when doing the calculations. Some of your mistakes that are leading you to claim "no paradox" in time travel causing situations seem to be related to you not understanding this lesson.

Now can you get to the rest of my post where I pointed out some of the ways you directly are contradicting yourself?

I'm not trying to sound arrogant or be argumentative, but from my perspective you are the one who is making unrealistic assumptions and contradicting yourself. So let's please try to avoid statements like that. I'll get to the rest of your email, once we agree on what the Twin Paradox actually teaches us. You keep missing the point and I'm just going to have to get better at explaining it, until you get it. This is actually something that should be in my paper, so I appreciate this discussion immensely. Coming to a consensus here will prevent errors there.

In your above statements, you are perfectly fine with the asymmetry where, the twin who travels has to accelerate to turn around and head back toward earth. But you ignore the acceleration that started the trip in the first place, as did the video that Dustin posted.

What I am trying to convey is, when the Twin (ship 2) left Earth, it accelerated to 0.6c using a Non-FTL drive. This acceleration phase resolves the paradox as follows;

1. During this first acceleration phase, Earth "seems" to lose 1.8 years as ship 2 accelerates to 0.6c away from Earth. But the Earth didn't go back in time, "his" space axis rotated CCW because he's moving away from it.

2. When the twin slows down to begin his turn back toward Earth his space axis rotates CW, momentarily re-aligns with the Earth frame, and the 1.8 years that was lost is restored. His axis at year 4 on his clock is simultaneously re-aligned with year 5 on the Earth clock. An FTL jump (instantaneous for him) will take him back to Earth at year 5, not year 3.2.

[edit: Regardless of what type of drive it is, sub-light or FTL, in order to go back to Earth, his space axis must swing back CW, through this re-alingment, until the twin/ship 2 is moving toward Earth at whatever speed and never goes backward in time.]

3. He continues to accelerates back toward Earth and Earth quickly ages another 1.8 years until reaching -0.6c.

4. He then decelerates when he arrives back home and his axis re-aligns with the Earth's frame, where his clock is at year 8 and the Earth clock is at year 10.

The FTL paradox such that ship 2 could go backwards along its space axis to Earth at year 3.2 rather than year 5, is like saying when the Twin returns to Earth, his brother only aged 6.4 years and not 10 years. It's the wrong answer.

By ignoring the first acceleration phase and assuming that the two frames are interchangeable, it leads to a paradox. By including all 3 acceleration phases, the paradox is resolved.

A distant galaxy moving away from us at 0.6c since the big bang is different. I would assume that the Milky way and that distant galaxy were both created and accelerated equally at the same time, by the same force (i.e, the Big Bang). Whereas, ship 2 and the Earth were not both accelerated at the same time by the same force. Only the ship was accelerated. That's the asymmetry. IMO, there is no way to have a symmetrical situation within our galaxy. There is ALWAYS an initial acceleration phase and ignoring it will fool you into seeing a paradox where there is none.

[dustinthewind]

  Okay then, back to the Twin Paradox. The twin on Earth calculates his brother traveling at 0.6c will age 8 years, the traveling twin calculates that his brother at home will age 6.4 years. One is right, the other is wrong. It's not symmetrical, their calculations are not even the same. The one who gets it wrong sees an illusion, because when he gets home he finds that his brother aged 10 years, not 6.4 years. "His" clock rate was slow, his brother's on Earth was not. Again, the rates are not physically symmetrical, so what he measures based on his slow clock is wrong.

An observer in the earth frame sees the traveler's clock as slow both outbound and inbound.
An observer in the outbound frame sees the Earth clock as slow the whole time, the outbound traveler's clock as normal speed, but slowing down greatly after turning around, to the net effect of being slower on average.
An observer in the inbound frame sees the Earth clock as slow, the outbound clock as really slow, and the inbound clock as normal.

