Is the Principle of Relativity Valid for Faster-than-Light Propagation?

[ghwellsjr]

There are two kinds of tests that the laws of physics must pass in order to adhere to a principle of relativity. The first is that the equations must be able to undergo a transformation and remain the same as they were before. This is a purely mathematical operation but it does require a specific transformation. The second test is purely experimental. The relevant features of the law under question must not provide a means for an isolated observer to determine his velocity in an absolute sense.

Prior to Maxwell the Principle of Relativity used the Galilean Transformation to determine if any particular law of physics adhered to the PoR. All mechanical laws did. But Maxwell's equations did not, which lead Maxwell to conclude that the PoR was not true and a test could indicate this. But all tests, especially MMX, did not support this conclusion.

So along comes Lorentz who discovered a different Transformation for the PoR that would support Maxwell's equations. But it didn't support all the other laws of mechanics so these were modified to make everything adhere to the new PoR under LT.

But everyone still assumed that there was a preferred state of rest, primarily because it never occurred to them that time could be relative. This was embodied in LET. Notice that the equations of LET do not change when going through the LT and there is no experiment that can discover velocity in an absolute sense. So LET adheres to the two requirements of the PoR based on LT.

Along comes Einstein who points out that you could take the defining characteristic of the ether frame, the one-way speed of light, and assume it to be true for any reference frame, and this results in time (and space) being relative.

It is clear that both SR and LET use the same transformation as the requirement to fulfill the mathematical aspects of the PoR. Einstein called this his first postulate. Whether or not Lorentz explicitly used the same terminology, the import is the same. Lorentz then assumed that the one-way speed of light was c only in the ether rest state, whether or not he explicitly stated this as a second postulate. Einstein's explicit second postulate ran counter to this stating that this was true in every inertial frame.

It's the fact that both of these two second "postulates" are not based on measurement or experiment that makes both LET and SR remain viable while still adhering to the new principle of relativity base on the Lorentz Transformation.

 

[Saw]

Agreed. And LET asserts the existence and reality of said PoR violating fairy-tale.

As to this, a more precise affirmation is that LET hypothesizes the existence of an aether that *would* act as a preferred frame *if* it existed. Differences with your interpretation:

- It is a hypothesis, something that is quite in conformity with the scientific method. People look for the Higgs boson or looked for the neutron in the past on the basis of hypothesis and that is regarded as legitimate.

- In this case, however, I do not think that LET really wants to find proof of the aether, since it is postulated by the theory that it is undetectable.

- Anyhow, if the aether were found due to some unexpected phenomenon that violates Lorentz-invariance, I gather it would also be possible to detect the velocity of each frame with regard to the aether. In that (unlikely) case, what we would do is feeding the equations with aether values and that would be in conformity with the PoR, through Galilean transformations.

The consequence is that LET adheres to the PoR no matter whether the hypothesis of the aether is confirmed or not:

- If it is not, LET adheres to the PoR based on LTs.
- If it is found, it comes back to the classical PoR, based on GTs.

LET only violates the PoR if you use measurable quantities like local time to express your equations

I suppose you are assuming here that LET holds that, because an aether exists, the PoR based on "local" (measurable) time is wrong or some other negative adjective.

It is not so historically. Lorentz, as shown above, admired and endorsed Einstein's view. So did Poincaré, among other things because he had anticipated almost the same himself, though in less categorical form.

As explained above, it is not so at logical level, either. You can hypothesize that there is an aether behind and however be quite happy with the practical PoR, which solves all your problems.

if you instead used the unmeasurable "real position" and "real time", then it is a Galilean-invariant theory albeit one that violates Occam's Razor.

I agree with the first part, I am not so sure about the second. It is true that the aether is a funny explanation in so far as it is postulated as unprovable. However, it is the *only* physical explanation that we have. Postulating the PoR, without further comment, is not an explanation, it is the assumption that the physical explanation, whatever it is, will conform to the PoR.

And I have been commenting, with no answer, that the aether idea serves at least for differentiating levels of precision associated to the PoR. Does any of you agree with the idea that a Galilean aether-based PoR would be ready to account for hypothetical FTL phenomena, whilst a Lorentzian-Einstenian PoR would not be precise enough to respond to those phenomena?

It is clear that both SR and LET use the same transformation as the requirement to fulfill the mathematical aspects of the PoR. Einstein called this his first postulate. Whether or not Lorentz explicitly used the same terminology, the import is the same. Lorentz then assumed that the one-way speed of light was c only in the ether rest state, whether or not he explicitly stated this as a second postulate.

