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

[Histspec]

The MM experiment did not refute LET. Since LET and SR use the same math, that means they are experimentally indistinguishable.

I wasn't talking about LET. I was talking about the Fresnel-Lorentz idea of a stationary aether, which was considered an observable entity when it was developed in 1818 by Fresnel and 1892 by Lorentz. Of course, it was later (between 1892-1904) modified by including the Lorentz transformation and all of its effects, in order to explain Michelson-Morley, Trouton-Noble, etc.. Though the resultant theory, now called LET, was never considered a viable alternative to special relativity.

Regards,

 

[Saw]

I wasn't talking about LET. I was talking about the Fresnel-Lorentz idea of a stationary aether, which was considered an observable entity when it was developed in 1818 by Fresnel and 1892 by Lorentz. Of course, it was later (between 1892-1904) modified by including the Lorentz transformation and all of its effects, in order to explain Michelson-Morley, Trouton-Noble, etc..

Ah, sorry, I misinterpreted you.

Yes, that is incorrect. LET assumes that Maxwell's equations are only valid in the aether frame, so it rejects the first postulate. The strange properties of the aether are proposed in order to make it so that even though Maxwell's equations are only valid in the aether frame our clocks and rulers are distorted in such a manner as to make it impossible to detect the deviations from Maxwell's equations in different frames.

That may be a good historic account of how Lorentz's ideas developed: first, he said that the PoR (Maxwell's equations are valid in all frames) did not apply (the equations are only valid in the aether frame), later he changed his mind (the PoR applies in all frames, because -as you say- " it is impossible to detect the deviations from Maxwell's equations in different frames"). But in the end LET accepts the PoR, doesn't it? Really, if person A accepts a principle without giving a reason and person B gives a reason (good or bad) but also accepts the principle, one has to admit that both A and B accept the principle. I may agree with you that that the reason given by B (LET) is "contrived, artificial, wrong or whatever you want to call it", but still it is a reason, which is lacking in what we call today SR.

rather it's Einstein's second postulate (the propagation of light is c in all frames) that LET rejects and instead affirms a different second postulate (the propagation of light is c only in the aether frame). It's only the choice between these two second postulates that makes the two theories different.

I do not see that. Again, it may be historically true (is it? Poincaré did affirm the principle of the constancy of the speed of light in connection with the PoR). But in any case, I do not see how one could today defend the existence of an aether, defend the first postulate, defend the LT and not defend the constancy of the speed of light in all frames.

I would add that the net effect of Einstein's second postulate is that any inertial frame you want to pick has all the properties of the one elusive aether frame. And this is why Einstein pointed out in his 1905 paper introducing Special Relativity that this second postulate is "only apparently irreconcilable with the former". He's saying it seems impossible that any frame could be a candidate for the frame which LET claims is unique but it turns out that it is possible.

I fully agree with this idea, which you often repeat. The gist of Einstein's idea is that all frames measure as if they were at rest wrt an aether, no matter if the latter exists or not. That is why the they all measure c as the speed of light and they find fault in all other frames (lack of sync, TD and LC). But that is fully compatible with LET, isn't it? LET simply adds to that that, in its opinion, an aether does exist.

To sum up: I admit I am splitting a hair…

 

[Saw]

The Principle of Relativity therefore becomes a derived result rather than a postulate.

Yes, that is it.

One ugly aspect is that if you want to extend LET to cover various branches of physics, you have to keep adding more postulates, e.g. that "mass dilates by the Lorentz factor relative to the aether" (equivalent to relativistic mass), etc, whereas Einstein's first postulate automatically encompasses all branches of physics.

Well, yes, when you give reasons, the problem is that your conclusions are limited by the nature and robustness of your reasons. But you also have advantages: you do not admit absurd conclusions like time travel...

I may be wrong, but I suspect there may never have been a rigorous statement of LET's postulates because the theory was abandoned before it gained much momentum.

You are right. In fact, it may be not worthwhile to develop LET any further. As I said before, it is more pragmatic assuming, as we do, that the 2 postulates work and that is it. As long as one does not think that he is giving an explanation for the postulates when he is not.

 

[Dale]

But in the end LET accepts the PoR, doesn't it?

LET views the principle of relativity in the same way that NASA conspiracy theorists view the moon landings. They recognize that there is a lot of evidence for it, but they believe that all of the evidence is faked, and it irritates them that they can't prove it. I wouldn't call that "accepting".

As long as you have an aether you are rejecting the principle of relativity, at least philosophically. However, if you throw out the philosophical baggage of the aether and just concentrate on the math then LET takes time dilation and length contraction as postulates and derives the principle of relativity and the invariance of c. SR takes the principle of relativity and the invariance of c as postulates and derives time dilation and length contraction.

Neither is deeper than the other as far as that goes nor does either provide more "reasons" than the other, they simply swap the assumptions and the conclusions.

