Proof of impossibility of superluminal signals?

[stevendaryl]

The proper time experienced in unaccelerated motion (which is also the maximal proper time you can have) is positive if A and B are timelike separated. And the limit for light-like separation is zero.

I meant for any two points along a light-like path.

 

[phyti]

kochanskij

1. A transmitter sends a signal at 12:00 from point A
3. Receiver at A detects the reply at 11:00

Why would the A clock run in reverse?

(Note: If the signal goes at infinite speed relative to A and the reply goes at infinite speed relative to B, then A will always get the reply before it transmits.)

Instantaneous is the speed limit.
The time interval would equal zero for the A clock.
A fundamental principle: you cannot detect a signal before it is emitted.

 

[Fredrik]

Why would the A clock run in reverse?

It's not running in reverse. The world line of the reply message is (or is close to) B's simultaneity line, which (assuming that B is moving away from A) intersects A's world line before A sent the original message. If you want to see a version of this scenario with the details written out, click the link in post #14.

 

[stevendaryl]

kochanskij
Why would the A clock run in reverse?
Instantaneous is the speed limit.
The time interval would equal zero for the A clock.
A fundamental principle: you cannot detect a signal before it is emitted.

I think there might be some miscommunication going on. The point is not to demonstrate that back-in-time communication is possible, but to demonstrate that FTL is impossible. It's a principle of logic that if A \wedge B \Rightarrow C, and C is impossible, then either A is false, or B is false.

In this case:
A = the principle of relativity
B = the assumption that FTL communication is possible
C = the conclusion that back-in-time communication is possible.

If you have relativity, and you also have faster-than-light communication, then you have back-in-time communication (signals arriving before they are sent).

 

[phyti]

In drawing ftl2 the ftl signal moves at 2c. B moves at .5c, with c=1
Using the SR synch convention (radar or pinging method), the emission event A(x,t)=(0,1) is assigned to B(x,t)=(-.58,1.15),
and the detection event A(x,t)=(0,1.67) is assigned to B(x,t)=(-.96,1.92).
B calculates the incoming signal as instantaneous,
and the outgoing signal at .96/(1.92-1.15)=1.25.

In drawing ftl3 the ftl signal is instantaneous. B moves at .5c, with c=1
Since the time of travel is zero, and equivalent to zero distance, emission, reflection, and detection events are simultaneous and coincident for A. Thus must be coincident for all frames.
There could be any number of cycles relative to A in zero time. No information can be obtained in zero time. The same radar method does not work for this case because it requires a finite amount of time.
This is the view of universal time, before SR, i.e. observers see events in real time(as it happens).

 

[Fredrik]

In drawing ftl2 the ftl signal moves at 2c. B moves at .5c, with c=1
Using the SR synch convention (radar or pinging method), the emission event A(x,t)=(0,1) is assigned to B(x,t)=(-.58,1.15),
and the detection event A(x,t)=(0,1.67) is assigned to B(x,t)=(-.96,1.92).
B calculates the incoming signal as instantaneous,
and the outgoing signal at .96/(1.92-1.15)=1.25.

In drawing ftl3 the ftl signal is instantaneous. B moves at .5c, with c=1
Since the time of travel is zero, and equivalent to zero distance, emission, reflection, and detection events are simultaneous and coincident for A. Thus must be coincident for all frames.
There could be any number of cycles relative to A in zero time. No information can be obtained in zero time. The same radar method does not work for this case because it requires a finite amount of time.
This is the view of universal time, before SR, i.e. observers see events in real time(as it happens).

Are you trying to show us that the reply doesn't arrive before the message was sent? I agree that you have found a scenario where it doesn't, but your scenario is very different from what we've been discussing. The speed of the reply message in B's rest frame is supposed to be the same as the speed of the original message in A's rest frame. Also, a speed of 2c (or any speed less than infinite) will be sufficient if and only if A and B are sufficiently far apart when the original message is sent.