Everyone agrees that the travelling twin experienced less time passing, and no one gets it wrong. The only "asymmetry" is that one twin accelerated half way through and the other didn't. The effects the travelling twin experienced as they accelerated to turn around include a lot of everyone else's clocks changing speed, or even "rewinding" to match his new frame. The lesson is to stick to inertial frames when doing the calculations. Some of your mistakes that are leading you to claim "no paradox" in time travel causing situations seem to be related to you not understanding this lesson.

Now can you get to the rest of my post where I pointed out some of the ways you directly are contradicting yourself?

I'm not trying to sound arrogant or be argumentative, but from my perspective you are the one who is making unrealistic assumptions and contradicting yourself. So let's please try to avoid statements like that. I'll get to the rest of your email, once we agree on what the Twin Paradox actually teaches us. You keep missing the point and I'm just going to have to get better at explaining it, until you get it. This is actually something that should be in my paper, so I appreciate this discussion immensely. Coming to a consensus here will prevent errors there.

In your above statements, you are perfectly fine with the asymmetry where, the twin who travels has to accelerate to turn around and head back toward earth. But you ignore the acceleration that started the trip in the first place, as did the video that Dustin posted.

What I am trying to convey is, when the Twin (ship 2) left Earth, it accelerated to 0.6c using a Non-FTL drive. This acceleration phase resolves the paradox as follows;

1. During this first acceleration phase, Earth "seems" to lose 1.8 years as ship 2 accelerates to 0.6c away from Earth. But the Earth didn't go back in time, "his" space axis rotated CCW because he's moving away from it.

2. When the twin slows down to begin his turn back toward Earth his space axis rotates CW, momentarily re-aligns with the Earth frame, and the 1.8 years that was lost is restored. His axis at year 4 on his clock is simultaneously re-aligned with year 5 on the Earth clock. An FTL jump (instantaneous for him) will take him back to Earth at year 5, not year 3.2.

[edit: Regardless of what type of drive it is, sub-light or FTL, in order to go back to Earth, his space axis must swing back CW, through this re-alingment, until the twin/ship 2 is moving toward Earth at whatever speed and never goes backward in time.]

3. He continues to accelerates back toward Earth and Earth quickly ages another 1.8 years until reaching -0.6c.

4. He then decelerates when he arrives back home and his axis re-aligns with the Earth's frame, where his clock is at year 8 and the Earth clock is at year 10.

The FTL paradox such that ship 2 could go backwards along its space axis to Earth at year 3.2 rather than year 5, is like saying when the Twin returns to Earth, his brother only aged 6.4 years and not 10 years. It's the wrong answer.

By ignoring the first acceleration phase and assuming that the two frames are interchangeable, it leads to a paradox. By including all 3 acceleration phases, the paradox is resolved.

A distant galaxy moving away from us at 0.6c since the big bang is different. I would assume that the Milky way and that distant galaxy were both created and accelerated equally at the same time, by the same force (i.e, the Big Bang). Whereas, ship 2 and the Earth were not both accelerated at the same time by the same force. Only the ship was accelerated. That's the asymmetry. IMO, there is no way to have a symmetrical situation within our galaxy. There is ALWAYS an initial acceleration phase and ignoring it will fool you into seeing a paradox where there is none.

Your right they do start off with the ship at full speed at 1:57.  That or its an instantaneous or violent acceleration seemingly instantly tilting the space axis so the ship is distorted in time.  From the ship perspective space is distorted in time (future in front).  (This FTL - I'm reminded of the Portal game and droping through 2 portals while being accelerated by gravity = impossible).  With the space axis always tilted up in the direction the ship travels, without FTL and its odd seeming momentum violation, the ship's only alternative it to travel into the future.  Behind the ship is the past.  Technically if the ships FTL distance is not limited it could jump as far into the past as it wants which is absurd.  If distance is an obstacle for the FTL all the ship has to do is approach the c limit and eventually all the past is still reachable by jumping backwards. 

Here is a paradox.  A ship is falling into a black hole.  Just before hitting the event horizon they jump into the past but preserving their velocity.  They fall again and keep jumping back till they themselves become a black hole.    