Woot! 10k posts!

 

[lugita15]

As long as you have an aether you are rejecting the principle of relativity, at least philosophically.

Not necessarily. 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. We could have had an analogous situation where Maxwell's equations needed to be modified in order for them to be true in all frames.

Neither is deeper than the other as far as that goes nor does either provide more "reasons" than the other, they simply swap the assumptions and the conclusions.

Lorentz's historical theory was "deeper" than SR in at least one sense: it tried to provide physical underpinnings for relativistic effects. For instance, Lorentz believed that a moving electron was compressed by its own electromagnetic field.

 

[ghwellsjr]

I was under the impression that LET postulates the existence of an aether such that:

• light speed is isotropic relative to the aether

The Principle of Relativity therefore becomes a derived result rather than a postulate.
...
I may be wrong, but I suspect there may never have been a rigorous statement of LET's postulates because the theory was abandoned before it gained much momentum.

One thing is for sure, LET does not accept Einstein's second postulate and whether or not any of its promoters prior to Einstein ever even considered it, they probably wouldn't have given it a second thought because they believed it was irreconcilable with the principle of relativity, whether or not that principle was formulated as a postulate or derived. But the LET that we talk about today does affirm the principle of relativity which Einstein said he raised to the status of a postulate (his first).

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

 

[Saw]

Woot! 10k posts!

Beware, you are becoming wordy!

LET views the principle of relativity in the same way that NASA conspiracy theorists view the moon landings. They recognize that there is a lot of evidence for it, but they believe that all of the evidence is faked, and it irritates them that they can't prove it. I wouldn't call that "accepting".

I do not know why you think so. Conspiracy theorists argue that NASA did NOT land on the Moon. LET affirms that the PoR DOES apply. A different thing is that LET thinks the PoR applies for a physical reason, which generates a fortunate compensation of effects.

Lorentz's historical theory was "deeper" than SR in at least one sense: it tried to provide physical underpinnings for relativistic effects. For instance, Lorentz believed that a moving electron was compressed by its own electromagnetic field.

Yes, with that I agree. As you imply, "deeper" here does not mean "better" since the underpinning may be wrong. An example to reinforce your point: you may model how hot a body is by measuring temperature and mass; for most purposes, that is good enough, but to gain a better understanding of the phenomenon, you may try to find a deeper-level explanation; in this sense, you may hypothesize that the physical reason is (a) a fluid that goes into the body or (b) the internal motion of particles. Both (a) and (b) are "deeper-level" explanations, although (a) is wrong.

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

As DrGreg pointed out, the problem with LET is that nobody knows very well what it means since it has never been fully developed. But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

When you say that for LET "light speed is isotropic only relative to the aether", we should clarify what we mean by that. If those concepts ("isotropic", "speed") are fed by absolute measurements of time and distances, then not only LET also I do affirm that light CANNOT be isotropic in any frame. But LET admits that absolute measurements are not in practice possible. We must content ourselves, in real life, with relative measurements. And if you feed the concept of speed with those relative measurements, you forcefully get (also for LET!) isotropic light speed.

 

[harrylin]

This interpretation is based on the concept that the ether is stationary and unmoving. Other interpretarions are possible if the ether is considered to exist and have the ability to move. Why are these other interpretations taboo?

Those other interpretations (presumably all of them, but it's hard to be sure about an undefined group) are incompatible with special and general relativity as well as some key experiments that give support for those theories. Special relativity emerged from Lorentz's electron theory which assumed a stationary ether model and succefully explained such things as the Fizeau "drag".

 

[harrylin]

Yes, but of a different level. Am I wrong if I assume that LET also endorses the two postulates?

There was no "LET". Einstein based the second postulate on Maxwell's theory which also was part of Lorentz's theories. Thus Lorentz didn't disagree with Einstein's 1905 paper, and Einstein clarified that the second postulate is made plausible by Lorentz's preceding theory of electrons. Moreover, Lorentz had next derived the Lorentz transformation equations (although not in their symmetrical form) in order to conform to the first postulate.

Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

Neither did Einstein think so, as he explained in a very elaborate way in his Leiden inauguration speech.

 

[harrylin]

[..] So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

 

[zonde]

I think that problem about LET is not whether or not speed of light is isotropic in all inertial frames (we just construct coordinate systems so that it is so).
I think that problem is about c being universal speed limit. Because Lorentz transform works only for one speed. Any other speed will be different after Lorentz transform. That universality is the unreasonable part. And that universality ensures that principle of relativity holds.

On the other hand we can view principle of relativity as external constraint. Matter that does not follow this principle can not change it's state of motion i.e. it will be fragile and break down when accelerated. If we assume that matter can replicate itself (say pair prodaction can happen only in presence of matter) then more flexible matter will be evolutionary preferable. At least that is my reasoning why principle of relativity holds.

