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

[harrylin]

So you're saying that Einstein's so-called second postulate is also a derived result, just like others on this thread have pointed out that the principle of relativity is a derived result for LET and not a first postulate?

No, I pointed out that common university textbooks don't properly phrase Einstein's second postulate, instead they make a shortcut for a simplified derivation of the Lorentz transformations. Basically what those textbooks call the second postulate is the second postulate combined with the first postulate.

 

[harrylin]

I think here Einstein is proving the compatibility of the first and second postulates, not the truth of the second postulate, which is of course an assumption of his theory.

Yes indeed; my point was that Einstein's second postulate is not inherently compatible with the first. As a matter of fact those two postulates are, as Einstein put it, "apparently irreconcilable". In contrast, the two postulates of common textbooks are obviously compatible.

 

[harrylin]

[..] LET nevertheless asserts the existence and reality of unmeasurable things. Thus, what is real is considered different from what is measured. Conversely, what is measured is considered to be an inaccurate reflection of reality. [..]

Right - that was also Newton's position. I think that it's a scientifically sound position: we must never assume that appearance equals reality.

LET argues that the PoR does not apply in reality, but that reality is unmeasurable.

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

 

[Dale]

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

Hmm, that is an interesting thought. I will have to think about that for a bit.

 

[lugita15]

The only attribute of the aether of LET is that it is a preferred frame, the one nature operates according to. It does not offer any other explanatory mechanisms regarding how nature interacts with light to cause length contraction or time dilation. So we don't want to conceive of LET as being SR plus something. It's the principle of relativity (which is not SR) plus something just like SR is the principle of relativity plus something else.

You are of course talking about the modern construct known as LET. I think historically, a fair characterization of Lorentz's theory would be Newtonian mechanics combined with length contraction, time dilation, and mass increase. And each of these effects would be explained as electromagnetic phenomena.

Prior to Maxwell, the principle of relativity was well established. As a result of Maxwell's discovery that his equations describing an electromagnet field predicted waves that happen to travel at c, he (incorrectly) concluded that this would provide a means to experimentally measure the rest state of that field and do away with the principle of relativity.

As far as I know, Maxwell was a firm believer in Newtonian mechanics and the Galilean principle of relativity. He was also presumably familiar that other wave equations had a preferred frame, like the wave equation for sound waves. Just as one could do an experiment involving sound in order to find the motion of the Earth with respect to air, he found it reasonable that we could use light to find the motion of the Earth with respect to the ether. This wouldn't contradict the PoR at all.

The principle of relativity (again, not to be confused with Special Relativity) was what forced Lorentz, et al, to formulate LET, not the other way around.

I would say that the apparent invariance of the speed of light in all reference frames plus the notion that the speed of light should only equal c in the ether frame is what forced Lorentz to LET; it had nothing to do with the PoR. The fact that the Lorentz transformations are symmetric was not known to Lorentz when he formulated them. The symmetry was a later (mathematical) discovery made by Poincare, and then of course Einstein developed SR in which the symmetry is not a coincidence.

 

[ghwellsjr]

Prior to Maxwell, the principle of relativity was well established. As a result of Maxwell's discovery that his equations describing an electromagnet field predicted waves that happen to travel at c, he (incorrectly) concluded that this would provide a means to experimentally measure the rest state of that field and do away with the principle of relativity.

As far as I know, Maxwell was a firm believer in Newtonian mechanics and the Galilean principle of relativity. He was also presumably familiar that other wave equations had a preferred frame, like the wave equation for sound waves. Just as one could do an experiment involving sound in order to find the motion of the Earth with respect to air, he found it reasonable that we could use light to find the motion of the Earth with respect to the ether. This wouldn't contradict the PoR at all.

What definition of PoR are you using that let's you identify a preferred frame by experiment?

The principle of relativity (again, not to be confused with Special Relativity) was what forced Lorentz, et al, to formulate LET, not the other way around.

I would say that the apparent invariance of the speed of light in all reference frames plus the notion that the speed of light should only equal c in the ether frame is what forced Lorentz to LET; it had nothing to do with the PoR.