 

[mfb]

Also, a speed of 2c (or any speed less than infinite) will be sufficient if and only if A and B are sufficiently far apart when the original message is sent.

The separation just scales the problem - as we are not interested in an absolute scale, the distance does not matter.

@phyti: That is a different scenario.

 

[Fredrik]

The separation just scales the problem - as we are not interested in an absolute scale, the distance does not matter.

OK, I agree. Distance matters for example when we say that the reply is sent 1 hour after the message is received. But it doesn't matter in the idealized scenario where the reply is sent at the time (same event) where the original message is received.

 

[phyti]

For clarification, I have one issue with the op.
The speed of B and the ftl signal do not affect the rate of the A clock.
The op seems to think a ftl signal somehow implies motion backwards in time.
Then he doesn't offer an explanation for the expected results.
The 1st case I submitted shows for any signal speed in the range of c to instantaneous, the return is always
positive/later for the A clock.
Since it is an incorrect assumption as part of his argument, he can't make a case using it.
B will have a different description, but that's not part of my disagreement.

 

[stevendaryl]

For clarification, I have one issue with the op.
The speed of B and the ftl signal do not affect the rate of the A clock
The op seems to think a ftl signal somehow implies motion backwards in time.

It does. FTL plus the principle of relativity implies motion backwards in time.

[edit] or better: FTL communication plus the Lorentz transformations plus the principle of relativity implies communication back in time.

 

[vela]

It does. FTL plus the principle of relativity implies motion backwards in time.

[edit] or better: FTL communication plus the Lorentz transformations plus the principle of relativity implies communication back in time.

I think phyti's point is that "superluminal implies backward in time" depends on the observer. Some observers will say that A sent the signal before B received it while other observers will disagree.

From A's perspective, for example, you will conclude it takes a positive amount of time for the signal to propagate from A to B and a positive amount of time for the return signal to propagate from B back to A. This doesn't change from A's perspective just because the signal travels at superluminal speeds, yet the OP simply asserts that A receives the return signal before the original signal was sent. It's not clear how the OP arrived at this conclusion.

 

[Fredrik]

From A's perspective, for example, you will conclude it takes a positive amount of time for the signal to propagate from A to B and a positive amount of time for the return signal to propagate from B back to A.

That second time is negative, i.e. A would describe the particles that carry the reply message from B to A as moving in the direction from A to B.

This doesn't change from A's perspective just because the signal travels at superluminal speeds, yet the OP simply asserts that A receives the return signal before the original signal was sent. It's not clear how the OP arrived at this conclusion.

I'm asserting it too, and I think I have made it clear how this conclusion is reached. (See the quote below).

I would agree that post #1 doesn't make it clear how the OP arrived at the conclusion, but everyone agrees that the description in post #1 is inadequate. So if you only meant to point that out, it's a bit late.

If you want to see the scenario described in more detail, see posts 133 and 134 here: https://www.physicsforums.com/showthread.php?p=2588832. Post 133 is a description of a scenario with infinite-speed messages (infinite speed in the sender's rest frame). I'm afraid I was too lazy to draw a diagram. Post 134 has a link to a spacetime diagram for a scenario with finite-speed FTL messages.

 

[stevendaryl]

From A's perspective, for example, you will conclude it takes a positive amount of time for the signal to propagate from A to B and a positive amount of time for the return signal to propagate from B back to A.

But that isn't the case. If we let e_1 be the event where the original signal is sent from A, and we let e_2 be the event where that signal is received by B (and also when the return signal is sent by B--we can assume there is a negligible delay) and we let e_3 be the event where the return signal is received by A, then

From the point of view of A:

• e_2 happens after e_1
• e_3 happens BEFORE e_1

So it's false that "it takes a positive amount of time for the return signal to propagate from B back to A". It takes a negative amount of time. The round trip takes a negative amount of time. The return signal from B arrives BEFORE the original signal is sent by A.