Regardless - if FTL exists it probably doesn't exist in the sense of instant teleportation, which causes energy violations even in a classical sense. 

As for the FTL signal, is that the same sense as a portal?  Are we talking a photon that gets teleported across a distance?  If so the same energy violation could be an issue.  A satellite could FTL/portal an incoming signal away.  The signal undergoes gravitational acceleration and gets sent out again to repeat its acceleration. 

vast distances a problem?  Put it in an extreme vacuum chamber and only do lots of short portal jumps. 

[WarpTech]

I'm not trying to sound arrogant or be argumentative, but from my perspective you are the one who is making unrealistic assumptions and contradicting yourself. So let's please try to avoid statements like that. I'll get to the rest of your email, once we agree on what the Twin Paradox actually teaches us. You keep missing the point and I'm just going to have to get better at explaining it, until you get it. This is actually something that should be in my paper, so I appreciate this discussion immensely. Coming to a consensus here will prevent errors there.

In your above statements, you are perfectly fine with the asymmetry where, the twin who travels has to accelerate to turn around and head back toward earth. But you ignore the acceleration that started the trip in the first place, as did the video that Dustin posted.

What I am trying to convey is, when the Twin (ship 2) left Earth, it accelerated to 0.6c using a Non-FTL drive. This acceleration phase resolves the paradox as follows;
...

Your right they do start off with the ship at full speed at 1:57.  That or its an instantaneous or violent acceleration seemingly instantly tilting the space axis so the ship is distorted in time.  From the ship perspective space is distorted in time (future in front).  (This FTL - I'm reminded of the Portal game and droping through 2 portals while being accelerated by gravity = impossible).  With the space axis always tilted up in the direction the ship travels, without FTL and its odd seeming momentum violation, the ship's only alternative it to travel into the future.  Behind the ship is the past.  Technically if the ships FTL distance is not limited it could jump as far into the past as it wants which is absurd.  If distance is an obstacle for the FTL all the ship has to do is approach the c limit and eventually all the past is still reachable by jumping backwards. 

Here is a paradox.  A ship is falling into a black hole.  Just before hitting the event horizon they jump into the past but preserving their velocity.  They fall again and keep jumping back till they themselves become a black hole.    

Regardless - if FTL exists it probably doesn't exist in the sense of instant teleportation, which causes energy violations even in a classical sense. 

As for the FTL signal, is that the same sense as a portal?  Are we talking a photon that gets teleported across a distance?  If so the same energy violation could be an issue.  A satellite could FTL/portal an incoming signal away.  The signal undergoes gravitational acceleration and gets sent out again to repeat its acceleration. 

vast distances a problem?  Put it in an extreme vacuum chamber and only do lots of short portal jumps.

Correct, instantaneous teleportation would require infinite energy, even in my JBIS warp drive paper. It doesn't propose any way to send a signal FTL. I think it would probably require some sort of probe that would travel FTL to communicate, but who knows what will happen once the principles are understood.

IMO, the past no longer exists because it would violate conservation of energy. The same for the multiverse. The energy that makes up this moment "now" carries forward to the next moment, and on into the future, energy is conserved. If the past were still there, then every moment in time would have to be replicating that much energy, down to intervals the size of the Planck scale to appear "continuous". Where is all that energy coming from? Why would we allow our most important law of physics to be violated on a large scale? I'm sorry, but IMO, time travel into the past is never going to happen.

[meberbs]

Just in case that you think I am being arrogant here, please remember that my confidence in my position does not come from my assessment of my own intelligence, but from the fact that my position is shared by literally every physicist I have ever seen describe relativity, and every paper or textbook in the field that I have ever read.

I'll get to the rest of your email, once we agree on what the Twin Paradox actually teaches us.

I don't think we will ever be able to get there unless you resolve at least the most blatant of contradictory statements you have made. You have within the same paragraph both claimed that there are all inertial reference frames are equivalent, and that some inertial reference frames are special. Pick one.