I agree with this up to the semicolon, I just don't know why you think "the apparent invariance of the speed of light in all reference frames" has nothing to do with PoR.

The fact that the Lorentz transformations are symmetric was not known to Lorentz when he formulated them. The symmetry was a later (mathematical) discovery made by Poincare, and then of course Einstein developed SR in which the symmetry is not a coincidence.

OK, but what has that got to do with PoR?

 

[lugita15]

What definition of PoR are you using that let's you identify a preferred frame by experiment?

I'm just using the traditional definition "The laws of physics are the same in all inertial reference frames." Maxwell believed that space and time are absolute, so in his mind the principle of relativity implied the Galilean transformations. So the fact that his equations predicted that the speed of light is c led Maxwell to conclude that his equations violated Galilean invariance and thus could only be exactly true in one preferred frame. So he wanted to conduct an experiment to determine that frame. If he was successful, that would not violate the principle of relativity, it would just mean that his equations would have to be modified in order to become Galilean invariant, so that measurements of the speed of light in other frames would be c+v or c-v, where v is the speed of the aether with respect to you.

Think about sound: if you're moving with respect to the air, the speed of sound would be different than what is predicted by the wave equation, only because the wave equation has the air as its preferred frame (which you can determine by doing a Michelson-Morley style experiment with sound instead of light). In order to find out the properties of sound in our moving frame, we have to use a modified wave equation which is Galilean invariant (I'm sure this is a fairly trivial exercise to perform: you can redo the derivation of the wave equation for sound from Newton's laws, just assume that the air molecules are moving rather than stationary).

I agree with this up to the semicolon, I just don't know why you think "the apparent invariance of the speed of light in all reference frames" has nothing to do with PoR.

The constancy of the speed of light is only a consequence of the PoR if it is in fact a law of physics that the speed of light is c. As I said above, Maxwell had no reason to believe that this was the case; he thought his equations would only be exactly accurate in the aether frame.

OK, but what has that got to do with PoR?

Lorentz believed that errors in measuring devices due to length contraction and time dilation were responsible for the apparent invariance of the speed of light. So he thought that speed of light measurements could never reveal the ether frame, but he held out the possibility that some clever experiment might one day find out the ether frame. For instance, if both observer A and observer B were moving with respect to the ether, but at different speeds, perhaps observer A could look at how much observer B's ruler was contracted compared to his own ruler, and use that to find out their speeds with respect to ether. But Poincare proved that was impossible by demonstrating the symmetry of the Lorentz transformations, so that the transformations connected not only observer A and observer B to the ether frame, but also to each other. (EDIT: Actually, you need a little more than just symmetry to show that any two frames are connected by an LT. You need to show that the inverse of an LT is an LT, but you also need to show that the composition of two LT's is an LT. As far as I know, Poincare succeeded in proving both of these facts, but it took Einstein to realize their significance.)

Lorentz would also be shocked to learn that all laws of physics are Lorentz invariant, not just electromagnetism.

 

[Saw]

... Poincare proved that was impossible by demonstrating the symmetry of the Lorentz transformations, so that the transformations connected not only observer A and observer B to the ether frame, but also to each other. (EDIT: Actually, you need a little more than just symmetry to show that any two frames are connected by an LT. You need to show that the inverse of an LT is an LT, but you also need to show that the composition of two LT's is an LT. As far as I know, Poincare succeeded in proving both of these facts, but it took Einstein to realize their significance.)

Lorentz would also be shocked to learn that all laws of physics are Lorentz invariant, not just electromagnetism.

I like this historical description. You succeed in showing that Lorentz and Poincaré were close to formulating SR but only Einstein did. And now that he did and we all believe in the PoR and invariant c, why do we believe so? Of course, because experiment proves it. But is there any physical reason? Well, if someone says, "because light is a wave that propagates through a medium called the aether", we could answer: "you cannot prove it" but we cannot say "you are wrong", either, since neither the PoR nor invariant c are logically incompatible with the aether. I suppose you agree with that.

 

[ghwellsjr]

What definition of PoR are you using that let's you identify a preferred frame by experiment?

I'm just using the traditional definition "The laws of physics are the same in all inertial reference frames."