I do not follow you here. If we admit that LET uses the same mathematical form, the LTs, then we admit that it is contented with "local measurements" and with the speed of light (c) which is obtained in any frame through said measurements and which is invariant (otherwise the LT does not work).

It is true that LET, apart from that, leaves open the possibility that an aether is found. But if it were actually found, then other "aether measurements" would be possible, it would also be possible to fix the velocity of each frame with regard to the aether, and we would come back to GTs, that is to say, another mathematical form…

 

[Dale]

As to this, a more precise affirmation is that LET hypothesizes the existence of an aether that *would* act as a preferred frame *if* it existed.

So you agree that if it exists the aether is a preferred frame. That is enough for me.

Regarding the rest, you are confusing postulates with hypothesis.

 

[ghwellsjr]

It is clear that both SR and LET use the same transformation as the requirement to fulfill the mathematical aspects of the PoR. Einstein called this his first postulate. Whether or not Lorentz explicitly used the same terminology, the import is the same. Lorentz then assumed that the one-way speed of light was c only in the ether rest state, whether or not he explicitly stated this as a second postulate.

I do not follow you here. If we admit that LET uses the same mathematical form, the LTs, then we admit that it is contented with "local measurements" and with the speed of light (c) which is obtained in any frame through said measurements and which is invariant (otherwise the LT does not work).

The value of the speed of light can be obtained in any frame through measurements and is invariant but the assignment of the one-way speed of light is not predetermined by any transform.

When confirming that the equations for a particular law of physics do not change after being transformed, there is no assignment of values. Everything is done purely at the symbolic level. All the variables are left as variables, they are not given values. The whole point of the exercise is to prove whether or not the equations themselves change when transformed. If you assign values to the variables then of course they are going to change after being transformed but that won't prove anything.

It is true that LET, apart from that, leaves open the possibility that an aether is found. But if it were actually found, then other "aether measurements" would be possible, it would also be possible to fix the velocity of each frame with regard to the aether, and we would come back to GTs, that is to say, another mathematical form…

No, LET doesn't leave open the possibility that an aether can be found any more or less than SR does. And I'm not sure what you mean by finding an aether. We already know that there is no preferred frame based on the conformity of the currently established laws of physics and the experimental evidence. If you are suggesting that a new law were to be discovered that did not transform intact under LT, then we would have to see if experimental evidence could identify a preferred frame. If it did, then the principle of relativity would be out the window along with LET and SR and a whole lot of other things. If it didn't, then we would have to come up with a new transformation that would work with this new law and we would then have to go back and modify all our other laws of physics to conform to this new transform but the modification for LET and SR would be identical. The only thing that would distinguish between LET and SR would be experimental evidence that the one-way speed of light could be measured which is the same thing as saying if time were absolute, but this would also violate the principle of relativity and negate both LET and SR. You really need to think through the implications of the idea that an aether could be found.

 

[harrylin]

[..] The PoR relates to the equations. In a theory (like LET) where the equations describe unmeasurable "reality" then the PoR does, in fact, relate to the unmeasurable "reality" also.

Not exactly. The PoR as formulated (in different ways) by Poincare as well as by Einstein (who based himself on Poincare) refers to the laws of nature which relate to observations of natural phenomena. Therefore Lorentz had no issues with Einstein's formulation of the PoR.

[..] Lorentz placed a strong fundamental distinction between "time" and "local time". The unmeasurable "time" was only valid in the aether frame, and when Maxwell's equations were expressed in terms of "time" they were therefore only valid in the aether frame. So, the aether still represents an unmeasurable violation of the PoR because the variables in the aether frame only apply to that frame.

That's a non-standard formulation of the PoR which doesn't permit verification; and it would similarly imply that Newtonian mechanics violates the PoR. As I know that Lorentz as well as Langevin accepted and taught special relativity, for me it's a line of thinking that doesn't lead anywhere.

 

[harrylin]

[..] It is true that LET, apart from that, leaves open the possibility that an aether is found. But if it were actually found, then other "aether measurements" would be possible, it would also be possible to fix the velocity of each frame with regard to the aether, and we would come back to GTs, that is to say, another mathematical form…

There is no requirement to determine all aspects of something (such as size, or colour, or velocity) in order to "find" it. For example, Lorentz and later also Einstein held that an ether exists (as some of its aspects had been "found"), without the possibility to determine our velocity with respect to it - that model doesn't constitute a preferred frame for the laws of nature.

