Proof of impossibility of superluminal signals?

[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.

 

[Mark_Laverty]

I really do believe we have the whole concept of superluminal anything and time travel completely wrong.

E.g a person hops in a wormhole and instantly travels across the galaxy nearly 100,000 light years away. The clocks at the place they left don't stop ticking, they carry on moving forwards in time. The person hops in a wormhole and travels instantly back to where they started a few seconds later by their clock.

They won't arrive back before the left, they arrive back a few seconds after they left measured by clocks at the place of departure/return.


And yes I understand concepts like light cones. The light from an event is not the event itself. Just because we perceive an event happening after it has happened does not mean it has not happened until we perceive it by observing its light.

Relativity predicts that superluminal travel is impossible and that it would lead to paradox's/cause before effect.

As such if superluminal travel is possible relativity has to be wrong. As such we can't use relativity to make reliable predictions about what would happen if superluminal travel were possible. We'd need a new theory...

That's what I think anyway...

 

[PeterDonis]

They won't arrive back before the left, they arrive back a few seconds after they left measured by clocks at the place of departure/return.

Here's the problem: you can't just *say* this. You have to *prove* it; that is, you have to show that it must be true using the assumptions and equations of relativity. Try doing that; you will see that it's not as simple as you think.

And yes I understand concepts like light cones. The light from an event is not the event itself. Just because we perceive an event happening after it has happened does not mean it has not happened until we perceive it by observing its light.

Nobody is claiming this, so you are attacking a straw man.

Relativity predicts that superluminal travel is impossible and that it would lead to paradox's/cause before effect.

That's not quite true. It's quite possible to construct scenarios in which objects travel at superluminal speeds, travel through wormholes, etc., that do not violate any requirements of relativity, do not violate causality, etc. You just have to be very careful to make the scenarios self-consistent, which does rule out a lot of the staple science fiction scenarios.

In fact, mathematically, general relativity even contains solutions, such as the Godel universe, which have closed timelike curves, i.e., curves along which objects traveling slower than light all the time end up in their own past. AFAIK nobody thinks these solutions are actually realized physically, but the fact that they exist means you have to be very careful saying what "relativity predicts".

if superluminal travel is possible relativity has to be wrong.

More precisely, if any of the staple science fiction scenarios are possible, the ones that violate requirements of relativity, then relativity has to be wrong.

As such we can't use relativity to make reliable predictions about what would happen if superluminal travel were possible. We'd need a new theory...

More precisely, if we ever got any evidence that any of the staple science fiction scenarios are possible, then we'd need a new theory. Feel free to wake me up when that happens...

 

[Fredrik]

Here's the problem: you can't just *say* this. You have to *prove* it; that is, you have to show that it must be true using the assumptions and equations of relativity. Try doing that; you will see that it's not as simple as you think.

I think he got that specific thing right. He's just talking about going through a wormhole to a distant location, and then immediately going back through the same wormhole.

 

[rjbeery]

E.g a person hops in a wormhole and instantly travels across the galaxy nearly 100,000 light years away. The clocks at the place they left don't stop ticking, they carry on moving forwards in time. The person hops in a wormhole and travels instantly back to where they started a few seconds later by their clock.

Define instantly. That's where you will find the problem.

 

[Mark_Laverty]

Hi,

The reference to the light cone thing was because last time I voiced these opinions they were put forward as an explanation of why they were wrong.

I wasn't aware of the rest of your points, I'll do some digging. Thank you :-)

As for the proof bit... Relativity is a theory, and theories themselves are not proof. You can not prove something with a theory, rather a theory requires proof.

What's more no theory can ever be 100% proven. Just tested to the point where you can be really really sure its right, but never 100% certain.

I'd even go so far as to say that the burdon of proof is the other way round. If relativity predicts cause before effect then that is an extrodinary claim that requires extrodinary evidence to support. Until I see proof of cause before effect due to superliminal travel personally I find it very hard to accept.

That last paragraph is probably a sign of my ignorance, but no matter how hard I try it j st doesn't seem right.

I'm not arguing that superluminal travel is possible, just that predictions of cause before effect rulling it out can't, I feel, be relied on.

 

[Mark_Laverty]

Define instantly. That's where you will find the problem.

Within a second according to their watch and the clocks of the place they left behind.

Just because the place they left behind doesn't see them appear 100,000 light years away until 100,000 years later (assuming they had a telescope to see the other side of the galaxy) doest mean they weren't there one second after they jumped into the wormhole.

 

[stevendaryl]

As for the proof bit... Relativity is a theory, and theories themselves are not proof. You can not prove something with a theory, rather a theory requires proof.

I think you misunderstood what people are saying. Special Relativity could certainly be wrong. The arguments about FTL signals are all conditional:

If SR is true, and FTL signals are possible, then ...

 

[PeterDonis]

I think he got that specific thing right. He's just talking about going through a wormhole to a distant location, and then immediately going back through the same wormhole.