That is a good definition but it has consequences as Richard Feynman points out in his chapter on Special Relativity from Lectures on Physics:

The principle of relativity was first stated by Newton, in one of his corollaries to the laws of motion: "The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line." This means, for example, that if a spaceship is drifting along at a uniform speed, all experiments performed in the spaceship and all the phenomena in the spaceship will appear the same as if the ship were not moving, provided, of course, that one does not look outside. That is the meaning of the principle of relativity.​

Maxwell believed that space and time are absolute, so in his mind the principle of relativity implied the Galilean transformations.

That's an understatement. At that time, all scientists believed the principle of relativity was embodied in the Galilean transformation.

So the fact that his equations predicted that the speed of light is c led Maxwell to conclude that his equations violated Galilean invariance and thus could only be exactly true in one preferred frame. So he wanted to conduct an experiment to determine that frame.

But violating Galilean invariance is the same as violating the principle of relativity. Here's how Feynman expresses it:

However, the Maxwell equations did not seem to obey the principle of relativity. That is, if we transform Maxwell's equations by the substitution of equations [of the Galilean transformation], their form does not remain the same; therefore, in a moving spaceship the electrical and optical phenomena should be different from those in a stationary ship. Thus one could use these optical phenomena to determine the speed of the ship; in particular, one could determine the absolute speed of the ship by making suitable optical or electrical measurements.​

If he was successful, that would not violate the principle of relativity, it would just mean that his equations would have to be modified in order to become Galilean invariant, so that measurements of the speed of light in other frames would be c+v or c-v, where v is the speed of the aether with respect to you.

No, if he was unsuccessful, it would mean his equations would have to be modified, or so they thought. Here's how Feynman expresses it:

A number of experiments...were performed to determine the velocity of the earth, but they all failed--they gave no velocity at all...something was wrong with the equations of physics. What could it be?...the first thought that occurred was the trouble must lie in the new Maxwell equations of electrodynamics, which were only 20 years old at the time. It seemed obvious that these equations must be wrong, so the thing to do was to change them in such a way that under the Galilean transformation the principle of relativity would be satisfied. When this was tried, the new terms that had to be put into the equations led to predictions that of new electrical phenomena that did not exist at all when tested experimentally, so this attempt had to be abandoned. Then it gradually became apparent that Maxwell's laws of electrodynamics were correct, and the trouble must be sought elsewhere.​

So if an experiment did determine the velocity of the earth, it would mean that the principle of relativity was not valid. But since the experiments were unsuccessful, the principle of relativity survived intact but since Maxwell's equations also survived, it meant that the Galilean transformation must be in error and that's what eventually was discovered to be the case and it was replaced by the Lorentz transformation but this was all done in the context of an absolute ether rest frame.

 

[whosapopstar?]

Could there be any meaning extracted from this question:
Why should ether wind not have such properties that on the contrary, light is a phenomenon that is not influenced by it, while other phenomenon are influenced?

 

[Dale]

I have spent some time thinking about two very interesting points that were raised. I thank both lugita15 and harrylin for their interesting comments. Before addressing them, however, I think that it is important to note two things:

First, the PoR, as I have usually seen it, refers to the equations. E.g. http://en.wikipedia.org/wiki/Principle_of_relativity. It states that the equations of physics have the same form with the same universal constants in all frames of reference.

Second, from Maxwell to Einstein, the leading scientists of the day believed that the PoR was not correct, or at least that it did not apply to EM phenomena. They considered the aether frame to be a preferred frame in the sense of violating the PoR. Specifically, that Maxwell's equations only applied in the aether frame.

Sound waves have a preferred frame, the rest frame of air, yet that doesn't invalid the principle of relativity, because the wave equation for sound waves is not a law of physics and thus does not need to be true in all frames.

I understand your point here, but the difference is that the velocity of the medium for acoustic waves can be detected by non-acoustic phenomena. So, we can say that the speed of sound is isotropic in any frame where a nearby anemometer reads 0, and that is true regardless of if the anemometer is moving in some other frame. Also, Newton's equations would still hold in all frames.