What you, and phyti, are saying is that no matter how fast signals propagate, a round trip always takes positive time. But SR + the assumption of FTL communication says otherwise. That's the reason people say that FTL is incompatible with SR, because together they imply seemingly nonsensical results, that a message reply can arrive before the original message is sent.

SR says that FTL in one frame means back in time for another frame. In the list of events above:

• e_1 \Rightarrow e_2 is FTL in A's frame, but back-in-time for B's frame.
• e_2 \Rightarrow e_3 is FTL in B's frame, but back-in-time for A's frame.
• The complete loop e_1 \Rightarrow e_2 \Rightarrow e_3 is back-in-time for BOTH A and B. Both of them agree that e_3 is before e_1.

 

[vela]

What you, and phyti, are saying is that no matter how fast signals propagate, a round trip always takes positive time. But SR + the assumption of FTL communication says otherwise. That's the reason people say that FTL is incompatible with SR, because together they imply seemingly nonsensical results, that a message reply can arrive before the original message is sent.

I'm not saying it always happens. I'm saying there are scenarios involving superluminal signals where, from A's perspective, nothing went backward in time. For example, event e1 can be at (t,x)=(0,0), event e2 can be at (1,2), and event e3 can be at (2,0). Events e1 and e2 are spacelike-separated, so a signal connecting them has to be superluminal. Similarly, e2 and e3 are connected by a superluminal signal. There are superluminal signals, yet, from A's viewpoint, nothing went backward in time.

I know this isn't the scenario that the OP and the others had in mind, but it does fit the general description of the situation given by (1) and (2) in the original post, that A sends a superluminal signal to B who, in turn, sends back a superluminal response. I think this was all phyti meant, that superluminal signals doesn't necessarily imply that A will always receive a response before sending out the original signal. (I'll leave it phyti to correct any misinterpretation I made.)

 

[mfb]

I'm saying there are scenarios involving superluminal signals where, from A's perspective, nothing went backward in time.

Sure, but where is the point in that?
It would be extremely weird if all possible message scenarios lead to time-travel, right?

 

[rjbeery]

If one allows for branching of worlds then none of this implies a contradiction (not that I believe in any sort of Many-World-type theories)...

 

[phyti]

fredrik: post 133 link

So if Alice receives a message at (0,0), no matter what that message is, we get a contradiction. If she doesn't receive a message at (0,0), she sends 1 at (8,0). Bob receives that message at (8,10), and replies with 1 at (8,10). So Alice receives 1 at (0,0), and we still have a contradiction.

There is no contradiction. You have a two part program that runs as a signal inverter. You don't need Bob. Setup his system in the A frame, and get the same results (but not by your explanation).
The drawing is setup per your instructions, on the left, with a time line for B for clarity.
Using time only, signals detected at A(0) must be sent at B(2.7). Signals sent at A(8) must be detected at B(7.5). Signals sent at B(7.5) must be detected at A(8). Each only gets to send one signal at each specified time since their clocks are running.
Your choice of an 8 unit delay conveniently coincides with the SR calculated assignment of event A(0) to B(7.5). This is misleading to the conclusion that A(0) and A(8) are temporally connected, which they are not. They would be if using ftl signals with c’=c/v which in this case is 1.25c. Then the A ftl signal will appear to be instantaneous to B. The problem and confusion is not with ftl signals but the SR synch convention.

The motion induced phenomena of length contraction and time dilation work in a complementary way to preserve a constant round trip time for light signals, which is experimentally verifiable. In the 1905 paper, Einstein states “there is an A time and a B time, but no common time”. Despite knowing A cannot assign an accurate local time to the remote reflection event at B, he extends the theory by defining the light path segments out and back to be equal. (We can’t measure it but we can at least make it consistent).
Later in “Relativity- The Special and General Theory” 1961 Crown Publishing, pg 28, he states, the equivalent of a disclaimer, “That light requires the same time to traverse the path AM as for the path BM (M being a position between A and B) is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity”.
The simultaneity axis is not real, it’s a calculated abstraction to provide an answer where none can be found (with current scientific knowledge).
I’m all for a general disclaimer: “All things mathematical do not correspond to physical reality”.