 

[Dale]

Not exactly. The PoR as formulated (in different ways) by Poincare as well as by Einstein (who based himself on Poincare) refers to the laws of nature which relate to observations of natural phenomena.

Please post a reference. I have only seen the PoR formulated in terms of the equations of a theory.

That's a non-standard formulation of the PoR which doesn't permit verification

No, it is a completely standard formulation of the PoR, see the Wikipedia link above. It is the theory that contains an entity which doesn't permit verification. The inability to verify the PoR comes from the application of the standard PoR to a theory with unverifiable entities, not from the PoR itself.

 

[lugita15]

It is the theory that contains an entity which doesn't permit verification. The inability to verify the PoR comes from the application of the standard PoR to a theory with unverifiable entities, not from the PoR itself.

Dalespam, I think we have exactly the same view of the principle of relativity.

 

[Saw]

I would like to comment all posts, they are filled with valid ideas. For lack of time, I will focus on the practical side.

So you agree that if it exists the aether is a preferred frame. That is enough for me.

Well, now we know what I think. What do you think yourself? Don't tell me that you believe in the PoR, based on experimental evidence. Everybody believes so. The question is the question I have been repeatedly asking, with no answer.

*As a general rule*, as commented, the aether is good for nothing, it is only "theoretically" preferred since without the aether you can solve all practical known problems. But it would make a "practical" difference in an *exceptional* case: if you also admit FTL travel.

For an example, I will quote myself from another thread:

Imagine a duel on a Train (red frame) […]. Duelers (Back and Front) shoot when they receive light signals from the mid-point of the wagon. Now, when Back is warned by the corresponding signal, a guy by him on the Ground (blue frame), shoots at Front (event P). He shoots a superluminal bullet (let us imagine, for simplicity, an instantaneous one) and wounds Front... when? If you follow with your finger the simultaneity blue line of the Ground frame (horizontal), you see that Front would be wounded at event Q. In the Ground frame, that means that Front is hurt before receiving its own signal. That is already unfair enough. Now Front Fires back the same bullet, which is supposed to travel also instantaneously. When does it hit the aggressor? If you follow with your finger the red simultaneity line of the Train frame (descending), you will find out that the aggressor is punished before he committed his own felony. So the bullet in question has traveled back in time and this has created an inconsistency, a paradox.

There are two possible positions:

A) As the recent controversy about neutrinos potential FTL velocity has reminded us, some scientists fear that "yes, such contradictions and violations of causality could arise".

B) My answer would be that "no, what is absurd cannot happen".

The two positions are obviously linked to our subject matter:

- For A, the Lorentzian-Einstenian PoR is so sacrosanct that we must accept that all frames are right to all effects, no matter if that leads to surprising consequences.
- For B, the Lorentzian-Einstenian PoR is only useful in non-FTL situations. For FTL challenges, frames feeding with their local simultaneity measurements should admit that their discrepant versions of what happens cannot be all of them right. However, if one frame happened to prove that it is the aether frame, all the others would bow to it, accepting that only such frame has the answer, based on its simultaneity measurement, since the latter is as good as if it had been made with clocks synced through instantaneous signals.

What do you agree with, A (no preferred frame + contradictions) or B (preferred frame + but you preserve reality)?

Note: I must say that the teaching of all this is that the aether concept is just an intellectual tool that helps you better reason and thus save money by not buying books about time travel. Funnily enough, the very idea of an aether seems to rule out FTL travel.

 

[Dale]

There is a very long thread already on this topic. I see no need to rehash it here. If you want my comments on the matter see
https://www.physicsforums.com/showthread.php?t=554741

 

[Saw]

There is a very long thread already on this topic. I see no need to rehash it here. If you want my comments on the matter see
https://www.physicsforums.com/showthread.php?t=554741

It is a really long and complicated thread... I have had a quick look at it and it seems that you and others' view is that if FTL brings about contradictions in SR, so does it in LET, i.e. the observer in the aether frame would also agree on the contradictions. Would you mind confirming this?

 

[Dale]

Yes.

 

[harrylin]

Please post a reference. I have only seen the PoR formulated in terms of the equations of a theory.

Sorry, that's not the PoR as originally formulated and you did not post a reference yourself. I'm on travel now and we far deviated from the topic but if you can't find the definitions by Poincare I can give them when I'm back. Anyway, here is the formulation by Einstein from 1905 and which leave no ambiguity about the fact that the PoR refers to laws that describe natural phenomena:

http://www.fourmilab.ch/etexts/einstein/specrel/www/ :

"It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. [..]
the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good."

