Any resolutions to FTL paradoxes?

[meberbs]

Relativity of Simultaneity deals with the apparent order of events, as observed by moving observers.  It says nothing about what the order actually is.

No it has to do with the actual order of events. No the order when light from them arrives. No inertial reference frame is special, so the definition of now for a moving observer is equally valid, and the moving observer's ansible would send a signal to t = -10 in the Earth frame, which means that the Earth frame ansible would receive confirmation of the signal reception 10 minutes before the signal is sent.

A ship with an ansible at high relative velocity experiences time dilation yes.  But all clocks keep moving forward, only the rates are different.  At what point does the ship travel 10 minutes into the past?

No, not discussing time dilation. The ship does not travel into the past in this scenario. When something accelerates to a high speed, its time axis shifts changing the definition of "now" for distant objects. This means its ansible signals can travel into the past or receive messages from the future according to an observer in the original frame.

Say a ship is moving ~0.93c and has a time dilation factor of 3.  It sends a message via ansilbe that says "Call back in 3 minutes".  The call comes in 1 minute later ship time. The reply will always come after the message.

You are simply not discussing the same case as me, 2 sets of ansibles moving at different speeds.

[Norm38]

Ansible signals don't travel into the past or future. They are simply instantaneous.  If the signals are in the past, then the ship is in the past too. But the ship didn't travel into the past, so we have a contradiction.

Edit: I retract all this, the time shift isn't real, it's an illusion of geometry. The only thing real is relativistic time dilation.

I think you're ignoring the amount of time it takes a ship to accelerate and achieve the time axis shift, with respect to the now.  A ship would have to accelerate nearly instantaneously, requiring nearly infinite energy.  I'm comfortable ignoring that case.
If it takes a ship just 10.001 minutes to time shift -10 minutes, then at no point is the ship actually in the past with respect to the original frame. It may appear from the ground to have reached velocity in 0.001 minutes, but I'd postulate that a ship cannot achieve a true negative time shift that would result in ansible signals creating a paradox.

[meberbs]

Instantaneous in what frame?

The scenario I described can have everything already moving at said speed, so the time for acceleration is irrelevant. Also, you can just pick a further away other end of the ansible if you did want to have enough time to accelerate.

You clearly have not read the link I posted, or watched the intro to relativity video posted early in this thread. If you don't make any attempt to understand the resources that you have been pointed to, there is no point in me retyping explanations that are widely available.

[missinglink]

(this comment meant to apply to "New Physics" in general, not necessarily to this thread)

 In the old Bad Astronomer forum, there was a section called Against the Mainstream (if I remember correctly) where anyone could present their pet theory proving Einstein (or whomever) wrong. They had a fairly rigorous set-up, with claimants having to agree to abide by certain rules, such as responding to questions/objections promptly or the thread would be closed. Non-responsive replies and willful obtuseness also could lead to the thread being shut down.

It was a big workload on the moderators, perhaps one of the reasons why that forum is now defunct. However, they did keep the queue moving and prevented belligerent or slow claimants from clogging up the works.

[Norm38]

I read the link again and watched the videos. All there is, is time dilation, light cones and some graphs based on the theory that nothing can go FTL.  But plotting an FTL course through non-FTL theory and getting a nonsense result doesn't equal time travel. There is nothing that indicates at exactly what point an FTL ship actually goes backwards in time.  It equals an inability of the theory to describe what is actually happening.

Instantaneous in all frames.  This isn't a thought experiment.  There is an entire galaxy of actual matter out there and all of it exists right now. Clocks running at different rates does not invalidate a common now.
I can envision a galaxy wide civil alert system. "Warning", the ansible calls out, "Eta Carine just went supernova. The effect will be visible in your section of the galaxy in 7500 Earth years." That would be an actual event, fixed in time and space.  Different observers see it happening at different times, but there was only one now at which it did occur. The shockwave will spread through the neighboring stars and impact them at specific singular points in time.  An FTL ship could observe all of that as it actually occurs. Regardless of what any relativistic ships plodding along think they see years later.

All the clocks out there are only ticking forward. Their rate doesn't matter, their change in rate doesn't matter. If the speed of light is the speed of causality, then if FTL is possible, it simply means a new speed of causality. No time travel, no paradox.

[meberbs]

I read the link again and watched the videos. All there is, is time dilation, light cones and some graphs based on the theory that nothing can go FTL.  But plotting an FTL course through non-FTL theory and getting a nonsense result doesn't equal time travel. There is nothing that indicates at exactly what point an FTL ship actually goes backwards in time.  It equals an inability of the theory to describe what is actually happening.