Notice in the drawings there are ftl signals, but none moving back in time!
The instantaneous signals require zero time, and don’t move forward or backward, and are the limit of speed.
So where does this association of ftl and time travel originate?

Consider a case where people are setting up an explosive device that will be triggered by an em signal. Just as they are about to leave for the bunker the signal is received, even though it was never sent.
With that possibility, there would be fewer controlled and isolated experiments. Physical phenomena would be less consistent and more chaotic.

Cause and effect imply order, let’s preserve it.

 

[stevendaryl]

Notice in the drawings there are ftl signals, but none moving back in time!
The instantaneous signals require zero time, and don’t move forward or backward, and are the limit of speed.
So where does this association of ftl and time travel originate?

Because it's provable that FTL plus SR plus the principle of relativity implies the possibility of sending signals into the past. This has been explained several times. I don't understand what it is that you don't understand.

 

[Fredrik]

fredrik: post 133 link

There is no contradiction. You have a two part program that runs as a signal inverter.

If the one and only message that's sent at (0,0) is "1", then the one and only message sent at (0,0) is "0". That's a contradiction. If the one and only message that's sent at (0,0) is "0", then the one and only message sent at that event is "1". That's a contradiction too.

You don't need Bob.

We do if the only non-standard assumption is that there exist transmitters that can send messages at infinite speed.

The drawing is setup per your instructions, on the left, with a time line for B for clarity.
Using time only, signals detected at A(0) must be sent at B(2.7).

This is wrong. A signal that has infinite speed in the sender's rest frame, is moving as described by one of the sender's simultaneity lines. These aren't horizontal lines in the diagram. B's simultaneity lines are parallel to the line between (0,0) and (8,10).

By the way, it's confusing to see coordinates from the inertial coordinate system that's comoving with B, in the diagram showing A's point of view. (I assume that's what the 2.7 and 7.5 are).

This diagram is all it takes to show the general idea.

We assume that A and B both have transmitters that can send messages at infinite speed (relative to themselves, of course). When A sends a message at event 1, it moves as described by one of his simultaneity lines, so B receives the message at event 2 and immediately sends his reply. When B sends a message, it moves as described by one of his simultaneity lines, so A receives the reply at event 3, which is clearly in the causal past of event 1.

 

[.Scott]

You can clearly set up an experiment where FTL results in a drilling back through time.
Say we had three trains (A, B, and C) of FTL transponders each traveling at near light speed, each running along the plane of Neptune's orbit and tangent to it, each traveling in the same direction as the orbit where they reached it, and those tangent points were 120 degrees apart from each other.

We'll number the transponders on the A train are number A1, A2, ..., and similarly with B and C.

Given the right spacing, you could set up this situation:
1) Just An reaches its tangent point, it sees Bn reaching its tangent point.
2) Just Bn reaches its tangent point, it sees Cn reaching its tangent point.
3) Just Cn reaches its tangent point, it sees A(n-1) reaching its tangent point.

Then with instantaneous data transmission, any message present at any tangent point at any time (ex, B9999) could be circulated around so that even A1, B1, and C1 would get the message as they passed their tangent points.

But as mfb said:

- such a device switching in the described way together with the transmissions just cannot be set up. This is basically the self-consistency principle. And the principle could be realized - see the thread Simulating Closed Timelike Curves through Quantum Optics.

In other words, if you travel backed in time before your parents were born to meet your grandfather, you don't kill him. No matter what your intentions or devices, you just don't succeed in killing him. If you do, you didn;t really travel back through your own time, did you?

 

[phyti]

If the one and only message that's sent at (0,0) is "1", then the one and only message sent at (0,0) is "0". That's a contradiction. If the one and only message that's sent at (0,0) is "0", then the one and only message sent at that event is "1". That's a contradiction too.