On the other hand, there was supposedly no other way to detect the aether other than its effect on the speed of light. The laws of physics were simply different in that frame. Transforming to another frame would not change anything except the speed of light measurement. Maxwell's equations would only hold in the aether frame.

"LET"'s argument is moot: the PoR relates to phenomena, not unmeasurable "reality".

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.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, 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.

 

[Saw]

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.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, 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.

I do not know why you insist on sticking to the historical side of the story. I thought it was much more interesting discussing, today, on a simple logical basis, whether aether, PoR and invariant c are intrinsically incompatible or not. But if we are in historical vain, we should not stop there. I am not an expert on the subject, but the little of the direct sources I have had access to, reveals that Lorentz, either alone or prompted by Poincaré or by Einstein's work, ended up accepting everything... Everything that is the essence of SR! That the LT applies between any frame, from aether frame to A, vice versa and from A to B and vice versa. That the aether time, since it is unmeasurable, is not what should feed the equations, but that role should be played by the originally called "local time", which then becomes (since there is nothing else) simply "time". It just happens that, on top of that, Lorentz and Poincaré kept alive the hypothesis of an aether, as a possible root cause for all those things, albeit admitting that Einstein's idea of leaving it aside had been great.

This is one of many possible quotations in that line (from The Einstein Theory of Relativity, by H.A. Lorentz, 1920, available in Project Gutenberg):

It is not necessary to give up entirely even the ether. Many natural philosophers find satisfaction in the idea of a material intermediate substance in which the vibrations of light take place, and they will very probably be all the more inclined to imagine such a medium when they learn that, according to the Einstein theory, gravitation itself does not spread instantaneously, but with a velocity that at the first estimate may be compared with that of light. Especially in former years were such interpretations current and repeated attempts were made by speculations about the nature of the ether and about the mutations and movements that might take place in it to arrive at a clear presentation of electro-magnetic phenomena, and also of the functioning of gravitation. In my opinion it is not impossible that in the future this road, indeed abandoned at present, will once more be followed with good results, if only because it can lead to the thinking out of new experimental tests. Einstein's theory need not keep us from so doing; only the ideas about the ether must accord with it.

Nevertheless, even without the color and clearness that the ether theories and the other models may be able to give, and even, we can feel it this way, just because of the soberness induced by their absence, Einstein's work, we may now positively expect, will remain a monument of science; his theory entirely fulfills the first and principal demand that we may make, that of deducing the course of phenomena from certain principles exactly and to the smallest details. It was certainly fortunate that he himself put the ether in the background; if he had not done so, he probably would never have come upon the idea that has been the foundation of all his examinations.

 

[Dale]

I do not know why you insist on sticking to the historical side of the story.

I think that is a completely incorrect characterization. I definitely addressed the historical side of the story, but I certainly didn't limit my comments to them either.

IMO, the aether is essentially synonymous with a preferred frame and therefore fundamentally incompatible with the PoR.

 

[lugita15]

First, the PoR, as I have usually seen it, refers to the equations. E.g. http://en.wikipedia.org/wiki/Principle_of_relativity. It states that the equations of physics have the same form with the same universal constants in all frames of reference.

I completely agree with this. The fact that you happen to interpret the equations differently does not invalidate the principle of relativity.

Second, from Maxwell to Einstein, the leading scientists of the day believed that the PoR was not correct, or at least that it did not apply to EM phenomena. They considered the aether frame to be a preferred frame in the sense of violating the PoR. Specifically, that Maxwell's equations only applied in the aether frame.

I don't think (based on Whitaker's excellent history of light and aether) that they saw the electromagnetic wave equation as invalidating the PoR, any more than the sound wave equation would. It's definitely true that they believed Maxwell's equations were only true in one frame, but the reason for this was because it violated Galilean invariance. So they concluded that for frames moving with respect to the ether, the equations governing electromagnetic phenomena would be modified slightly, so that they would predict that the speed of light would be c+v or c-v, where v is the speed of the eather.

I understand your point here, but the difference is that the velocity of the medium for acoustic waves can be detected by non-acoustic phenomena. So, we can say that the speed of sound is isotropic in any frame where a nearby anemometer reads 0, and that is true regardless of if the anemometer is moving in some other frame. Also, Newton's equations would still hold in all frames.