 

[Dale]

Sorry, that's not the PoR as originally formulated and you did not post a reference yourself.

I did in post 61. Just a basic Wikipedia reference. The first sentence is "In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference".

http://en.wikipedia.org/wiki/Principle_of_relativity

Anyway, here is the formulation by Einstein from 1905 and which leave no ambiguity about the fact that the PoR refers to laws that describe natural phenomena:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Yes, the PoR refers to laws, which are equations, as I said above. Note his specific focus on the equations in defining the PoR:
"the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate"

 

[Saw]

Yes.

Thanks. I see your point. The answer to that can be:

- Contradictions are illogical, so the contradictory facts cannot take place.

- One should reach that conclusion after analyzing the problem from *any* frame, *if* one adequately interprets the data measured in the same plus the concepts fed with those data.

- It may happen, however, that some perspective, some frame is more convenient in that it makes the solution more apparent, easier to perceive.

- Once the solution is found on the basis of one frame's data, we know that it should also be reached from any other frame. It may be more or less difficult to explain it, since sometimes concepts are very entangled, but the goal is forcefully reachable.

- To judge a situation from a given frame you do not need to be physically placed on that frame. You do not need to have "detected" that frame. It is not even necessary that such frame "exists" at all! You can act "as if" that frame existed. I think this links with something harrylin has said a few posts ago. Science works on the basis of models, which do not need to have a match in physical reality, it suffices that each of their elements is well characterized.

- Thus one can build a model where there is a frame (called the "aether") that serves as the medium for propagation of light (and any other causal influence), a medium that is non-ponderable and immovable.

- It is logical to presume that in this frame one would carry out "aether sync" and would measure "aether simultaneity", meaning that between two simultaneous events there can be no causal connection *even if the connecting agent travels instantaneously*.

- If all frames could also measure that type of simultaneity, they would and their measurements would be related by the GT. However, it is in the essence of an immovable (non-draggable) aether that such thing is impossible. So other frames measure relative (= local = non-aether) time. Fortunately, nevertheless, all measurements can be related through the LTs and they are all valid and on equal footing (among themselves and with the aether frame) for the purpose of solving practical problems… IFF the agent of the problem is not FTL.

- Thus if someone poses a problem involving FTL travel and suggests that violations of causality may arise, the counter-argument is easy:

* I analyzed the problem from the aether frame and concluded that no contradictions may arise.
* From any other frame you can conclude the same but not by looking at a spacetime diagram that is built on the basis of relative measurements, related by the LTs, since such diagram will only depict the solution to problems where the premise of the theory (FTL travel is impossible) is true.
* If you still want a solution from those frames, use your imagination. Imagine that you somehow get the conversion unit between your local time and aether time. Then feed your equations with that aether time and thus you will predict the same outcome.
* Unfortunately, that is not possible right now. By logic we can infer that two contradictory things cannot happen. But we cannot predict what single thing will happen, if the FTL influence will arrive in time, for example, to save the heroine from the villain.

Conclusion: it is true that the math, the LT, is the same for SR or LET but it is more important to know what the symbols of the equation (for both theories, with or without aether model) mean. If you are using the LT, that means that you are feeding the concepts with time measured through instruments whose oscillation is based on the known forces, which are not FTL. So they are not apt for solving FTL challenges.

Sorry for the long post.

That is how I avoid logical contradictions, armed with the aether model and a shiny Occam's razor.

How do you? Some do by resorting to parallel universes, cosmic police, lately quantum teleportation… Not very Occam-like methods…

 

[Saw]

Sorry, that's not the PoR as originally formulated and you did not post a reference yourself. I'm on travel now and we far deviated from the topic but if you can't find the definitions by Poincare I can give them when I'm back.

Maybe you mean this one, given by Poincaré at the St-Louis exhibition in 1904:

". . . the principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation, so that we have not or could not have any means of discerning whether or not we are carried along in such a motion."

Edit: whole text here

 

[Dale]

That is how I avoid logical contradictions, armed with the aether model and a shiny Occam's razor.

How do you?

See my many posts in the other thread. In summary, if the law of physics describing the FTL phenomenon is Lorentz-invariant then it is possible to violate causality in the aether frame. If the law of physics describing the FTL phenomenon is not Lorentz-invariant then LET is contradicted just as much as SR (but LET would be easier to patch up).