At least we "agree" on one thing:

You keep missing the point and I'm just going to have to get better at explaining it, until you get it. This is actually something that should be in my paper, so I appreciate this discussion immensely. Coming to a consensus here will prevent errors there.

This is something I would say to you. Explaining special relativity to you greatly helps me get better at explaining relativity.

In your above statements, you are perfectly fine with the asymmetry where, the twin who travels has to accelerate to turn around and head back toward earth. But you ignore the acceleration that started the trip in the first place, as did the video that Dustin posted.

Here is the trick with that one. The initial/final acceleration takes place when both twins are in the same location, so the travelling twin doesn't see the other twin's clock fast-forward or rewind during the (implicitly assumed) brief acceleration. If the other twin was the one that accelerated at the start and end, or if the they had both accelerated some amount, nothing would change about the results.

As a result, your explanation where the initial/final acceleration matters is simply inconsistent. For one thing just after the acceleration completed they could send messages to each other with fairly short delays and see that 1.8 years hadn't passed for the non-accelerated twin. Second, the 1.8 years that you claim happen during the initial acceleration require that he travel 5 years before turning around. If he decides to turn around sooner or later, your explanation breaks down.

A distant galaxy moving away from us at 0.6c since the big bang is different. I would assume that the Milky way and that distant galaxy were both created and accelerated equally at the same time, by the same force (i.e, the Big Bang). Whereas, ship 2 and the Earth were not both accelerated at the same time by the same force.

But what is different? Given 2 objects, one that came from that other galaxy and one that came from ours, and accelerated to match speed how could you tell which was which?

IMO, there is no way to have a symmetrical situation within our galaxy.

Rather than opinion, why don't you do math and work out the example I suggested using only Earth orbital velocity.

[RonM]

IMO, the past no longer exists because it would violate conservation of energy. The same for the multiverse. The energy that makes up this moment "now" carries forward to the next moment, and on into the future, energy is conserved. If the past were still there, then every moment in time would have to be replicating that much energy, down to intervals the size of the Planck scale to appear "continuous". Where is all that energy coming from? Why would we allow our most important law of physics to be violated on a large scale? I'm sorry, but IMO, time travel into the past is never going to happen.

That's one the reasons why people say FTL travel is impossible. Under General Relativity FTL equals time travel.

If FTL travel is possible, we don't have the math or understanding of the universe to figure it out. Maybe after unifying GR and Quantum Theory.

The issue with the twin paradox is that we're trying to describe it under Special Relativity and that does not include accelerating frames of reference. It's above my pay grade, but I bet if we did the math under GR there would not be a problem since we can include the acceleration of the spaceship.

[Bob012345]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Also, regarding the twin paradox, if two ships discover each other at some relative velocity, and each is ignorant of the history of the other and themselves, can it be established how they age relative to each other with no external references. It there enough information? Thanks.

[WarpTech]

Just in case that you think I am being arrogant here, please remember that my confidence in my position does not come from my assessment of my own intelligence, but from the fact that my position is shared by literally every physicist I have ever seen describe relativity, and every paper or textbook in the field that I have ever read.

I know this. I've been trying to teach people this alternative for a long time. Eventually, some people do get it, but others just want to argue. If we work together, we can make it so that FTL is possible and the paradoxes are not. That's my goal. Is it yours?

I'll get to the rest of your email, once we agree on what the Twin Paradox actually teaches us.

I don't think we will ever be able to get there unless you resolve at least the most blatant of contradictory statements you have made. You have within the same paragraph both claimed that there are all inertial reference frames are equivalent, and that some inertial reference frames are special. Pick one.

I am trying to avoid a full blown lecture on QED and the Polarizable Vacuum theory of General Relativity. The simplest way to explain it is with Math. So;

ds² = K*dx² - (1/K)*c²dt²

Where, K = g₁₁ = -1/g₀₀ for simplicity.

If K = 1, this is a Minkowski (flat) space-time. We can draw a space-time diagram, where c=1, and the speed of light is represented by a light-cone with a 45-deg slope.