It is not a limitation of the ability of the theory to describe what is happening, but of your understanding of the theory. An FTL course in special relativity just means you are discussing spacelike separated events. For any pair of spacelike separated events, there is always a frame where they happen in opposite order.

Instantaneous in all frames.

You are going to have to let go of your intuition.  Your intuition says that their is a single "now" that everyone agrees on. This however is not true when you get to relativistic speeds.

The scenario you wrote down is incompatible with the fact that observers in in different reference frames all see light moving at the speed of light relative to themselves, regardless of how fast they are moving relative to anything else. If you try to write down a set of rules that are consistent with this, you end up with the Lorentz transformations, which are the basis for special relativity.

Lets work through an example:

There is a ship flying past earth at speed 0.6 c. We define the origin of both the ship's reference frame and the Earth's reference frame to be the event when the ship passes the Earth.

Lets also say that there are 2 star systems at x = -10 and x = -5 in the Earth frame (opposite direction that the ship is travelling in, and at rest in the Earth frame.)

The star at x = -10 goes nova at time t = 0, so we can define to more events in spacetime at x=-10, t = 0, when the star goes nova, and x = -5, t = 5 when the nova is seen at the second star system.

Using the Lorentz transformation, we can see when these events happen in the ship frame (This is when they happen, not when the light reaches the ship)

The gamma factor for the ship is 1.25.
For the nova:
t' = 1.25*(0 - (0.6*-10)) = 7.5  (7.5 years in the future)
x' = 1.25*(-10 - 0) = -12.5 light years
For the star system seeing the nova:
t' = 1.25*(5 - (0.6*-5)) = 10
x' = 1.25*(-5 - 0.6*5) = -10 light years

You can see that the speed of light is the same, it takes 2.5 years for light to travel the 2.5 light years between these 2 events in the ship frame.

You can also see how a paradox can come about if you allow FTL, because as the ship is passing Earth an ansible on Earth would receive the communication that the star went nova. They can relay this information to the ship that is passing by Earth. For the ship, the star will not go nova for 7.5 years. If it sends an ansible message to that star, the message will arrive years before the star goes nova, because "now" for the ship is different from "now" on Earth.

[Norm38]

It's becoming clear to me that the paradox is not created by FTL, but by the Lorentz transformations trying to define relativistic travel.
You say that the nova star and second star system are 2.5ly apart in ship frame. But the two stars are actually 5ly apart.  The ship would know that from its charts. It would know that light cannot travel 5ly in 2.5yr. The speed of light did not increase and the two stars did not move closer together. It is the time dilation on the ship that makes it appear that the two events are 2.5ly apart. By that, the ship knows that it is not an "at rest" reference frame, but is suffering relativistic effects.

Similarly, the t's for the two events ship frame result from plotting world lines for those events in its clock slowed reference frame, but those are not real, they are illusions. The nova, the 2nd star system, Earth and the ship all exist at real points in space. Nothing is moving except the ship and it is not going backwards in time. An ansible network in constant communication with all 4 as the ship accelerates from 0 to 0.6c would observe the time dilation, but would only see the ship's clock continuing to move forward.  At no point does it slip into the past. The ansible keeps all the clocks in sync and exposes the illusion.  But there is no paradox, information cannot be sent into the past.

[as58]

It's becoming clear to me that the paradox is not created by FTL, but by the Lorentz transformations trying to define relativistic travel.
You say that the nova star and second star system are 2.5ly apart in ship frame. But the two stars are actually 5ly apart.  The ship would know that from its charts. It would know that light cannot travel 5ly in 2.5yr. The speed of light did not increase and the two stars did not move closer together. It is the time dilation on the ship that makes it appear that the two events are 2.5ly apart. By that, the ship knows that it is not an "at rest" reference frame, but is suffering relativistic effects.

Similarly, the t's for the two events ship frame result from plotting world lines for those events in its clock slowed reference frame, but those are not real, they are illusions. The nova, the 2nd star system, Earth and the ship all exist at real points in space. Nothing is moving except the ship and it is not going backwards in time. An ansible network in constant communication with all 4 as the ship accelerates from 0 to 0.6c would observe the time dilation, but would only see the ship's clock continuing to move forward.  At no point does it slip into the past. The ansible keeps all the clocks in sync and exposes the illusion.  But there is no paradox, information cannot be sent into the past.

You're effectively saying that the problem is created by the theory of relativity, not FTL. Sure, if you're willing to give up Einstein's theory of relativity FTL could well be possible. But it's going to be hard to convince anyone else...

[meberbs]

You say that the nova star and second star system are 2.5ly apart in ship frame.