I am exhausted on the topic and not willing to further discuss it here.

 

[Dale]

". . . the principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation, so that we have not or could not have any means of discerning whether or not we are carried along in such a motion."

Again, laws of physical phenomena are equations.

 

[Saw]

See my many posts in the other thread. In summary, if the law of physics describing the FTL phenomenon is Lorentz-invariant then it is possible to violate causality in the aether frame. If the law of physics describing the FTL phenomenon is not Lorentz-invariant then LET is contradicted just as much as SR (but LET would be easier to patch up).

I am exhausted on the topic and not willing to further discuss it here.

I understand that. I may start another thread to see if someone can clarify that to me, because (thinking aloud) I agree on the importance of the nature of the FTL phenomenon, but do not see how you can still find causality violations. If the FTL is just like light but faster ("superlight"), you should measure (sync clocks, fix distances, register durations) with it and then you'd get a ST diagram where the space-like events become superlight-like events and hence there is no discrepancy between frames as to their sequence...

But never mind, if we leave aside that issue, if we remain in the domain where the LT solves all problems without contradictions, then the discussion is only why it does so.

You say that, according to LET, the PoR under the LT applies only because the universe conspires to deceive us (we only see appearances) but reality is that there is a preferred frame where true simultaneity shines up. If we define LET that way (to agree with you), then LET is a bad conceptual explanation. Einstein more or less said (I may embellish the expression a little) that concepts are not carved out in a stone waiting for us to discover them. There is not an a priori realm where they lie, with a predefined content and meaning. They are what they empirically happen to be. So if we measure relative time, that is reality.

A different thing is that you may invent another concept of time, with another content, to solve intellectual challenges, even if that concept exists only in your mind. That is the aether time I talked about before, which has the same content as Newtonian time (although classically it was assumed that all frames would measure the same time, which is not the case with aether time).

What is radically forbidden, however, is to mix the two things up, which is what happens when you end up accepting causality violations, but sorry I am coming back to the other subject, not to be discussed here.

 

[ghwellsjr]

Maybe you mean this one, given by Poincaré at the St-Louis exhibition in 1904:

". . . the principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation, so that we have not or could not have any means of discerning whether or not we are carried along in such a motion."

Edit: whole text here

That's a very interesting paper by Poincaré published just one year before Einstein's paper introducing Special Relativity. Thank you very much for that link. I don't know how anyone could claim that Poincaré was on the verge of coming up with SR on his own. He knew something was amiss but he didn't know what direction to go in.

You quoted from a section where he briefly touched on the principle of relativity but his fuller discussion about it begins later on page 7 ending with this comment:

Thus, the principle of relativity has been valiantly defended in these latter times, but the very energy of the defense proves how serious was the attack.

He is talking about how the PoR based on the Galilean transformation was violated by Maxwell's equations and it wasn't until the experiments of Michelson that PoR was defended but it required a new transformation attributed to Lorentz. Yet, Poincaré still also defends an absolute state of rest as expressed by LET. So prior to Einstein, we've got the principle of relativity based on the Lorentz transformation and a belief in an absolute rest state.

Note that the Galilean transformation permits FTL because it doesn't have a "c" in the equations for the transformation. But the Lorentz transformation does have a "c" and as soon as "v" reaches "c" the transformation falls apart.

Poincaré realized this and he stated at least twice in his paper that FTL was impossible, once at the top of page 7 ("no velocity can surpass that of light") and once in the last paragraph ("the velocity of light would become an impassible limit"). So even with LET and a belief in an absolute rest state, FTL is impossible. We can never return to the principle of relativity based on the Galilean transformation, even if we claim an ether, because Maxwell's equations describing EM processes don't remain intact after going through GT, (which would permit FTL). Instead we need a principle of relativity based on LT which doesn't permit FTL. Remember, this is all before Einstein's Special Relativity.

 

[Saw]

I don't know how anyone could claim that Poincaré was on the verge of coming up with SR on his own. He knew something was amiss but he didn't know what direction to go in.

Probably. It is clear that Lorentz and Poincaré were more timid and Einstein bolder. More specifically, reading for example the accounts of the history of SR in mathpages and wikipedia one gets the impression that:

- The former, especially Lorentz, were refrained by the physical explanation they had in mind. They were focused on the aether and EM phenomena and thus their conclusions were less far-reaching. In this line, the consideration of local time as not true or "real" time.

- Einstein loses those constraints and he generalizes. Thus he claims that local time is simply time, "real" time for all purposes.