What happens when K is not 1?
When K > 1, the light-cone gets narrower and c < 1.
When K < 1, the light-cone gets wider and c > 1.

You can prove this by setting ds = 0, and solving for the coordinate speed of light;

dx/dt = c/K

As long as K is a "constant", then it is an inertial reference frame. A "scaled" version of space-time. The scaling must be done correctly using dimensional analysis,(M,L,T) but it is fairly easy. Simply replace the dimensional values as follows. The value where K=1 will be signified with a subscript, "0".

Mass M = M₀*K^3/2
Length L = L₀/√K
Time T = T₀*√K

In doing so, we have an infinite number of inertial reference frames, each defined by a different refractive index, K. When we are immersed in this reference frame, rulers and clocks are always normalized so that the local value of c = 1. The relative value of K can only be measured by a distant observer. Typically, we take the distant observer to be far from all matter and we define this "special" case as K=1, and then any gravitational fields have values of K > 1. Any FTL field will have a value of K < 1.

K doesn't have to be a constant, it can be a variable of the coordinates, such as the Schwarzschild metric. It is ALWAYS composed of the metric coefficients from GR and represents the gravitational field. The variable refractive index is the result of a variable Damping Factor which acts on the quantum harmonic oscillators that compose matter. So where K > 1, i.e, in a gravity well, the damping factor is larger. Far from matter, we expect the damping factor to go to zero, where K = 1 is defined for the distant observer.

Motion relative to the local baseline gravitational field also increases the damping factor, so gravitational time dilation and length contraction, and the effects of motion through the field, are both caused by increased damping. In that regard, motion relative to the "local baseline gravitational field" and the renormalization of K=1 locally, is what gives us Special Relativity. But non-locally, inertial reference frames with different values of K have different scaling. It is a Conformal theory of gravity.

In your above statements, you are perfectly fine with the asymmetry where, the twin who travels has to accelerate to turn around and head back toward earth. But you ignore the acceleration that started the trip in the first place, as did the video that Dustin posted.

Here is the trick with that one. The initial/final acceleration takes place when both twins are in the same location, so the travelling twin doesn't see the other twin's clock fast-forward or rewind during the (implicitly assumed) brief acceleration. If the other twin was the one that accelerated at the start and end, or if the they had both accelerated some amount, nothing would change about the results.

As a result, your explanation where the initial/final acceleration matters is simply inconsistent. For one thing just after the acceleration completed they could send messages to each other with fairly short delays and see that 1.8 years hadn't passed for the non-accelerated twin. Second, the 1.8 years that you claim happen during the initial acceleration require that he travel 5 years before turning around. If he decides to turn around sooner or later, your explanation breaks down.

You got me on that one. I didn't think through my wording very well, but I understood that the 1.8 years was referring to when he was 4-years down the road. My point was, when he is moving "away" his space-axis rotates CCW, and when he's moving toward Earth, his space-axis is rotated CW, and it is always "his space-axis" that is rotating, not the Earth's, and we should acknowledge that his axis rotates at every acceleration phase, including the first one where he leaves Earth. Even with FTL, there is no way I can think of to approach something and have the axis tilted as if moving away from it.

A distant galaxy moving away from us at 0.6c since the big bang is different. I would assume that the Milky way and that distant galaxy were both created and accelerated equally at the same time, by the same force (i.e, the Big Bang). Whereas, ship 2 and the Earth were not both accelerated at the same time by the same force.

But what is different? Given 2 objects, one that came from that other galaxy and one that came from ours, and accelerated to match speed how could you tell which was which?

The relative baseline is different, but I gave this some more thought and you're right in that it doesn't matter. My conjecture was that the big bang was identical to launching 2 ships from Earth in opposite directions, but launching 1 ship was different. Launching 2 ships does create a symmetrical situation. However, the Earth's clock rate is still faster than either ship. If both ships were at +/- 0.6c relative to Earth, and both ships FTL jump back to Earth after 4 years, the clock on Earth will be at 5 years, and both ships would be at 4 years. If the one ship jumped to the other, both ships would be at 4 years, because they have the same relative change in damping, relative to the field around the Earth they were launched from.