On the other hand, there was supposedly no other way to detect the aether other than its effect on the speed of light. The laws of physics were simply different in that frame. Transforming to another frame would not change anything except the speed of light measurement. Maxwell's equations would only hold in the aether frame.

First of all, I think that detecting ether was viewed as a difficult experimental challenge, not physically impossible. Second of all, what do you think would happen if we lived in a world where it was impossible to detect air, and the only way we even knew air existed was by hearing sounds? In that case, I don't think measuring the speed of sound differently in different reference frames, and using that to determine the rest frame of air, would have invalidated the PoR in any way.

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.

LET provides a transformation between the unmeasurable aether frame and the measurable frame. So, LET is an odd mishmash of parts. When you express Maxwell's equations in terms of local time then the equations for all different local frames are the same, reflecting the PoR for all measurable quantities.

However, 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.

Yes, if we expressed the equations governing electromagnetism in terms of "aether position" and "aether time", the equations would only be Maxwell's equations in the aether frame, and in other frames they would be different. They would be similar, they would just contain extra terms in the Ampere-Maxwell Law and Faraday's law which depend on the speed of the aether. These modified equations were found by Hertz, but they're of course useless from an experimental standpoint because it's impossible to find the aether frame and thus impossible to find out what time and position it would "really" be if our clocks and rulers didn't suffer from relativistic effects. But the important thing to note is that Hertz's modified Maxwell equations are Galilean invariant, so that according to the Lorentz aether theory the Galilean transformations are "really" correct and it is only due to measurement error that the Lorentz transformations seem to be correct. Either way, the principle of relativity survives unscathed.

 

[Saw]

I think that is a completely incorrect characterization. I definitely addressed the historical side of the story, but I certainly didn't limit my comments to them either.

That is true. I was just answering that side of your comments, to go little by little... But would you then admit that the story of LET does not end before Einstein and that Lorentz did defend a theory which is a combination of SR + aether? I think this quotation is quite definitive. Einstein himself was in the best terms with Lorentz and I remember having read something like "that is when Professor Lorentz and I invented the theory of relativity" (special one, of course).

IMO, the aether is essentially synonymous with a preferred frame and therefore fundamentally incompatible with the PoR.

This is for me the most interesting side and where I will try to go a little deeper. I am not going to deny that an aether (if such thing existed at all) would be a privileged frame in the sense that you would obtain there privileged information. Taking the example of simultaneity, I mentioned before that the synchronisation obtained in such frame would be more perfect (more precise!) in as much as it would provide us with very ambitious knowledge: if two events happen by clocks synched in such frame, one can trust that none of them can have causal influence over the other, even if that influence happened to travel at infinite velocity, in no time, instantaneously. Instead, relative simultaneity (or a synch operation done through Einstein convention in any other non-aether frame) does not supply so much information. If two events are simultaneous in a non-aether frame, then the space-time distance between them is space-like, meaning that all frames agree that there can be no causal influence between the two events… as long as we talk about a non-superluminal influence. But what if, for the purpose of discussion, we admit FTL travel? To make things simpler, what if we admit the possibility of instantaneous communication? In that case, the concept of relative simultaneity turns out to be insufficient. Some frames will seem to indicate that the causal influence is impossible, others that it is possible. Who is right? Not all of them, obviously. Here the reasonable answer is that *we do not know*, since the concept of relative simultaneity does not go that far. Fortunately, that is not serious, since FTL travel is impossible. Hence the information provided by the aether frame is in the end unnecessary, since we can solve all known practical problems (with CERN's and neutrinos' permission) on the basis of relative simultaneity.

Conclusion: the aether only leads to a theoretically preferred frame, which is good for nothing practical; it only rules out a fairy-tale PoR where all frames attain a level of information which is as beautiful as unnecessary; however, it is compatible with a realistic PoR, where all frames, based on their empirical measurements, are equally placed to solve all existing practical needs.

 

[Dale]

It's definitely true that they believed Maxwell's equations were only true in one frame, but the reason for this was because it violated Galilean invariance. So they concluded that for frames moving with respect to the ether, the equations governing electromagnetic phenomena would be modified slightly

That is essentially the definition of a violation of the PoR.