We do if the only non-standard assumption is that there exist transmitters that can send messages at infinite speed.


This is wrong. A signal that has infinite speed in the sender's rest frame, is moving as described by one of the sender's simultaneity lines. These aren't horizontal lines in the diagram. B's simultaneity lines are parallel to the line between (0,0) and (8,10).

By the way, it's confusing to see coordinates from the inertial coordinate system that's comoving with B, in the diagram showing A's point of view. (I assume that's what the 2.7 and 7.5 are).

This diagram is all it takes to show the general idea.

We assume that A and B both have transmitters that can send messages at infinite speed (relative to themselves, of course). When A sends a message at event 1, it moves as described by one of his simultaneity lines, so B receives the message at event 2 and immediately sends his reply. When B sends a message, it moves as described by one of his simultaneity lines, so A receives the reply at event 3, which is clearly in the causal past of event 1.

The B simultaneity axis is a convention defined by Einstein, and as he stated, has nothing to do with the physical propagation of light. Neither the actual or calculated refection event can be verified. It merely provides consistency regarding c. The reason it works is because the round trip time for light for any moving frame is equivalent to the hypothetical fixed frame.

 

[phyti]

fredrik: post 133 link

Additional analysis (to avoid long posts).
It's easy to get conditioned to the idea of time as a continuum, and this is one example.
A light (or mechanical) clock establishes a frequency standard or tick rate which by its nature is discrete. The computers contain internal clocks (synchronized to the local clocks) which allot an integral number of ticks to each operation to maintain order during processing.
Review the programs using time only.
At A(0) the (instantaneous) input 0 is processed, requiring k ticks (either type clock).
At A(8) the output is 1.
At B(7.5) the (instantaneous) input 1 is processed, requiring k ticks.
At B(7.5 + k ticks) the output is 1.
At A(8 + K ticks) the input is 1.
A and B are now loopless in Seattle!

 

[stevendaryl]

The B simultaneity axis is a convention defined by Einstein, and as he stated, has nothing to do with the physical propagation of light. Neither the actual or calculated refection event can be verified. It merely provides consistency regarding c. The reason it works is because the round trip time for light for any moving frame is equivalent to the hypothetical fixed frame.

You're right that simultaneity is just a convention in SR. There is nothing physically significant about it. On the other hand, if A sends a signal at time t_1, and the reply from B arrives at time t_2, and t_2 < t_1, that's not a matter of convention. For two timelike separated events, all observers agree on the relative order.

Look, your argument here is, I think, outside the parameters of Physics Forum discussions. You're really arguing against very established facts of physics. That they are firmly established doesn't mean that they are right, of course, but it means that Physics Forums is not the right place to argue about them.

 

[Fredrik]

The B simultaneity axis is a convention defined by Einstein, and as he stated, has nothing to do with the physical propagation of light. Neither the actual or calculated refection event can be verified. It merely provides consistency regarding c. The reason it works is because the round trip time for light for any moving frame is equivalent to the hypothetical fixed frame.

Yes, Einstein's synchronization procedure is a good way to find B's simultaneity line. But regardless of how we find it, it's a fact that all events on that line are assigned the same time coordinate by B. This means that a message from B to A that's instantaneous to B has to move as described by this simultaneity line.

Do you agree now that A gets the reply before he sends the original message?

At A(0) the (instantaneous) input 0 is processed, requiring k ticks (either type clock).
At A(8) the output is 1.
At B(7.5) the (instantaneous) input 1 is processed, requiring k ticks.
At B(7.5 + k ticks) the output is 1.
At A(8 + K ticks) the input is 1.

I don't know what you meant by "loopless", but I hope you agree that the last line in this quote contradicts the first.

I'm neglecting the time it takes to send or receive a message because it's irrelevant to the main idea. It is however relevant when we start talking about loopholes in this argument against the existence of FTL messages.