[meberbs]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Any of the above. They all would allow for time travel, unless there was some explicit mechanism that would prevent any of the causality breaking scenarios, such as one wormhole disrupting the possibility of creating a parallel wormhole that has some relative velocity. As I understand it, the OP for this thread was basically asking for what mechanisms could do this.

Also, regarding the twin paradox, if two ships discover each other at some relative velocity, and each is ignorant of the history of the other and themselves, can it be established how they age relative to each other with no external references. It there enough information? Thanks.

Yes, but they would both see the other as aging slower. This is because of the relativity of simultaneity, "now" is reference frame dependent. To get them to agree on their relative age, you have to have them meet back up, so there is an "event" that they are both present for, so they have to agree on each other's current age when they pass by each other. If they met back up, the relative age would depend on which turned around to meet up with the other.

I would be curious as to WarpTech's answer to this, as he seems to think objects somehow store the history of the accelerations they have undergone and that their dynamic behavior is somehow different as a result.

[WarpTech]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Also, regarding the twin paradox, if two ships discover each other at some relative velocity, and each is ignorant of the history of the other and themselves, can it be established how they age relative to each other with no external references. It there enough information? Thanks.

The debate is whether FTL requires time travel. I say, FTL is possible, time travel is not and there are no paradoxes when we understand GR and SR in the correct context. However, this context is not in the text books so I'm fighting an uphill battle to teach people how to re-interpret what they think they already know.

To answer your question, they would need to be in communication, and preferably have a local interaction so that they can synchronize a pair of clocks, in the same place at the same time. Then go merrily on their way.

Edit: I agree with @meberbs, they would need to meet back up a 2nd time to compare clocks.

[Bob012345]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Any of the above. They all would allow for time travel, unless there was some explicit mechanism that would prevent any of the causality breaking scenarios, such as one wormhole disrupting the possibility of creating a parallel wormhole that has some relative velocity. As I understand it, the OP for this thread was basically asking for what mechanisms could do this.

Also, regarding the twin paradox, if two ships discover each other at some relative velocity, and each is ignorant of the history of the other and themselves, can it be established how they age relative to each other with no external references. It there enough information? Thanks.

Yes, but they would both see the other as aging slower. This is because of the relativity of simultaneity, "now" is reference frame dependent. To get them to agree on their relative age, you have to have them meet back up, so there is an "event" that they are both present for, so they have to agree on each other's current age when they pass by each other. If they met back up, the relative age would depend on which turned around to meet up with the other.

I would be curious as to WarpTech's answer to this, as he seems to think objects somehow store the history of the accelerations they have undergone and that their dynamic behavior is somehow different as a result.

Thanks. I'm absorbing your answer....I may have to dig out my copy of Wheeler and Taylor.

[Bob012345]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Also, regarding the twin paradox, if two ships discover each other at some relative velocity, and each is ignorant of the history of the other and themselves, can it be established how they age relative to each other with no external references. It there enough information? Thanks.

The debate is whether FTL requires time travel. I say, FTL is possible, time travel is not and there are no paradoxes when we understand GR and SR in the correct context. However, this context is not in the text books so I'm fighting an uphill battle to teach people how to re-interpret what they think they already know.

To answer your question, they would need to be in communication, and preferably have a local interaction so that they can synchronize a pair of clocks, in the same place at the same time. Then go merrily on their way.

Edit: I agree with @meberbs, they would need to meet back up a 2nd time to compare clocks.

Thanks!

[KelvinZero]

In general, is this a debate over whether Alcubierre warp bubbles or wormholes could ever exist, or whether literal FTT travel through space cannot exist? Thanks.

Hi Bob012345,
When I started this thread, the goal was to find a definition of FTL that avoids paradox. It is not about the theory of any particular method or whether it actually exists, just if you can describe what you are claiming it would allow you to do.