I fear, however, lest the virtue might become the defect.

What do we understand by "real" time? Time is a human invented concept. If the invention process is good, it is based on an empirical basis and has an empirical purpose. Time is what you empirically measure with an instrument and your goal is predicting what may empirically happen to a real-life agent and thus solve problems. Between the two things, instrument and real-life agent, there must exist an analogy, so that the former "mirrors" the latter. And that depends precisely on the physical mechanism that is behind each process! Hence you cannot absolutely generalize. You cannot affirm that your measurement is valid for all purposes, it will be valid only for capturing processes ruled by the same physical mechanism.

Thus Einstein's insight is that the speed of light is not only the speed of light but also the speed of causality no matter the physical mechanism, i.e. the force responsible for the relevant interaction, since all of them are essentially equivalent, at least in this respect. To put it in modern terminology, all force-mediating particles travel at c. His merit is hence this generalization.

However, as you point out, it is essential to this theory that nothing can surpass the speed c, though not by chance, not by some whimsical decree but due to some (unknown but for sure existing) physical reason.

What if, however, FTL appears on the scene? Then the generalization is not valid any more, because that FTL travels must be animated by a different force.

[…] the Lorentz transformation does have a "c" and as soon as "v" reaches "c" the transformation falls apart. .

I am just trying to specify in what sense it falls apart. Take a real situation, like the duel defined in post #79.

We have ST diagrams of a certain story drawn with the measurements of two frames, red and blue. Those measurements are related by the LTs. Now we imagine that a FTL signal, even an instantaneous one, joins events P and Q. Is the ST diagram, is the LT with which it has been built still valid? Yes, of course. The LT is still telling us the truth it is meant to provide: if blue clock reads blue t at event Q, then red clock will read red t as provided by the LT. The clocks mechanisms are not based on a FTL mechanism, so blue can perfectly predict red and vice versa. What the LT cannot tell us is whether the signal in question, departing from P at blue time t will arrive at Q, where blue time is also t.

And that is where the aether model turns out to be helpful, as an intellectual tool. No matter if the aether exists or not (I do not care) this model helps me speak out the solution. If the instantaneous signal does so, that is because the blue frame is the aether frame. Hence when the signal returns (also instantaneously) it should hit the aggressor at event P itself (not at R, traveling back in time, as a defective reading of the diagram would suggest).

[Of course, an instantaneous signal (infinite velocity) is an absurd idea. Imagine the signal is just almost instantaneous.]

 

[harrylin]

Maybe you mean this one, given by Poincaré at the St-Louis exhibition in 1904:

". . . the principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation, so that we have not or could not have any means of discerning whether or not we are carried along in such a motion."

Edit: whole text here

Yes indeed, that's one of the citations that I referred to - thanks!
The PoR that special relativity refers to (according to Poincare, Lorentz, Einstein etc.) concerns descriptions of physical phenomena - laws that are expressed with equations - and not claims about unmeasurable reality. If there is still an issue with that topic then I'll start a thread on it.

 

[harrylin]

[..] Thus Einstein's insight is that the speed of light is not only the speed of light but also the speed of causality no matter the physical mechanism, i.e. the force responsible for the relevant interaction, since all of them are essentially equivalent, at least in this respect. To put it in modern terminology, all force-mediating particles travel at c. His merit is hence this generalization.

In fact Poincare explained in 1904, based on Lorentz' paper, that his "new mechanics, [..] would be, above all, characterized by this fact, that no velocity could surpass that of light". [PS: I now see that ghwellsjr already mentioned that fact.]

However, as you point out, it is essential to this theory that nothing can surpass the speed c, though not by chance, not by some whimsical decree but due to some (unknown but for sure existing) physical reason.

In the footnote Poincare explained the physical reason for matter as follows:
"Because bodies would oppose an increasing inertia to the causes which would tend to accelerate their motion; and this inertia would become infinite when one approached the velocity of light."

What if, however, FTL appears on the scene? Then the generalization is not valid any more, because that FTL travels must be animated by a different force. [..]

Yes, Poincare also speculated on that and stressed that then "we should observe discrepancies which would render evident the common translation of the two stations" - in other words, that would allow to break the PoR. Thus if one assumes the PoR, measurable FTL cannot be possible. However, we know from QM theory that FTL propagation can be imagined that cannot directly be measured but only inferred. In such a case FTL can be conceived while the PoR (that is, the PoR of Poincare and Einstein) is still not broken.