 

[stevendaryl]

Look, your argument here is, I think, outside the parameters of Physics Forum discussions. You're really arguing against very established facts of physics. That they are firmly established doesn't mean that they are right, of course, but it means that Physics Forums is not the right place to argue about them.

Just to be clear what it is that I'm saying that is firmly established:

FTL communication in any frame implies instantaneous communication in any frame

Assume that there is some speed W > c such that for any inertial frame F, it is possible to send a signal that travels at speed W from any point, at any time, to any other point. In other words, if one of these signals is sent from point x_1 at time t_1 (where the coordinates of F are used) to another point x_2, then it will arrive at time t_2 given by: t_2 = t_1 + |x_2 - x_1|/W.

If that is true for every frame, then in every frame F, it is possible to send an instantaneous signal between any two points (where "instantaneous" means that it arrives at the same time it was sent, according to frame F).

Proof: Suppose you are at rest in frame F. You want to send a signal from point x=0 at time t=0 and have it arrive at point x=L at time t=0. Then pick a second frame, F' that is moving at velocity v = -\dfrac{c^2}{W} in the x-direction relative to F. Have an ally at rest in this frame send a signal from x'=0 at time t'=0 to x' = \gamma L. It will arrive at time t' = \dfrac{x'}{W} = - \dfrac{c^2 \gamma L}{v}

Now, transform back to the frame F, and you'll see that it arrives at
x = L at time t=0

Instantaneous communication in any frame implies communication back in time

Assume that for any inertial reference frame F, it is possible to send an instantaneous signal between any two points. Then it is possible to send a message such that the reply message arrives before the original message is sent.

Proof:

Again, assume that you are at rest in frame F and that you have an ally that is at rest in a second frame F' that is moving at speed v in the +x direction, relative to frame F.

You are at rest at point x=0. At time t=0, send an instantaneous signal from x=0 to x=L. (Instantaneous from the point of view of frame F). It will arrive at time t=0. In frame F', the arrival time is given by: t' = \gamma (t - \dfrac{vx}{c^2}) = - \gamma \dfrac{vL}{c^2}. Now, have your ally immediately send an instantaneous (from the point of view of frame F') message back to you. Since the return signal is instantaneous, according to frame F', that means that its arrival time is the same as its sending time. So it arrives at time

t' = - \gamma \dfrac{vL}{c^2}

The arrival time t in frame F is related to t' through:

t' = \gamma (t - \dfrac{vx}{c^2})

Since the arrival location is where you are, x=0, we find:

t' = \gamma t

But we already know t' = - \gamma \dfrac{vL}{c^2}. So we have:

- \gamma \dfrac{vL}{c^2} = \gamma t

So t = - \dfrac{vL}{c^2}

That's a negative number. So the return message arrives before the original message was sent.

 

[phyti]

Yes, Einstein's synchronization procedure is a good way to find B's simultaneity line. But regardless of how we find it, it's a fact that all events on that line are assigned the same time coordinate by B. This means that a message from B to A that's instantaneous to B has to move as described by this simultaneity line.

Do you agree now that A gets the reply before he sends the original message?


I don't know what you meant by "loopless", but I hope you agree that the last line in this quote contradicts the first.

I'm neglecting the time it takes to send or receive a message because it's irrelevant to the main idea. It is however relevant when we start talking about loopholes in this argument against the existence of FTL messages.

A zero length object in one frame remains a zero length object in all frames, the two ends are coincident, thus coincident in all frames.

How does a zero length time interval for an instantaneous signal in one frame, become a finite length interval in a different frame?

Zero duration implies no motion, i.e. the time to travel from A to B is independent of the distance A to B.

Notice B cannot assign a local time for the A(0) event until the return at B(13.5) of the signal sent at B(1.5).

These are basic questions about object and light motion, and time, and instantaneous signals which appear to violate causality.

 

[Fredrik]

A zero length object in one frame remains a zero length object in all frames, the two ends are coincident, thus coincident in all frames.