Second of all, what do you think would happen if we lived in a world where it was impossible to detect air, and the only way we even knew air existed was by hearing sounds?

Then I think we would conclude that the laws of acoustics are not frame invariant and that there exists a preferred frame.

 

[lugita15]

That is essentially the definition of a violation of the PoR.

It would only be a violation if the Maxwell equations were in fact laws of physics. But they believed that the correct equations of electromagnetism included terms that depended on the speed of the aether, as I discussed in the end of my post (#64).

Then I think we would conclude that the laws of acoustics are not frame invariant and that there exists a preferred frame.

Yes, but I don't think we'd reject the principle of relativity, we would just come up with new laws of acoustics that depended on the speed of air (as undoubtedly people have in real life).

 

[Dale]

It would only be a violation if the Maxwell equations were in fact laws of physics. But they believed that the correct equations of electromagnetism included terms that depended on the speed of the aether, as I discussed in the end of my post (#64).

Which would be a preferred frame!

Look, your idea of the principle of relativity is essentially meaningless. There is simply no way for a law of physics to not obey the principle of relativity in your view. All you would have to do is take any velocity-dependent terms, say that those represent the velocity relative to some otherwise undetectable medium, and claim that therefore it follows the principle of relativity.

You have watered down the principle of relativity so far that it is simply a tautology. Not only all known laws of physics, but all possible laws of physics obey it. So it means nothing to say that a law follows it.

If you disagree with the above then please explain how a law of physics could, in your view, violate the PoR.

 

[Dale]

Conclusion: the aether only leads to a theoretically preferred frame, which is good for nothing practical; it only rules out a fairy-tale PoR where all frames attain a level of information which is as beautiful as unnecessary; however, it is compatible with a realistic PoR, where all frames, based on their empirical measurements, are equally placed to solve all existing practical needs.

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

 

[lugita15]

Which would be a preferred frame!

Look, your idea of the principle of relativity is essentially meaningless. There is simply no way for a law of physics to not obey the principle of relativity in your view. All you would have to do is take any velocity-dependent terms, say that those represent the velocity relative to some otherwise undetectable medium, and claim that therefore it follows the principle of relativity.

You have watered down the principle of relativity so far that it is simply a tautology. Not only all known laws of physics, but all possible laws of physics obey it. So it means nothing to say that a law follows it.

If you disagree with the above then please explain how a law of physics could, in your view, violate the PoR.

This might end up to be a philosophical issue; I apologize in advance if it is. I have to admit that according to my conception of the PoR, for any theory T which violates the PoR there exists a theory T' experimentally indistinguishable from T which obeys the PoR. You might view this as a great indictment of my view, but I think what I said is equally applicable to any physical principle, e.g. conservation of momentum. Suppose you had a theory T that said any collision involving a neutrino does not conserve momentum. Then you could have an experimentally indistinguishable theory T' that says that whenever a neutrino has a collision, an undetectable fairy gains or loses momentum which exactly compensates for the violation of the conservation law. Or it could say that whenever a neutrino has a collision, the fairy provides an external force which explains why the momentum of the system was not conserved. This isn't an indictment of the conservation of momentum; a theory can follow a fundamental physical principle like the principle of relativity or the conservation of momentum and still violate other things we want theories to satisfy, like Occam's Razor.

Getting back to my hypothetical situation, in which air has never been detected: If we were confronted with the fact that the speed of sound is isotropic in only one reference frame I think it would be reasonable to construct a theory in which sound was a longitudinal wave in an invisible medium called air whose rest frame is the reference frame we've found in our experiments. This would be a sound working hypothesis, and tomorrow we would go out and try to see whether we can get even more confirmation, holding out the possibility that we might one day be able to detect this mysterious air or find some indirect side effects of air, just as in the nineteenth century people thought that electromagnetism was an effect of the ether.

Anyway, I go back to what I talked about in the end of post #64: LET only violates the PoR if you use measurable quantities like local time to express your equations; 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. But I think we already knew that LET is a severe Occam violator.

 

[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.