Another way of looking at it could be "Guilt-free FTL rules for HardSF writers". You don't need to explain the machine. It Glows. It makes noises. Things spin. But you do have to explain the characters. Who can understand a universe full of characters living in a universe where you could create a paradox with a few simple steps, and no one does it, and no one talks about it?

I started this thread thinking we could demonstrate a paradox with a single FTL flight. At the moment we have a claim that you can avoid all paradoxes by limiting FTL to a special frame, such as the CMB rest frame. I don't think anyone has been able to directly discredit that yet.. though we don't necessarily like it :-)

Im sort of waiting for some wizzes at relativity to come along and pull the rug out from under that one with a specific example that shows it still produces paradoxes. That is where we are at the moment.

One really weird thing about a universe like that, is that travelling in one particular direction you would be travelling into the past, just not far enough to get back in time to cause paradox. So I guess your friend could jump a lightyear to the left and you could see them immediately jump out of their ship and start waving to you, because all this happened a year ago over there, and the light has been travelling towards you all that time!

[laszlo]

So you're trying to find rules obeying relativity to do something that relativity absolutely prohibits?

Sounds a bit like atheists trying to justify themselves through theology.

Seems the more honest thing to do is to acknowledge that relativity totally prohibits FTL and either throw relativity out completely (atheist) or throw FTL out completely (church lady).

[meberbs]

At the moment we have a claim that you can avoid all paradoxes by limiting FTL to a special frame, such as the CMB rest frame. I don't think anyone has been able to directly discredit that yet.. though we don't necessarily like it :-)

Im sort of waiting for some wizzes at relativity to come along and pull the rug out from under that one with a specific example that shows it still produces paradoxes. That is where we are at the moment.

Having suggested the existence of a special frame to begin with, I feel I should clarify. If there is such a thing as a special frame that you limit FTL to, the entire theory of relativity collapses, because this directly contradicts its most fundamental assumption. I have no idea what, if anything, you could replace it with unless you want to ignore untold numbers of experimental results.

So you're trying to find rules obeying relativity to do something that relativity absolutely prohibits?

Which is why the best solution I could come up with is to break the one fundamental assumption underlying relativity.

[KelvinZero]

Having suggested the existence of a special frame to begin with, I feel I should clarify. If there is such a thing as a special frame that you limit FTL to, the entire theory of relativity collapses, because this directly contradicts its most fundamental assumption. I have no idea what, if anything, you could replace it with unless you want to ignore untold numbers of experimental results.

So you're trying to find rules obeying relativity to do something that relativity absolutely prohibits?

Which is why the best solution I could come up with is to break the one fundamental assumption underlying relativity.

Im not sure I am understanding you. We are probably saying the same thing and just wording it differently. To be clear, you are not talking about changing the universe in a way that invalidates current experiments, correct? All those experiments have to still deliver the same outcomes.

Breaking the assumption is fine, If I know what you mean. Relativity can be perfect like a sphere without being a statement that there is no such thing as a cube, or that you won't suddenly come across a cube embedded in your sphere.

This is why Im only concerned with paradoxes, or solutions that require current experiments to suddenly deliver different outcomes, and Im still not convinced there is not still a nasty paradox hidden in there somewhere. Im still expecting someone to pull the rug out from under this with an example that shows it is just as nonsensical as general FTL.

[WarpTech]

At the moment we have a claim that you can avoid all paradoxes by limiting FTL to a special frame, such as the CMB rest frame. I don't think anyone has been able to directly discredit that yet.. though we don't necessarily like it :-)

Im sort of waiting for some wizzes at relativity to come along and pull the rug out from under that one with a specific example that shows it still produces paradoxes. That is where we are at the moment.

Having suggested the existence of a special frame to begin with, I feel I should clarify. If there is such a thing as a special frame that you limit FTL to, the entire theory of relativity collapses, because this directly contradicts its most fundamental assumption. I have no idea what, if anything, you could replace it with unless you want to ignore untold numbers of experimental results.

So you're trying to find rules obeying relativity to do something that relativity absolutely prohibits?