If both ends of the wormhole are at rest relative to each other, yes, I think it would (or at least could) be that simple. But what if the ends are in relative motion?

 

[PeterDonis]

Relativity is a theory, and theories themselves are not proof. You can not prove something with a theory, rather a theory requires proof.

And relativity has the "proof" (you recognize in your next sentence that you can never really "prove" a theory, which is why I put the word in quotes), in the form of extensive experimental evidence confirming its predictions.

If relativity predicts cause before effect then that is an extrodinary claim that requires extrodinary evidence to support. Until I see proof of cause before effect due to superliminal travel personally I find it very hard to accept.

I'm confused about the position you are defending. Relativity predicts that *if* FTL travel were possible, *and* some other assumptions were true (the ones that ground the sci-fi scenarios I referred to), then causality would be violated. Since relativity says causality can't be violated, therefore, relativity predicts that, either FTL travel is impossible period, or, if it is possible, it is only possible *if* the other assumptions (the ones that ground the sci-fi scenarios) do not hold. In other words, if relativity is correct, than the kinds of scenarios that are possible that include FTL travel are very limited, because they have to be self-consistent: that is, there has to be one single spacetime model that includes any "causal loops" without breaking consistency, i.e., without assigning multiple physical outcomes to the same event. (Google "Novikov self-consistency principle" if you want to see more detail along these lines.)

Do you agree with the above paragraph, or are you arguing against it?

I'm not arguing that superluminal travel is possible, just that predictions of cause before effect rulling it out can't, I feel, be relied on.

Why not? Again, relativity has a huge amount of experimental support, so we are justified in having a high degree of confidence in its predictions. Also, once again, relativity does not "predict cause before effect"; it only says that *if* FTL travel were possible, *and* some other assumptions held, *then* you would have cause before effect. Relativity does *not* claim that that combination of conditions actually holds; so I don't see why you seem to be saying that relativity "predicts" that we should see evidence of cause before effect. It doesn't; that's the point.

 

[Chronos]

A wormhole that permits instantaneous travel to a distant point must be bounded by causality. The 'exit' obviously cannot be located wrt the past, which suggests a wormhole exit can only move relative to the present location of the 'entrance' - which would be very weird. On causal grounds I would argue this suggests wormholes are phantoms.

 

[rjbeery]

Within a second according to their watch and the clocks of the place they left behind.

Just because the place they left behind doesn't see them appear 100,000 light years away until 100,000 years later (assuming they had a telescope to see the other side of the galaxy) doest mean they weren't there one second after they jumped into the wormhole.

"Within a second" is still presuming that there is an actual moment 100,000 LY away which represents "instantly", when the reality is this moment changes based on the movement of the observers at each point.

That's the crux of the entire argument! If we had a way to transport "instantly" across the galaxy then I could travel 100,000 LY away and you, waiting for me there and under relative motion, could travel "instantly" back to my departure point before I left.

You are having a problem because you're thinking of time marching forward uniformly across the entire Universe as Newton did.

 

[phyti]

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.

Currently, SR deals with events that communicate at light speed c.
If a method of faster than light communication was discovered that propagated in space at c', coordinate measurements would have to be done at c' to maintain compatibility.
Speed c' would assume the role of c as the limiting speed.
Pics 3 & 4 show the ftl signal becoming more horizontal in the B frame as the measurement signals increase to c'.
Using space-time pics shows the backward in time interpretation results from the measurement signal speed not equal to the info/message speed!

 

[Fredrik]

Currently, SR deals with events that communicate at light speed c.
If a method of faster than light communication was discovered that propagated in space at c', coordinate measurements would have to be done at c' to maintain compatibility.
Speed c' would assume the role of c as the limiting speed.

We're talking about the possibility that something that carries information can move faster than the invariant speed. If such a thing moves at c'>c, it wouldn't change the role of c, the only invariant speed in the theory.

 

[stevendaryl]

Currently, SR deals with events that communicate at light speed c.
If a method of faster than light communication was discovered that propagated in space at c', coordinate measurements would have to be done at c' to maintain compatibility.

Look, we've already verified that a clock moving at constant speed v relative to an inertial reference frame experiences time dilation according to

\dfrac{d\tau}{dt} = \sqrt{1-\frac{v^2}{c^2}}

If that formula is correct, then it can't also be correct if you substitute c' for c.

So no, you can't just replace c by some other speed c'. That would be nonsensical.

 

[Mark_Laverty]

@peterdonnis

I just wrote out a nice reply in which I agreed with you and said I think we were saying similar things but you explained it better than me!

E.g. I missed your emphasis on the word 'proof'.

I hit post and it didn't post and I'm struglinng for time to rewrite it (pun not intended!).

You are having a problem because you're thinking of time marching forward uniformly across the entire Universe as Newton did.

OK, this may be the problem, I'll think about this.