How does a zero length time interval for an instantaneous signal in one frame, become a finite length interval in a different frame?

Lorentz transformations tilt simultaneity lines. The synchronization procedure will give you the same result. Not sure what more I can tell you.

When you compare the length of an object in two different inertial coordinate systems, you're comparing numbers that two different coordinate systems are assigning to two different spacelike lines. When you compare the duration of an FTL trip in two in different inertial coordinate systems, you're comparing numbers that two different coordinate systems are assigning to the same pair of events.

A better comparison would be to the fact that two events at the same spatial coordinate in one inertial coordinate system are at two different spatial coordinates in another inertial coordinate system.

Zero duration implies no motion,

In a way, yes. Infinite speed motion is more like a very long object that pops in and out of existence in an instant. But infinite speed implies that the time coordinate of departure and arrival are the same. If the arrival has a greater time coordinate than the departure, then the average velocity $(x_A-x_D)/(t_A-t_D)$ is finite.

If the idea of infinite speed bothers you, then just consider an extremely high speed. Large enough to make the world line of A's message to B almost horizontal. This isn't going to change anything important. It's just going to make it more difficult to figure out the exact slope of the world line of the message from B to A.

Notice B cannot assign a local time for the A(0) event until the return at B(13.5) of the signal sent at B(1.5).

Such issues are irrelevant. Their comoving inertial coordinate systems assign coordinates to all events, whether these guys are aware of what those coordinates are or not.

...and instantaneous signals which appear to violate causality.

That's the point of this scenario. It was thought up as an argument against the existence of tachyons.

 

[phyti]

Scenario in the linked post 133.
Fidelity of signal is lost due to program A swapping characters.

Scenario is revised eliminating programs.
Pic 1 has revised ct axis, with a common origin for simplification.
A event is A(0, 4.5).
A sends instantaneous signal (magenta) to B, pic 1.
B assigns time of 7.5 to A event using SR convention (blue), pic 1 and 2.

We assume that a tachyon emitted by one of these transmitters will move at infinite speed in the rest frame of the transmitter that emitted them.

This is contradicted in pic 2, since an instantaneous signal would have no history.
The A to B signal could be interpreted as moving backward in time, but can be explained as the result of using two different standards; an instantaneous signal for communication, and a signal at c for measuring coordinates.
In pic 3, c'=2c, so v=.8/2=.4, with 1/γ=.917.
The B radar round trip is 2.75 to 6.19, assigning A event to 4.47, offset by .34
In pic 4, c'=10c, so v=.8/10=.08, with 1/γ=.997.
The B radar round trip is 4.14 to 4.86, assigning A event to 4.50, offset by 0.
As the radar speed increases, the communication signal becomes near instantaneous in the B frame.
If a different messenger entity existed that moved ftl, the SR synch convention would have to be revised to include it as a replacement for the role of upper speed limit.
Instantaneous signals eliminate the role of cause and effect and an orderly, predictable world, and therefore undesirable.
There is a similar response in the linked post 132, to the suggestion of "abandoning causality" with
"So, instead of pushing to abandon the idea of a preferred temporal order, why not take the radiative arrow of time as fundamental vis the adoption of its archetypal form as the fundamental wave dynamic?
Anyway, this seems to me to be conceptually preferable to taking calculational conveniences as literally corresponding to the real world."

My quotes from the author of SR were intended to show the same, that his "stipulation" is only a convenience, and does not correspond to real world phenomena.

 

[stevendaryl]

Scenario in the linked post 133.
Fidelity of signal is lost due to program A swapping characters.

I have no idea what your point is. You seem to be arguing with what people are saying to you, but your argument is not in the form of declarative sentences, so it's very hard to tell what you are talking about.

 

[Fredrik]

phyti, it's impossible to tell what your point is. I don't even understand what you're talking about. Increasing radar speed? We're talking about special relativity, not fantasy.