No, due to length contraction, they are 5/1.25 = 4 light years apart. The second star spends the next 2.5 years travelling towards where the nova happened at 0.6c so the time that passes in the ship frame between the 2 events is 2.5 years. (The nova remnants are also moving at the same speed so they remain 4 light years away from the second star.)

But the two stars are actually 5ly apart.  The ship would know that from its charts.

They are NOT 5 light years apart. They are 4 light years apart in the ship frame. Saying that they are 5 light years apart would mean that the Earth frame is some kind of special rest frame. This is simply untrue.

It is the time dilation on the ship that makes it appear that the two events are 2.5ly apart. By that, the ship knows that it is not an "at rest" reference frame, but is suffering relativistic effects.

No. You seemed to have missed this point: EVERY inertial reference frame is an "at rest frame." From the ship's perspective it is the clocks on Earth that run slow.

[Nomadd]

Calling time dialation an "illusion" indicates a very basic flaw in understanding to me. Saying that nothing is moving except the ship doesn't make much sense. Everything is moving relative to everyting else. There are relativistic effects with any two objects not at exactly the same reference. Just not enough to measure in some cases. The only illusion is that all these twisted analogies have much to do with the world. I haven't seen an argument in here that doesn't assume some state that has no basis in reality and completely invalidates the conclusion.

[Norm38]

Time dilation is not an illusion, that is the only thing that is real.  The gamma factor of relativistic travel is real and that is what separates the reference frames from each other. The Solar system and surrounding stars are moving at about 0.00075c.  That is what separates our reference frame from that of a 0.6c ship.

The ship knows the two stars were 5ly apart when it was also moving at 0.00075c and are still 5ly apart.   The acceleration of the ship did not cause the second star to also accelerate to 0.6c (where does that energy come from?). That is part of the illusion. The ship observes the two stars as 4ly apart (not 2.5 sorry) and knows that time dilation is distorting its observations of surrounding objects.

I'm not giving up the Theory of Relativity.  I'm giving up a graphical projection that says a relativistic ship has time shifted into the past.  It hasn't.

[WarpTech]

...
You can also see how a paradox can come about if you allow FTL, because as the ship is passing Earth an ansible on Earth would receive the communication that the star went nova. They can relay this information to the ship that is passing by Earth. For the ship, the star will not go nova for 7.5 years. If it sends an ansible message to that star, the message will arrive years before the star goes nova, because "now" for the ship is different from "now" on Earth.

The message sent "to" that star is moving "toward" the star, not away from it. In the frame of the message, the space-time axis must rotate so as to approach the star, not move away from it as in the ship's frame. The paradox is caused by ignoring this 3rd reference frame of the message "approaching" the star.

IMO, I agree with the one statement in that paper I found, and that is; if we can't travel into the past while at rest or moving STL, then we can't do it moving FTL either, because all motion is relative.

[as58]

Time dilation is not an illusion, that is the only thing that is real.  The gamma factor of relativistic travel is real and that is what separates the reference frames from each other. The Solar system and surrounding stars are moving at about 0.00075c.  That is what separates our reference frame from that of a 0.6c ship.

Moving at 0.00075c or 0.6c relative to what? You seem to be assuming that there is some special reference frame, which is in contradiction with relativity.

[meberbs]

Time dilation is not an illusion, that is the only thing that is real.  The gamma factor of relativistic travel is real and that is what separates the reference frames from each other. The Solar system and surrounding stars are moving at about 0.00075c.  That is what separates our reference frame from that of a 0.6c ship.

Moving relative to what?

The ship observes the two stars as 4ly apart (not 2.5 sorry) and knows that time dilation is distorting its observations of surrounding objects.

Read my post again.

Due to length contraction, they are 5/1.25 = 4 light years apart. The second star spends the next 2.5 years travelling towards where the nova happened at 0.6c so the time that passes in the ship frame between the 2 events is 2.5 years. (The nova remnants are also moving at the same speed so they remain 4 light years away from the second star.)

I'm not giving up the Theory of Relativity.  I'm giving up a graphical projection that says a relativistic ship has time shifted into the past.  It hasn't.

The very foundation of relativity is that all inertial reference frames are equivalent. If you give this up, the rest goes out the window. The "graphical representation" simply reflects the basic math of the situation.

Without the length contraction and the temporal shift of the events, there is no way to explain the fact that using the time measured by the ship and distance measured by the ship, light still would be travelling at c towards the (stationary) ship.

[meberbs]

The message sent "to" that star is moving "toward" the star, not away from it. In the frame of the message, the space-time axis must rotate so as to approach the star, not move away from it as in the ship's frame. The paradox is caused by ignoring this 3rd reference frame of the message "approaching" the star.