 

[ghwellsjr]

[..]So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

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?

 

[lugita15]

No, the isotropy of light in any inertial frame is a derived result, although most textbooks for students skip that. As Einstein put it in 1905:
"We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."

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.

 

[lugita15]

On the other hand we can view principle of relativity as external constraint. Matter that does not follow this principle can not change it's state of motion i.e. it will be fragile and break down when accelerated.

What exactly do you mean by this? Why can't an object which does not "follow" the PoR change its state of motion?

 

[zonde]

What exactly do you mean by this? Why can't an object which does not "follow" the PoR change its state of motion?

Object that does not follow PoR would have to have different structure for different states of motion. Well, I am assuming that object can't have many different stable configurations and smoothly slip from one structure to other without breaking down. Something like that.

 

[lugita15]

Object that does not follow PoR would have to have different structure for different states of motion.

I still don't understand what you're talking about. And in any case, it doesn't really make sense to talk about objects "following" the PoR; you can only talk about laws of physics which follow it or not. For example, in Aristotelian physics the law was "An object at rest stats at rest, and an object in motion comes to rest", which is obviously incompatible with the PoR. How could a law of this kind lead to structural instability of physical objects?

 

[Dale]

But LET admits that absolute measurements are not in practice possible.

This is true, but the problem with the rest of your comments is that 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.

Conspiracy theorists argue that NASA did NOT land on the Moon. LET affirms that the PoR DOES apply.

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

But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether.

So we should make a convention that we agree you are right? I prefer the convention where we all agree with me.

 

[zonde]

I still don't understand what you're talking about.

Ok, let me try one more time.
Object has different interactions that determine it's structure - different molecular bonds, interactions determining structure of atom and interactions inside nucleons.
Let's say that interactions all happen at different speeds. They have at some distance potential minimum. When we change speed of object this minimum potential distance changes by different amounts for different interactions (because of different interaction speed - you can imagine that we use Lorentz transforms for different interactions with different values of "c"). So if internal distances determining structure of object do not change in unison it should eventually break.

 

[Saw]

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

Again it depends on what we mean by PoR. If by PoR we mean knowing absolute simultaneity, then, yes, LET argues that we do not have that knowledge. And so do I... Don't you? I would think anybody would agree on that, maybe I am wrong, but it looks quite obvious... (By absolute simultaneity I mean the one that would be established in the eather frame, if the aether existed, or by an instantaneous means of communication, if such thing were possible.)

Instead if by PoR we mean that, even if we do not have such ambitious knowledge (absolute simultaneity), we live quite well without it (we can solve all known practical problems), then LET should agree with that.

 

[ghwellsjr]

So the only significant difference between LET and SR is that although they both affirm the principle of relativity, LET postulates the existence of an aether such that light speed is isotropic relative to the aether (and only to the aether), whereas SR postulates that light speed is isotropic in any inertial frame.

As DrGreg pointed out, the problem with LET is that nobody knows very well what it means since it has never been fully developed. But for the purpose of this discussion, can we make a convention? Let us define LET as SR (= PoR + invariant c) plus the hypothesis that the reason for all this is an aether. Are the two things logically incompatible? I do not think so.

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.

When you say that for LET "light speed is isotropic only relative to the aether", we should clarify what we mean by that.

I was using DrGreg's terminology in my quote. I usually use Einstein's terminology such as "light always propagates at c" or "any ray of light moves at c" but they mean the same thing. In LET, light propagates at c only in the aether.

If those concepts ("isotropic", "speed") are fed by absolute measurements of time and distances, then not only LET also I do affirm that light CANNOT be isotropic in any frame. But LET admits that absolute measurements are not in practice possible. We must content ourselves, in real life, with relative measurements. And if you feed the concept of speed with those relative measurements, you forcefully get (also for LET!) isotropic light speed.

There is no measurement that can determine how light propagates. If there were, we wouldn't have the principle of relativity which means we wouldn't have either LET or SR because they are both based on that principle (plus a postulate about how light propagates).

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. When MMX could not experimentally measure the rest state of that field, the principle of relativity was upheld and LET was formulated to explain what was happening still based on a field at absolute rest. 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. This resulted in time and space being absolute even though they were aware of the concepts of time dilation and length contraction for objects moving with respect to the aether but it never occurred to them that space itself or time itself, in other word's, nature, could ever be relative. In this sense, absolute time and absolute space are derived results from the experimental evidence of the principle of relative plus the postulate that light travels at c only in one rest state (the one nature operates on).

Einstein's two postulates, along with his definition of a Frame of Reference incorporating the amalgamation spacetime (instead of leaving space and time as independent coordinates) had a derived result of time and space being relative to the defined Frame of Reference rather than an absolute of nature.

 

[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?