Which is why the best solution I could come up with is to break the one fundamental assumption underlying relativity.

My post from earlier today does not contradict relativity. What are the "fundamental assumptions", or the Postulates of Special Relativity?

1. The laws of physics are the same in all inertial frames of reference.
2. The speed of light in vacuum has the same value c in all inertial frames of reference.

Regarding the 2nd postulate; as I said in my post, M, L & T are scaled as functions of K. Rulers and clocks are "normalized" such that the value of c is constant in all "local" inertial reference frames.

Regarding the 1st postulate; using the dimensional conversions,

Mass M = M₀*K^3/2
Length L = L₀/√K
Time T = T₀*√K

Calculate how Forces depend on K. Simple;

Force = (Mass)*(Length)/(Time)² = (M₀*K^3/2)*(L₀/√K)/(T₀*√K)²

So => M*L/T² = M₀*L₀/T₀²

In other words, the forces we measure in experiments are completely independent of the local value of K. So all inertial reference frames will experience the same forces and have the same results to ALL experiments that verify SR and GR. The effects of K cannot be measured "locally" because our rulers and clocks are renormalized. Therefore, the only change to the postulates is to add the word "local". Nothing else in SR or GR changes, except the interpretation of what we already know.

[WarpTech]

Having suggested the existence of a special frame to begin with, I feel I should clarify. If there is such a thing as a special frame that you limit FTL to, the entire theory of relativity collapses, because this directly contradicts its most fundamental assumption. I have no idea what, if anything, you could replace it with unless you want to ignore untold numbers of experimental results.

So you're trying to find rules obeying relativity to do something that relativity absolutely prohibits?

Which is why the best solution I could come up with is to break the one fundamental assumption underlying relativity.

Im not sure I am understanding you. We are probably saying the same thing and just wording it differently. To be clear, you are not talking about changing the universe in a way that invalidates current experiments, correct? All those experiments have to still deliver the same outcomes.

Breaking the assumption is fine, If I know what you mean. Relativity can be perfect like a sphere without being a statement that there is no such thing as a cube, or that you won't suddenly come across a cube embedded in your sphere.

This is why Im only concerned with paradoxes, or solutions that require current experiments to suddenly deliver different outcomes, and Im still not convinced there is not still a nasty paradox hidden in there somewhere. Im still expecting someone to pull the rug out from under this with an example that shows it is just as nonsensical as general FTL.

I found this. I can't really make heads or tails out of it yet.

https://arxiv.org/pdf/1407.2528.pdf

[ppnl]

I know this. I've been trying to teach people this alternative for a long time. Eventually, some people do get it, but others just want to argue. If we work together, we can make it so that FTL is possible and the paradoxes are not. That's my goal. Is it yours?

And this is what is wrong with your entire argument. You cannot make anything so simply by working toward it. Things are so or not so regardless of what you want. You are engaged in motivated reasoning toward a goal. That's how creationists believe in a 7000 year old earth. That's how the flat earth society is still a thing. If you are willing to bend logic reason and evidence to fit your preselected desire then you have killed science. Your goal should not be proving FLT is possible. Your goal should be understanding the truth what ever it may be.

Nobody wants the limit of light speed. There is no vast political movement to prevent FTL travel. There is no conspiracy to hide the truth. It is just what the evidence points to. Now you are free to disagree with almost the entire scientific community if you wish. And I wish you luck. Honestly I do. It would be wonderful. But at the same time I gotta be honest and say that your chances are better buying a lotto ticket.

[ppnl]

The issue with the twin paradox is that we're trying to describe it under Special Relativity and that does not include accelerating frames of reference. It's above my pay grade, but I bet if we did the math under GR there would not be a problem since we can include the acceleration of the spaceship.

The twin paradox is specifically a special relativity phenomena. General relativity reduces to special relativity in the flat space that we use to describe the twin paradox. There is literally no math to do.

In both general relativity and special relativity things that are simultaneous in one frame are not simultaneous in another. This is the central fact that fuels the twin paradox.  It is built in to the geometry of spacetime.