IMO, I agree with the one statement in that paper I found, and that is; if we can't travel into the past while at rest or moving STL, then we can't do it moving FTL either, because all motion is relative.

Defining an FTL frame causes problems, so to work around that you can simply and validly just look at what happens in the STL inertial frames.

In the Earth frame, the ansible sends information from the nova to Earth travelling on an apparent path of that follows the t = 0 line in that frame. (you can give it some small positive slope if you want, the effective result doesn't change.)

You had previously correctly stated the postulates of relativity. Per the first of those, the laws of physics are the same on the ship. As a result, a signal in the ship frame should also be able to travel to the star that goes nova following the t = 0 line in that frame.

...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.

[Norm38]

Moving relative to everything we see around us. Our galaxy, the local group. Effectively the fabric of spacetime itself.  We don't observe anything whizzing around at near luminal velocities. (At further scales it is space itself that is moving, not objects through space)  For the velocities we observe, the Lorentz factor is close enough to 1 to be ignored.

But the ship is not stationary and Gamma is not 1. The ship witnessed the acceleration and knew quite well that it was not the entire universe around it suddenly accelerating to a large fraction of c.
The ship witnessed the apparent length contraction and knows it to be illusion of it's high relative velocity.  It knows the entire galaxy did not suddenly shrink around it.  The ship knows that when it slows back down, every star will appear to go back to where it was, after accounting for the ship's new position.

And the ship knows that whatever temporal shift appears to be happening according to the math is just the illusion of it's one clock running much slower than the billions of other clocks around it.

[meberbs]

Moving relative to everything we see around us. Our galaxy, the local group.

Which are all moving at different speeds in different directions and made up of individual things doing the same.

The first postulate that underlies all of special relativity:

All inertial reference frames are equivalent.

If you ignore this, there is no way to explain the constancy of the speed of light across reference frames.

[WarpTech]

The message sent "to" that star is moving "toward" the star, not away from it. In the frame of the message, the space-time axis must rotate so as to approach the star, not move away from it as in the ship's frame. The paradox is caused by ignoring this 3rd reference frame of the message "approaching" the star.

IMO, I agree with the one statement in that paper I found, and that is; if we can't travel into the past while at rest or moving STL, then we can't do it moving FTL either, because all motion is relative.

Defining an FTL frame causes problems, so to work around that you can simply and validly just look at what happens in the STL inertial frames.

In the Earth frame, the ansible sends information from the nova to Earth travelling on an apparent path of that follows the t = 0 line in that frame. (you can give it some small positive slope if you want, the effective result doesn't change.)

You had previously correctly stated the postulates of relativity. Per the first of those, the laws of physics are the same on the ship. As a result, a signal in the ship frame should also be able to travel to the star that goes nova following the t = 0 line in that frame.

...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.

In your previous post you said;

"The very foundation of relativity is that all inertial reference frames are equivalent. "

but the first postulate of relativity actually says;

"The laws of physics are the same in all inertial frames of reference."

These two statements are NOT the same thing. Your statement is an "assumption" of what you think it means, but I gave examples on page 6 of this thread, showing that we CAN have different inertial reference frames with different scaling parameters and still, "The laws of physics are the same in all inertial frames of reference.", regardless of how that frame is scaled.

So you see, there is a hidden assumption that if the laws of physics are the same, then the inertial reference frames are "equal", but my example proves that this is not necessarily true. We can have inertial reference frames that are not equal and have different scaling and still the laws of physics do not change.

[Norm38]

If we have a Gamma of 1, and the ship has a Gamma of 1.25, how are those equivalent? How do I ignore that a ship that has accelerated is pretending it did nothing of the sort?

All the factors you list explain the consistency of the speed of light. What they don't explain is how acceleration equals an actual time shift into the past that would cause an ansible communicated paradox.

An observer's state of motion cannot affect an observed object, but it can affect the observer's observations of the object.

[meberbs]

If we have a Gamma of 1, and the ship has a Gamma of 1.25, how are those equivalent? How do I ignore that a ship that has accelerated is pretending it did nothing of the sort?

All the factors you list explain the consistency of the speed of light. What they don't explain is how acceleration equals an actual time shift into the past that would cause an ansible communicated paradox.

An observer's state of motion cannot affect an observed object, but it can affect the observer's observations of the object.

Gamma is only defined in a relative sense between 2 frames, and it goes both ways.

The Earth's clocks are running slow by a factor of 1,25 according to the ship. Just as in the ship frame the 2 stars are only 4 light years apart, in the Earth frame, the length of the ship is shrunk by a factor of  4/5.